# MODELING THE PLANKTON–ENHANCING THE INTEGRATION OF BIOLOGICAL KNOWLEDGE AND MECHANISTIC UNDERSTANDING

EDITED BY: Christian Lindemann, Dag L. Aksnes, Kevin J. Flynn and Susanne Menden-Deuer

PUBLISHED IN: Frontiers in Marine Science and Frontiers in Ecology and Evolution


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ISSN 1664-8714 ISBN 978-2-88945-365-8 DOI 10.3389/978-2-88945-365-8

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## **MODELING THE PLANKTON–ENHANCING THE INTEGRATION OF BIOLOGICAL KNOWLEDGE AND MECHANISTIC UNDERSTANDING**

Topic Editors:

**Christian Lindemann,** University of Bergen, Norway **Dag L. Aksnes,** University of Bergen, Norway **Kevin J. Flynn,** Swansea University, United Kingdom **Susanne Menden-Deuer,** University of Rhode Island, United State**s**

'Plankton recoded' by Jan Heuschele

In light of climate change and allied changes to marine ecosystems, mathematical models have become an important tool to examine processes and predict phenomena from local through to global scales. In recent years model studies, laboratory experiments and a better ecological understanding of the pelagic ecosystem have enabled advancements on fundamental challenges in oceanography, including marine production, biodiversity and anticipation of future conditions in the ocean.

This research topic presents a number of studies that investigate functionally diverse organism in a dynamic ocean through diverse and novel modeling approaches.

**Citation:** Lindemann, C., Aksnes, D. L., Flynn, K. J., Menden-Deuer, S., eds. (2017). Modeling the Plankton–Enhancing the Integration of Biological Knowledge and Mechanistic Understanding. Lausanne: Frontiers Media. doi: 10.3389/978-2-88945-365-8

# Table of Contents

*06 Editorial: Modeling the Plankton–Enhancing the Integration of Biological Knowledge and Mechanistic Understanding* Christian Lindemann, Dag L. Aksnes, Kevin J. Flynn and Susanne Menden-Deuer

### **Improving cell based representations**

*09 The Physiological Response of Picophytoplankton to Temperature and Its Model Representation*

Beate Stawiarski, Erik T. Buitenhuis and Corinne Le Quéré


### **Making trade-offs count**


Neil S. Banas, Eva F. Møller, Torkel G. Nielsen and Lisa B. Eisner

*102 Spatial Modeling of* **Calanus finmarchicus** *and* **Calanus helgolandicus***: Parameter Differences Explain Differences in Biogeography*

Robert J. Wilson, Michael R. Heath and Douglas C. Speirs

*117 Resource Competition Affects Plankton Community Structure; Evidence from Trait-Based Modeling*

Marc Sourisseau, Valerie Le Guennec Guillaume Le Gland, Martin Plus and Annie Chapelle

### **Resolving trophic details**

*131 Modeling What We Sample and Sampling What We Model: Challenges for Zooplankton Model Assessment*

Jason D. Everett, Mark E. Baird, Pearse Buchanan, Cathy Bulman, Claire Davies, Ryan Downie, Chris Griffiths, Ryan Heneghan, Rudy J. Kloser, Leonardo Laiolo, Ana Lara-Lopez, Hector Lozano-Montes, Richard J. Matear, Felicity McEnnulty, Barbara Robson, Wayne Rochester, Jenny Skerratt, James A. Smith, Joanna Strzelecki, Iain M. Suthers, Kerrie M. Swadling, Paul van Ruth and Anthony J. Richardson


Caroline Ghyoot, Kevin J. Flynn, Aditee Mitra, Christiane Lancelot and Nathalie Gypens

### **From physics to biology**

*194 Key Drivers of Seasonal Plankton Dynamics in Cyclonic and Anticyclonic Eddies off East Australia*

Leonardo Laiolo, Allison S. McInnes, Richard Matear and Martina A. Doblin

*208 Modeling Larval Connectivity of Coral Reef Organisms in the Kenya-Tanzania Region*

C. Gabriela Mayorga-Adame, Harold P. Batchelder and Yvette. H. Spitz

## Editorial: Modeling the Plankton–Enhancing the Integration of Biological Knowledge and Mechanistic Understanding

#### Christian Lindemann<sup>1</sup> \*, Dag L. Aksnes <sup>1</sup> , Kevin J. Flynn<sup>2</sup> and Susanne Menden-Deuer <sup>3</sup>

*<sup>1</sup> Department of Biology, University of Bergen, Bergen, Norway, <sup>2</sup> Department of Biosciences, Swansea University, Swansea, United Kingdom, <sup>3</sup> Graduate School of Oceanography, University of Rhode Island, Narragansett, RI, United States*

Keywords: planktonic food web, ecosystem, biogeochemistry, functional diversity, Climate change simulation

#### **Editorial on the Research Topic**

### **Modeling the Plankton–Enhancing the Integration of Biological Knowledge and Mechanistic Understanding**

In marine science numerical models, and especially ecosystem models, have developed into an important tool for policy advice and environmental management applications (Rose et al., 2010; Holt et al., 2014; Robson, 2014; Lynam et al., 2016). The predictive capabilities of these models, in particular under changing environmental conditions, naturally rely strongly on the model formulation, including choice of functional groups and the form of their representation, i.e., their parameterisation.

In recent years, new knowledge generated regarding organism physiology; ecosystem functioning; new data types and increased resolution of data acquisition, particularly those collected by satellites, autonomous platforms and through genetic analyses; as well as new approaches to model marine systems have emerged, altering the way we think about modeling the plankton.

Mechanistic descriptions which can reflect physiological, behavioral and life-history traits (Baklouti et al., 2006), can improve the individual representation and thus provide a more robust platform, valid for a wider range of circumstances. Trait-based modeling and size-based scaling approaches have emerged as fruitful approaches, in some marine systems, to categorizes biological entities by their ecological meaningful characteristic (Litchman and Klausmeier, 2008). This can be done by using certain defining characteristics, such as cell size (Andersen et al., 2016), to scale related processes and functions.

Papers in this research topic provide insights into novel developments in the representation of plankton groups and how these improvements affect model outcomes. The scope of articles covers a wide range of different aspects, from viruses to fish larvae, from single cell mechanisms to improved description of community structure, from purely theoretical approaches to data heavy applications.

Though viruses have been recognized as an important player in the marine food web (Suttle, 2005) their inclusion in models remains rare. In a combination of review and modeling study, Record et al., assess key characteristics of marine viruses and the trade-offs between lysogenic and lytic strategies, particularly as a function of nutrient inputs to the system.

Similarly the ability of many phytoplankton and microzooplankton species to be mixotrophic, which has been known for decades with some attempts made to provide a conceptual basis for models (reviewed by Stoecker, 1998), is only now becoming mainstream. Ghyoot et al. tackle the challenge of modeling mixotrophy, proposing modifications to one of the classic approaches to modeling plankton, the Shuter approach (Shuter, 1979), that enables the simulation of the two main groups of mixotrophs, namely of the constitutives ("phytoplankton that eat") and non-constitutives ("microzooplankton that photosynthesizes") growing in the North Sea.

Using bulk nutrient uptake observations in combination with allometric scaling predictions, Atkins et al. suggest that net nitrogen dynamics can be quantified at an assemblage

Edited and reviewed by: *Angel Borja, AZTI Pasaia, Spain*

\*Correspondence: *Christian Lindemann chris.lindemann@uib.no*

#### Specialty section:

*This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Marine Science*

Received: *13 October 2017* Accepted: *25 October 2017* Published: *07 November 2017*

#### Citation:

*Lindemann C, Aksnes DL, Flynn KJ and Menden-Deuer S (2017) Editorial: Modeling the Plankton–Enhancing the Integration of Biological Knowledge and Mechanistic Understanding. Front. Mar. Sci. 4:358. doi: 10.3389/fmars.2017.00358* scale using size dependencies of Michaelis-Menten uptake parameters and that their method can be applied to particle size distributions that have been routinely measured in eutrophic systems.

Exploiting a statistical approach, Stawiarski et al. compare different strains of picokaryotes in relation to Eppley's empirical relationships of temperature dependent growth (Eppley, 1972). Their results indicate that, when compared to picoeukaryotes, prokaryotic picoplankton have lower growth temperatures and a narrower temperature range. Interestingly they also find that the temperature tolerance range follows a unimodal function of cell size, with the Q<sup>10</sup> values for picoeukaryotes and picoprokaryotes being 2.3 and of 4.9, respectivly.

Sourisseau et al. explore the usefulness of a trait-tradeoff approach to help improve descriptions of the success of the harmful algae bloom dinoflagellate Alexandrium minutum under conditions of changing temperature and the hydrographic conditions of the estuary.

Based on recent experimental data published on evolutionary change in a coccolithophore, Denman provides evidence that genetic mutations alone do not suffice to explain rapid thermal adaptation. This study contributes significant new knowledge to the field of organismal adaptation in the face of global warming.

Satellites have long been an important tool in oceanography as their measurement capacity is uniquely suited to transcend the large spatial scales of the global and dynamic ocean. Gregg and Rousseaux incorporate key characteristics of radiative transfer into a biogeochemical model and identified quantifiable trade-offs between nutrient concentration, phytoplankton type and directionality and attenuation wavelength that could affect net primary production and chlorophyll-a concentration from negligible to over 25%.

Laiolo et al. examine the seasonal plankton dynamics of cyclonic and anticyclonic eddies using satellite data, in situ observations and assimilating chlorophyll-a data into biogeochemical models of different complexity. Due to the shallower mixed layer, model simulations of cyclonic eddies show higher chlorophyll-a concentrations and higher concentration of large phytoplankton driven by higher light availability due to the mixed layer shoaling.

Increasing data and information use have been suggested as a step toward improving management applications (Dyble et al., 2008; Lynam et al., 2016). Everett et al. present a review on the current practices in zooplankton observation and modeling. They detail two ways that zooplankton biomass/abundance observations can be used to assess models: data wrangling that transforms observations to be more similar to model output; and observation models that transform model outputs to be more like observations.

Resolving zooplankton feeding traits to a sufficient degree can provide important insights into zooplankton dynamics and the dynamics of marine ecosystems. Wilson et al. use a trait-structured modeling approach to understand possible causes of differences between the C. finmarchicus and C. helgolandicus biogeographies. Based on their analyses they hypothesize that food quality is a key influence on the population dynamics and distribution of the two species.

Dufour et al. quantified intra-guild predation on copepod eggs by two dominant arctic species, Calanus hyperboreus and Metridia longa as a function of temperature, egg and alternative prey concentration. Incorporating these remarkably variable empirical data in a model simulation showed that M. longa predation had minimal impact on C. hyperboreus recruitment, but did benefit M. longa's metabolic demands.

In size-spectrum models smaller zooplankton are often lumped together with phytoplankton, whereas larger (meso) zooplankton are categorized as fish. In the study by Heneghan et al. resolving zooplankton feeding traits explicitly led to an overall increase in fish biomass but also to a tradeoff between productivity and stability. While herbivorous zooplankton supported more productive fish communities with higher resilience to fishing pressure, carnivorous zooplankton had a stabilzing effect on fish communities.

Life history can play an important role in the survival strategy of marine plankton, nevertheless it is often ignored in marine ecosystem models (Rose et al., 2010). Exemplified with species of the Calanus genus, Banas et al. modeled copepod life history traits and adaptation in seasonal environments. Their modeling experiments demonstrate that patterns in copepod community composition and productivity may be predicted from only a few key constraints on the individual energy budget.

Coupling ocean circulation models with Individual-Based-Models, Mayorga-Adame et al. investigated the effects of larval life-history on the connectivity of different organisms in between east African coral reefs. Long pelagic larval duration with active migration abilities, such as fish, had a much higher settling probability (>20%) than passive species like coral larvae (<1%).

Clearly, this research topic has attracted a varied range of modeling types, investigating functionally diverse organisms and probing a multitude of processes, from individual life histories to ecosystem nutrient dynamics and biophysical interactions driving the abundance, distribution and ultimately the biogeochemical footprint of plankton. Our ability to model key processes in plankton ecology and oceanography still lags behind the highly species-specific physiologies and behaviors of phylogenetically diverse plankton in a dynamic ocean (Menden-Deuer and Kiørboe, 2016). The contributions compiled here take important steps forward in demonstrating how modeling plankton yields important insights. Moreover, this compilation hopefully inspires others to integrate their empirical and analytical approaches with modeling, for equally fruitful outcomes.

### AUTHOR CONTRIBUTIONS

All authors wrote a summary for the articles they edited. CL wrote the initial draft of the editorial. All editors commented on the editorial.

### FUNDING

SM received support from the National Science Foundation Biological-Oceanography award 1736635.

### REFERENCES


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Lindemann, Aksnes, Flynn and Menden-Deuer. This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# The Physiological Response of Picophytoplankton to Temperature and Its Model Representation

#### Beate Stawiarski\* † , Erik T. Buitenhuis and Corinne Le Quéré

Tyndall Centre for Climate Change Research, School of Environmental Sciences, University of East Anglia, Norwich, UK

#### Edited by:

Christian Lindemann, University of Bergen, Norway

#### Reviewed by:

Aleksandra M. Lewandowska, University of Oldenburg, Germany Gemma Kulk, University of Groningen, Netherlands

#### \*Correspondence:

Beate Stawiarski beate.stawiarski@io-warnemuende.de

> † Present Address:

Beate Stawiarski, Leibniz Institute for Baltic Sea Research Warnemünde, Rostock-Warnemünde, Germany

#### Specialty section:

This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Marine Science

Received: 25 May 2016 Accepted: 24 August 2016 Published: 09 September 2016

#### Citation:

Stawiarski B, Buitenhuis ET and Le Quéré C (2016) The Physiological Response of Picophytoplankton to Temperature and Its Model Representation. Front. Mar. Sci. 3:164. doi: 10.3389/fmars.2016.00164 Picophytoplankton account for most of the marine (sub-)tropical phytoplankton biomass and primary productivity. The contribution to biomass among plankton functional types (PFTs) could shift with climate warming, in part as a result of different physiological responses to temperature. To model these responses, Eppley's empirical relationships have been well established. However, they have not yet been statistically validated for individual PFTs. Here, we examine the physiological response of nine strains of picophytoplankton to temperature; three strains of picoprokaryotes and six strains of picoeukaryotes. We conduct laboratory experiments at 13 temperatures between –0.5 and 33◦C and measure the maximum growth rates and the chlorophyll a to carbon ratios. We then statistically validate two hypotheses formulated by Eppley in 1972: The response of maximum growth rates to temperature (1) of individual strains can be represented by an optimum function, and (2) of the whole phytoplankton group can be represented by an exponential function Eppley (1972). We also quantify the temperature-related parameters. We find that the temperature span at which growth is positive is more constrained for picoprokaryotes (13.7–27◦C), than for picoeukaryotes (2.8–32.4◦C). However, the modeled temperature tolerance range (1T) follows an unimodal function of cell size for the strains examined here. Thus, the temperature tolerance range may act in conjunction with the maximum growth rate to explain the picophytoplankton community size structure in correlation with ocean temperature. The maximum growth rates obtained by a 99th quantile regression for the group of picophytoplankton or picoprokaryotes are generally lower than the rates estimated by Eppley. However, we find temperature-dependencies (Q10) of 2.3 and of 4.9 for the two groups, respectively. Both of these values are higher than the Q<sup>10</sup> of 1.88 estimated by Eppley and could have substantial influence on the biomass distribution in models, in particular if picoprokaryotes were considered an independent PFT. We also quantify the increase of the chlorophyll a to carbon ratios with increasing temperature due to acclimation. These parameters provide essential and validated physiological information to explore the response of marine ecosystems to a warming climate using ocean biogeochemistry models.

Keywords: picophytoplankton, picoeukaryotes, Eppley, phytoplankton growth rates, temperature tolerance, phytoplankton size scaling, physiological parameterization, chlorophyll a to carbon ratio

### INTRODUCTION

Picophytoplankton contribute 26–56% to the global phytoplankton biomass (Buitenhuis et al., 2013) and about half of the global ocean primary productivity (Grossman et al., 2010). They dominate over wideocean areas, such as the oligotrophic subtropical gyres, and decrease polewards relative to other phytoplankton (Alvain et al., 2008; Buitenhuis et al., 2012). They play a significant role in the recycling of organic matter within the microbial loop of the surface ocean (Azam et al., 1983; Fenchel, 2008), but contribute little to the sinking of particulate matter to the intermediate and deep ocean (Michaels and Silver, 1988). With the projected extension of the oligotrophic subtropical gyres as a consequence of climate warming (Polovina et al., 2008), the recycling of nutrients within the microbial loop and consequently the contribution of picophytoplankton to the phytoplankton community may gain more importance in the marine biogeochemical cycles (Morán et al., 2010).

Temperature is an important environmental variable that determines, directly or indirectly, the biomass, productivity, and cell composition of all phytoplankton groups, single species and even ecotypes (Eppley, 1972; Sarmiento, 2004; Zinser et al., 2007). In particular, temperature directly affects the physiological processes that regulate the growth rates, the temperature span at which growth rates are positive, and the chlorophyll a to carbon ratios, among others (Eppley, 1972; Raven and Geider, 1988). In the field, temperature also influences the physical dynamics of the water column and the availability of nutrients and light (Eppley, 1972; Behrenfeld et al., 2006; Johnson et al., 2006), making it difficult to isolate the specific effect of temperature.

The contribution of picophytoplankton to the phytoplankton biomass was shown to correlate with in situ temperature (Agawin et al., 2000; Morán et al., 2010). Also a direct effect of temperature on the phytoplankton community size structure was found in the global ocean (Mousing et al., 2014; López-Urrutia and Morán, 2015). However, Marañón et al. (2014) argue that the correlation between temperature and size structure is due to an indirect effect through nutrient supply as they did not find a direct effect of temperature when data from similar nutrient supply regimes were used.

To isolate the specific effect of temperature on the physiology of different phytoplankton groups, representative laboratory strains must be used under controlled nutrient conditions. Furthermore, physiological temperature relevant parameters need to be defined and quantified to identify groups with common traits. It is well established that the maximum growth rate of phytoplankton at optimum conditions is correlated with the cell size and can be represented by a unimodal function of cell size, with decreasing maximum growth rates above and below 2µm (Chisholm et al., 1992; Bec et al., 2008). This correlation has been shown to be independent of the optimum temperature (Chen et al., 2014) or nutrient supply (Bec et al., 2008), but other temperature-related parameters, such as the temperature tolerance range, have not yet been tested against cell size. It is essential to gain a detailed understanding of the effect of temperature on the physiology to constrain all relevant parameters in ocean biogeochemistry models. These models explicitly represent different phytoplankton and zooplankton groups with common traits, namely PFTs, to make projections about the implications of a warming climate on the marine ecosystem and its biogeochemical cycles (Le Quéré et al., 2005).

Ocean biogeochemistry models use the generalized equation proposed by Eppley (1972) for modeling the response of maximum growth rates of a phytoplankton community to temperature. Eppley formulated two major hypotheses: First, the maximum growth rates of individual species can be represented by an optimum function in response to temperature, and second, the maximum growth rates of a phytoplankton community can be represented by an exponential function in response to temperature. In addition, he formulated an equation which describes the exponential fit to the upper limit of the maximum growth rates of a phytoplankton community in response to temperature (Equation 1 in Eppley, 1972). Neither of these two hypotheses was statistically verified in Eppley (1972). Montagnes et al. (2003) showed that the maximum growth rates of most individual species are better represented by a linear fit than an exponential fit, but they did not consider an optimum fit, nor did they test the whole phytoplankton community. Bissinger et al. (2008) showed that the upper 99th quantile of the maximum growth rates of a mixed phytoplankton community can be represented by an exponential fit in response to temperature, with a Q<sup>10</sup> value similar to Eppley (1972), but with a higher maximum growth rate at 0◦C. However, Bissinger et al. (2008) did not test other functions.

Temperature also affects the chlorophyll a to carbon ratio (θ) of phytoplankton (Geider, 1987). This effect needs to be quantified when using chlorophyll a from field observation to estimate biomass, growth rates, or the community composition. For example, its divinyl derivatives are measured by satellites to identify the picoprokaryote Prochlorococcus sp. within a phytoplankton assemblage in the field (Chisholm et al., 1992; Alvain et al., 2005). However, the chlorophyll a to carbon ratio is a variable component within the cell. Generally, it decreases with temperature due to low temperature chlorosis, slower metabolic reactions or the increase in lipids to maintain membrane fluidity (Geider, 1987). The variability of the chlorophyll a to carbon ratio can be amplified by exposure to high light intensities (Geider, 1987). A positive effect of temperature on lightharvesting components and a negative effect on photoprotective components has previously been found between 16 and 24◦C for picoprokaryotes and picoeukaryotes (Kulk et al., 2012). However, more data over a wide range of temperatures need to be collected to identify and quantify significant relationships.

The present study will investigate the influence of temperature on the physiology of nine picophytoplankton strains, with the aim of informing the representation of picophytoplankton in ocean biogeochemistry models. It will specifically: (a) quantify the response of maximum growth rates to temperature; (b) evaluate the two hypotheses of Eppley (1972); (c) extract the temperature-related parameters, separately for individual strains and the group of picoprokaryotes, picoeukaryotes, and picophytoplankton; and investigate the relationship (d) between cell size and the temperature-related parameters, and (e) between the chlorophyll a to carbon ratio and temperature.

### MATERIALS AND METHODS

### Cultures and Experimental Setup

Representative strains of picophytoplankton from diverse taxonomic classes were obtained from the Roscoff culture collection (RCC, Vaulot et al., 2004), to investigate the effect of temperature on the maximum growth rates of picophytoplankton. They include three picoprokaryotes, represented by Synechococcus sp. (RCC 30), a high light (HL), and a low light (LL) ecotype of Prochlorococcus sp. (RCC 296 and 162, respectively), as well as the picoeukaryotes Bolidomonas pacifica (RCC 212), which was recently renamed as Triparma eleuthera (Ichinomiya et al., 2016), Micromonas pusilla (RCC 1677), Picochlorum sp. (RCC 289), Nannochloropsis granulata (RCC 438), Imantonia rotunda (RCC 361), and Phaeomonas sp. (RCC 503) (**Table 1**). All strains were grown in artificial seawater medium (ESAW) (Berges et al., 2001) with ammonium [882µM (NH4)2SO4] as the nitrogen source and addition of 10 nM selenium (Na2SeO3). The physiological experiments in response to temperature were conducted in 55 ml tubes (Pyrex Brand 9826), which were placed into a temperature gradient bar The temperature gradient bar was built with space for 65 culture tubes in 13 rows and 5 columns. A temperature gradient is generated by heating one of the short ends and cooling the other end to achieve a gradient between −0.5 and 33◦C. Each tube is lighted by an individual ultrabright LED (Winger WEPW1-S1 1W, 95 Lumen, white), achieving a light intensity of up to 480µmol photons m−<sup>2</sup> s −1 inside the tubes. The LED drivers are connected to mains electricity through a timer in the control unit, running on a 14:10 h light-dark cycle. Light was measured with a Radiometer (Biospherical Instruments Inc. QSL-2101) to be 291 ± 18µmol photons m−<sup>2</sup> s −1 for 8 strains and 81 ± 5µmol photons m−<sup>2</sup> s −1 for the low light Prochlorococcus sp. strain. These values are consistent with the average species specific light saturation levels (Stawiarski, 2014). To exclude any effect of light limitation or light inhibition, near optimum light conditions were chosen for each strain. A separate study with incubations at light intensities between 10 and 720µmol photons m−<sup>2</sup> s <sup>−</sup><sup>1</sup> has been conducted beforehand. The low light Prochlorococcus strain reached its highest growth rates with light saturation between 64 and 120µmol photons m−<sup>2</sup> s −1 , but was light inhibited at light intensities > 120µmol photons m−<sup>2</sup> s −1 . All other strains reached light saturation between 120 and 330 m−<sup>2</sup> s −1 . No light inhibition occurred at light intensities < 330µmol photons m−<sup>2</sup> s −1 .

Temperatures were measured with a Grant Squirrel 1000. Thanks to the insulation at the sides and top of the temperature gradient bar, the average temperature gradient is linear (linear regression of temperature difference between adjacent sets of tubes, p = 0.9). However, the middle tubes in each column tend to be slightly colder at the cold end (up to 0.5◦C), and as a consequence the standard deviation of the temperature in the five tubes is higher (p = 0.002). To prevent this from biasing the results, measurements are reported at the temperature measured in each tube.

### Analyses

For measuring the maximum growth rates, cultures of each strain were acclimated at 13 different temperatures for at least four divisions to reach balanced growth before daily in vivo fluorescence measurements were taken with a Turner Design Fluorometer (10 AU) (Anderson, 2005). Samples were placed in the dark prior to measurements and were measured until the signal stabilized. Only acclimated cultures were used within the present study, hence the fluorescence signal is considered as proportional to the low cell densities which were used (Anderson, 2005). The benefit of using this method instead of collecting cell counts was that the culture tube from the temperature gradient bar fits into the sample slot of the Fluorometer. Thus, no volume needed to be removed from the culture tube. The average cell size of the picophytoplankton strains was either provided by the RCC or obtained from the literature for T. eleuthera (Guillou et al., 1999).

To obtain chlorophyll a to carbon ratios, samples of particulate organic carbon (POC) and chlorophyll a were collected while the culture was still in exponential growth phase. POC was sampled on pre-combusted 13 mm GF/F filters for all strains. A layer of 3 filters was used for both Prochlorococcus sp. strains, because preliminary tests showed that their cells did not pass through, but were too small to remain on a single filter. Medium blanks were collected for each number of filter



layers. Samples of chlorophyll a were collected on pre-combusted 25 mm GF/F filters for 7 strains, but on 25 mm polycarbonate filters (0.2µm) for both Prochlorococcus sp. strains. Both filter types were shown to lead to comparable chlorophyll a results using phytoplankton samples (Hashimoto and Shiomoto, 2000). Depending on the cell density of the culture, between 5 and 20 ml per sample were filtered and rinsed with Milli-Q water. After sampling all filters were frozen in liquid nitrogen immediately, and stored at −80◦C until analyses. The cell numbers were measured by flow cytometry (BD Biosciences FACSCalibur, flow cytometer) and the flow rate was calibrated using the method of Marie et al. (2005).

For analysis, the POC samples were dried at 40◦C for 24 h, placed into pre-combusted tin capsules and analyzed with an elemental analyser (Exeter Analytical, CE-440 Elemental Analyser), which was calibrated with acetanilide (Exeter Analytical). The chlorophyll a samples were extracted in 10 ml acetone (Fisher Scientific, 99.8+ %) in 15 ml centrifuge tubes and disintegrated by shaking and vortexing. The tubes were then wrapped in aluminum foil and stored at 4◦C for 24 h. Prior to analysis, the samples were centrifuged and the supernatant was analyzed in a Fluorescence Spectrometer (PerkinElmer LS 45 Luminescence Spectrometer). After reading a sample, 3 drops of 8% HCl were added into the cuvette to measure the background signal caused by chlorophyll degradation products such as phaeopigments. The concentration of the calibration standard (SIGMA product No C5753) was also obtained prior to analyses (Parson et al., 1984).

### Calculations

The maximum growth rates of all strains were calculated by linear regression through at least three consecutive measurements of the log-transformed in vivo fluorescence measurements during the exponential growth phase. To test for the best representation of the response of the maximum growth rates to temperature, a linear, an exponential, and an optimum fit (Equations 1– 3) were applied to the maximum growth rate measurements of each strain, of each of the two groups (picoprokaryotes or picoeukaryotes) and also of all strains combined, representative for a group of picophytoplankton.

$$\text{linear:} \qquad \mu\_{\text{max}} = \mu\_{\text{max}, 0^{\circ}C} + \text{slope} \times T \tag{1}$$

exponential: µmax = µmax,<sup>0</sup>

$$\mathbf{a}\_{\text{max},\mathbf{0}^{\circ}\mathbf{C}} \times \mathbf{Q}\_{10}^{\frac{\mathbf{r}}{10}} \tag{2}$$

(3)

$$\text{optimium:} \qquad \mu\_{\text{max}} = \mu\_{\text{Opt}} \times \exp\left(-\frac{\left(T - T\_{\text{Opt}}\right)^2}{\Delta T^2}\right)$$

where µmax is the maximum growth rate, µmax,<sup>0</sup> ◦<sup>C</sup> is the maximum growth rate at 0◦C, T is the temperature, Q<sup>10</sup> is the temperature dependence, which is a measure for the increase of the maximum growth rate with the increase of temperature by 10◦C, µOpt is the optimum growth rate, TOpt is the optimum temperature, and △T is half the width of the temperature range at µOpt × exp (−1), which will be referred to as temperature tolerance range, not to be confused with Tmax − Tmin, which will be referred to as the temperature span.

The temperature-related parameters and their standard errors were estimated by minimizing the sum of squares between the fits and the measurements using the Gauss-Newton method in Mystat 12 (Systat software). The obtained parameters were not unique for the optimum fit to the combined data of all strains, because the optimum temperature was indefinite. For this reason, the sum of squares between the model and the data were calculated 15 times with varying starting values and it was found, that there was only a minor variability in the residual sum of squares (< 0.03%) and the parameters.

The relative quality of the three fits to equations 1–3 was compared using the Akaike's Information Criterion (AIC), which compares fits with different numbers of parameters (Equation 4, Burnham and Anderson, 1998).

$$\begin{array}{c} \text{Akaike's Information Criterion} \\ \dots \end{array}$$

$$AIC = n\_{obs} \log \left( \sigma^2 \right) + 2n\_{param} \tag{4}$$

where nobs is the number of observations, σ 2 is the standard deviation and nparam is the number of parameters given in the equation of the fit. The lowest AIC value indicates the best fit. Although there is no formally defined significance level associated with the value of AIC, we have used the definition in Burnham and Anderson (1998), who state that if an AIC differs by less than 2 from the lowest value, this fit is also appropriate.

The data were also compared to the exponential fit presented in Eppley (1972) to the upper limit of the maximum growth rates of a mixed group of phytoplankton, which will be referred to as the absolute maximum growth rates, in response to temperature (Equation 5).

$$\text{Eppley (1972)} \qquad \mu\_{\text{max}} = .0.59 \times 1.88^{\frac{T}{17}} \tag{5}$$

where the first constant is µmax,<sup>0</sup> ◦<sup>C</sup> and the second constant is the Q10.

To calculate the absolute maximum growth rates for a group of picophytoplankton and picoprokaryotes in response to temperature, we followed the method used by Bissinger et al. (2008). For this, we calculated the upper 99th quantile of the maximum growth rates for both groups by applying a linear quantile regression through the log-transformed maximum growth rates. The Software R with the software package quantreg was used (Koenker, 2006) with a significance level of p < 0.001. The resulting coefficients were then exponentially converted and the fit was compared to the fit presented in Eppley (1972). As an alternative means of showing the absolute maximum growth rates of a picophytoplankton community, we also calculated the linear, exponential and optimum fitthrough the optimum temperatures vs. optimum growth rates of the nine strains only.

### Statistical Analysis

To test for significant differences in the maximum growth rates or in the obtained temperature related parameters between the two picophytoplankton groups, the Wilcoxon-Mann–Whitney-U-test was used (p ≤ 0.05, df = 1).To test for cell size related trends of the temperature related parameters, the Mitchell-Olds and Shaw test was used (p ≤ 0.05) (Mitchell-Olds and Shaw, 1987). It tests for an intermediate maximum, in contrast to a monotonic relationship with extreme values at each end. For the linear trends in the response of the chlorophyll a to carbon ratios to temperature, a linear regression was applied and the obtained coefficients were analyzed by one-way ANOVA (p ≤ 0.05).

### RESULTS

### Temperature-Response of Individual Picophytoplankton Strains

The maximum growth rates of picoprokaryotes range from 0.07 to 0.82 d−<sup>1</sup> and of picoeukaryotes from 0.005 to 2.04 d−<sup>1</sup> over the full range of tested temperatures (**Figure 1**). These rates generally increase with temperature up to an optimum temperature (TOpt), above which they decrease (**Figure 1**) for all individual picophytoplankton strains. The AIC values are also smallest for the optimum fit (Equation 3) for seven of the nine individual strains (**Table 2**; **Figure 1**) compared to the linear (Equation 1) or exponential fit (Equation 2). For the two remaining strains, the AIC values for the optimum fit are within the range of an acceptable representation. M. pusilla did not grow at all above the optimum temperature. Therefore, there was no acclimated growth rate above the optimum temperature that would have been needed to get a good fit to the optimum function, and its growth rates are better represented by a linear fit. T. eleuthera grew at only four temperatures, thus the available data for this strain were insufficient to distinguish between the fits. The generally best agreement with the optimum fit suggests that three temperature-related parameters need to be quantified for the representation of the response of growth rates of individual strains to temperature: µOpt, TOpt, and 1T (**Table 3**).

The derived optimum growth rates (µOpt) differ significantly (p = 0.04, df = 1) between the two groups, the average for picoprokaryotes is 0.47 ± 0.17 d−<sup>1</sup> and for picoeukaryotes it is 1.05 ± 0.47 d−<sup>1</sup> . The average optimum temperature (TOpt) of the individual strains is 23.3 ± 2.7◦C and the temperature tolerance range (1T) is 8.2 ± 3.3◦C, with no significant difference in these two temperature-related parameters (pTOpt = 0.8; p1<sup>T</sup> = 0.12, df = 1) between picoprokaryotes and picoeukaryotes. None of the three temperature-related parameters was correlated with the latitude of isolation of the strains (**Figure 2**), i.e., tropical strains did not have a significantly higher TOpt than temperate strains. However, the overall temperature span at which the growth rates are positive is narrower for the three investigated strains of picoprokaryotes (13.7–27◦C, **Table 3**) than for the six strains of picoeukaryotes (2.8–32.4◦C). Nannochloropsis granulata, M. pusilla and Picochlorum sp., the three intermediate sized picoeukaryotes, grow at the most measured temperatures spanning up to 27◦C, which is reflected in their higher 1T values. Cell size has an effect on the temperature-related parameters for the individual picophytoplankton strains tested within this study. A significant unimodal relationship was found between the temperature tolerance range (1T) and cell size (R <sup>2</sup> = 0.73, p = 0.018), but not between µOpt (R <sup>2</sup> = 0.49, p = 0.17), or TOpt (R <sup>2</sup> = 0.25, p = 0.43) and cell size. The cell size at which 1T is maximal is 1.8µm (**Figure 2**). There is also statistical support (p < 0.01, Mitchell-Olds and Shaw test) for a maximum of µOpt at the higher end of measured values of 1T, although µOpt does not increase significantly with 1T (p = 0.1, linear regression, one-way ANOVA).

### Temperature-Response of Picophytoplankton

The maximum growth rates for the picoprokaryotes in response to temperature can be described equally well by all three fits (similar AIC values; **Table 2**), but the maximum growth rates for the picoeukaryotes are best described by either the linear or the optimum fit. Finally, the maximum growth rates for the group of picophytoplankton are best described by the exponential fit (**Figure 3**) and can be quantified by the two temperature-related parameters µmax,<sup>0</sup> ◦<sup>C</sup> and Q<sup>10</sup> (**Table 3**).

In order to compare the temperature response of the group of picophytoplankton or of picoprokaryotes to the parameters obtained by Eppley (1972) and Bissinger et al. (2008), a fit to the upper exponential 99th quantile of the maximum growth rates was calculated (**Figure 3**). For the group of picophytoplankton (µpic) the calculated Q<sup>10</sup> is 2.3 (Equation 6) but of picoprokaryotes (µpro) the temperature response is stronger and results in a much higher Q<sup>10</sup> of 4.9 (Equation 7). For the picoeukaryotes (µeuk) the Q<sup>10</sup> would be 2.8 (Equation 8), but the AIC does not give support for an exponential fit as an acceptable representation of the maximum growth rates in response to temperature for this group (**Table 2**). Hence we will exclude this fit from the further discussion.

TABLE 2 | AIC values for the linear, exponential and optimum fits for individual picophytoplankton strains, both groups of picoprokaryotes and picoeukaryotes, and picophytoplankton.


The lowest values are shown in bold print, other appropriate values (1AIC < 2) are underlined.

$$
\mu\_{pic} = 0.22 \times 2.3^{\frac{T}{10}} \tag{6}
$$

$$
\mu\_{\rho ro} = 0.023 \times 4.9^{\frac{T}{16}} \tag{7}
$$

$$
\mu\_{euk} = \; 0.19 \times 2.8^{\frac{T}{16}} \tag{8}
$$

The corresponding coefficients for the linear regression to the logarithmically transformed data are presented in **Table 4**.

A different method to represent the response of the absolute maximum growth rates of the group of picophytoplankton to temperature is to test the fits through the optimum values of the nine strains (**Figures 3**, **4**). With this method, the AIC value is lowest for the linear fit (−5.41), is also appropriate for the exponential fit (−5.3), but clearly better than for the optimum fit (−2.68).

### Chlorophyll a to Carbon Ratios

The chlorophyll a to carbon ratio (θ) for the group of picophytoplankton increases significantly with temperature between 0.004 and 0.037 g Chl g−<sup>1</sup> C (R <sup>2</sup> = 0.42, p < 0.001, **Figure 5**), and can be described by Equation (9).

$$
\theta = \left[1.01 \ast 10^{-3} + 9.38 \ast 10^{-4}T\right] \tag{9}
$$

This relationship is also significant (p ≤ 0.05) for individual strains (see Supplementary Material), unless a strain grew only over a narrow temperature range (both Prochlorococcus sp. strains and Imantonia rotunda), or there was a high variability in the data over a low range of chlorophyll a to carbon ratios (Micromonas pusilla). Four strains show a drop in chlorophyll a to carbon ratio above TOpt (both Prochlorococcus sp. strains, Picochlorum sp., and Nannochloropsis granulata).

The cellular chlorophyll a concentration increases significantly (p < 0.05) with temperature for seven strains

TABLE 3 | Temperature-related parameters for a linear, exponential, and optimum fit to represent the response of the maximum growth rates to temperature for individual picophytoplankton strains, both groups of picoprokaryotes and picoeukaryotes, and picophytoplankton.


The asymptotic standard error is shown in brackets. The number of measured maximum growth rates is n, the measured minimum temperature (Tmin), and maximum temperature (Tmax ), define the temperature span at which growth rates were positive.

(see Supplementary Material). For M. pusilla it becomes significant (p = 0.005) if the four highest outliers over the whole temperature range are excluded. For I. rotunda a significant (p = 0.038) increase in chlorophyll a is found up to its optimum temperature. There is also a stronger significance (p < 0.001) for N. granulata up to its optimum and a decrease, however not significant above its optimum temperature. No significant trend was found for the high light Prochlorococcus sp. strain. Phaeomonas sp. shows a significantly (p = 0.037) decreasing trend with increasing temperature.

The cellular carbon concentration increases significantly with temperature for the low light Prochlorococcus sp. strain (p = 0.004). It decreases significantly for the three picoeukaryotes N. granulata (p < 0.001), Phaeomonas sp. (p = 0.001), and for Picochlorum sp. between 14 and 27◦C (p = 0.016). No significant trends were established for the other strains.

TABLE 4 | Coefficients obtained from a linear 99th quantile regression to the log-transformed maximum growth rates of a group consisting of picoprokaryotes, and of picophytoplankton, using strains examined within this study with standard errors.


Coefficients for picoeukaryotes are provided for completeness.

### DISCUSSION

### Temperature-Response of Individual Picophytoplankton Strains

In agreement with the first hypothesis formulated by Eppley (1972), our results show strong evidence that the maximum growth rates of individual picophytoplankton strains in response to temperature are best represented by an optimum function. Thus, the best way to parameterize this response is to describe their optimum growth rates, optimum temperatures, and temperature tolerance ranges.

The optimum growth rates, which were obtained for the individual strains of picoprokaryotes are lower than

of picoeukaryotes. This confirms theoretical assumptions concerning the deviation of picophytoplankton from the classical allometric relationship with decreasing maximum growth rate with cell size in this group (Raven, 1998; Bec et al., 2008). The optimum temperatures, are slightly lower for Prochlorococcus sp. than for Synechococcus sp., which is also in agreement with previous studies (Moore et al., 1995; Johnson et al., 2006; Zinser et al., 2007). However, our estimated values are both lower than previously reported values of 24–25 and 28◦C, respectively for the two species. There are different reasons which may cause this discrepancy. A possible reason is that none of these studies applied an optimum fit to their results. Instead TOpt was only described as the temperature at which the highest growth rate (µOpt) was measured, even though TOpt and µOpt may be achieved between the tested temperatures. We have shown that the optimum function gives the best fit of the response of growth rates of individual picophytoplankton strains to temperature. We therefore conclude that our technique is more accurate in defining TOpt, because it is able to interpolate between data points and provide error intervals. Another potential reason could be the change of photophysiological properties with temperature. We show that the increase in chlorophyll a to carbon ratio is due to the significant increase in cellular chlorophyll a concentration for most strains. This is in agreement with the expected increase of light harvesting compounds with increasing temperature and is also associated with the decrease of photoprotective compounds (Geider, 1987). This effect may also contribute to the shift of the optimum temperature with light intensity (Geider, 1987). The strains used by Moore et al. (1995) and those in the present study were

grown under light saturation. For this an extensive series of light experiments has been conducted for the strains examined here beforehand (Stawiarski, 2014). However, these different strains also have different light optima. Hence, the differences in temperature optima may also be attributed to the natural variability of ecotypes, which may be linked to the adaptation to different light conditions (Johnson et al., 2006; Zinser et al., 2007). The optimum temperatures for picoeukaryotes obtained within the present study are similar to those presented in previous studies (20–25◦C) (Throndsen, 1976; Cho et al., 2007). A full description of the light response at constant temperature of some of these strains will be published in a separate paper (Stawiarski et al., in prep.).

TOpt is a common temperature-related parameter, which is used for modeling the distribution of different phytoplankton groups. Our results demonstrate that there are no significant differences in TOpt between picoprokaryotes and picoeukaryotes. Also there is no relationship between optimum temperature or latitude of isolation for the strains examined here, but both groups have been shown to occupy different thermal niches in the field (Buitenhuis et al., 2012). One could argue that culturing conditions may have led to a genetic adaptation and a shift in TOpt, but we found that Picochlorum sp., the tropical strain which has been in culture the longest, shows the strongest deviation (>9 ◦C) from its permanent culturing temperature. Contrary to our results, a study, in which an optimum function was used to obtain temperature-related parameters for 194 different strains of phytoplankton, found that TOpt follows an unimodal function of latitude and annual mean temperature of isolation (Thomas et al., 2012). We may not have found this trend in our data because of the much smaller number of data points we could obtain. However, they also find that TOpt shows considerable deviations from the annual mean temperature in polar and temperate waters, which suggests that TOpt is not the ultimate parameter controlling the distribution. Peak in situ abundances of different phytoplankton groups are not found at optimum temperatures, because of the combination of fluctuations in local temperature and the sharp drop in growth rates above TOpt.

The temperature span at which growth was positive for individual strains in our study is comparable to their in situ distribution. Peak in situ abundances of Prochlorococcus sp. were reported at both lower (19◦C) and higher temperatures (25– 28◦C) than their optimum temperature (Zinser et al., 2007) with strong inhibition above 28◦C (Moore et al., 1995). The upper limit of the temperature span for the Prochlorococcus sp. strains presented here is consistent with those results, and the lower limit of the temperature span is consistent with the results of Kulk et al. (2012). We show that some picoeukaryotes grow over a wider span of temperatures than the smaller picoprokaryotes. However, we do not find a direct correlation between 1T and latitude of isolation, which is in agreement with the study by Thomas et al. (2012). Instead, we find evidence that 1T, is significantly correlated with picophytoplankton cell size and can be represented by a unimodal function. The bigger picoprokaryote Synechococcus sp. grew over a wider span of temperatures than the smaller Prochlorococcus sp., consistent with earlier studies (Moore et al., 1995; Malinsky-Rushansky et al., 2002; Mackey et al., 2013). Also, the picoeukaryotes of an intermediate size (∼2µm) had a higher 1T than othersized members of the group. Together with the higher maximum growth rates of this intermediate size class (Bec et al., 2008) we suggest that their relatively high temperature tolerance range may contribute to their ubiquitous distribution. However, cell size and its variability would explicitly need to be measured over the full range of temperatures to gain a better understanding of this relationship.

We also find that a higher optimum growth rate is achieved by picophytoplankton strains with a high temperature tolerance range. In practice this would favor generalists in the field rather than allowing the coexistence of several specialist strains in different niche spaces. A field study has shown that 90% of analyzed gene sequences of picoeukaryotes can be attributed to Prasinophyceae, of which M. pusilla, an intermediate sized picoeukaryote, is an important member, with higher contributions in temperate and polar areas (Vaulot et al., 2008). In agreement with these results, we show that M. pusilla has a relatively high temperature tolerance range and a relatively high optimum growth rate. However, the study by Vaulot et al. (2008) was biased toward coastal areas and other factors such as light, nutrients, and water column stratification also need to be considered, especially in the open and oligotrophic ocean when investigating the community structure (Johnson et al., 2006; Bouman et al., 2011).

### Temperature-Response of Picophytoplankton

In agreement with the second hypothesis formulated by Eppley (1972), our results show that the maximum growth rates for the group of picophytoplankton in response to temperature are best represented by an exponential function (**Table 2**, **Figure 3**). This representation is also appropriate for the group of picoprokaryotes alone (**Table 2**). Hence, for the calculation of the absolute maximum growth rates of these two groups we follow the approach by Bissinger et al. (2008), who confirmed the Q<sup>10</sup> (1.88) estimated by Eppley (1972) for a mixed phytoplankton group. Our results show that for a group of picophytoplankton the temperature-dependence is higher and for a group of picoprokaryotes more than twice as high (**Table 4**, **Figure 3**, Equations 6, 7) as for this group of mixed phytoplankton. These results are in agreement with recent studies on picophytoplankton, which found a higher Q<sup>10</sup> value for picophytoplankton compared to larger species (Chen et al., 2014) and also higher values for picoprokaryotes (3.6–4.4) than for picoeukaryotes (1.7–2) (Kulk et al., 2012). It should be noted that the variance in the data increases with temperature, which could bias the statistical results at small sample size. We found that the main contributor to the increase in variance is the interspecific variation of µopt. However, the average squared residuals have a quite similar distribution as a function of temperature for the three functions. In addition, our sample size of 224 growth rates is large, so that the increase in variance would not bias the results, and we conclude that the comparison of Delta AIC to decide which function fits the data best seems valid despite the increase in variance with temperature in the observations.

The fit to the absolute maximum growth rates of the group of picophytoplankton in response to temperature presented in our study is lower than the fit presented in Eppley (1972). This can be explained by the generally lower maximum growth rates of picophytoplankton compared to those of other phytoplankton groups, e.g., diatoms (Furnas, 1990). The study by Eppley (1972) contained various groups of faster-growing phytoplankton and a substantial number of diatoms (43%). However, Bissinger et al. (2008) showed that a higher proportion of diatoms (68%) would not affect the fit. It is unclear, though, how high the proportion of picophytoplankton was in the database used in Bissinger et al. (2008). The lower absolute maximum growth rates and the higher Q<sup>10</sup> of the picophytoplankton examined here compared to mixed phytoplankton highlight the importance of quantifying the response of different phytoplankton groups to temperature individually. Especially in ocean regions where picoprokaryotes dominate the phytoplankton biomass, the influence of their higher Q<sup>10</sup> must be considered when modeling the response of the phytoplankton community to increased temperature as a consequence of climate warming.

We find that the group of picoeukaryotes grow over a wider span of temperatures than the smaller picoprokaryotes. Although our sample size of picoeukaryote species is larger than of picoprokaryote species, and we therefore have to be cautious about the interpretation of the wider temperature span of the picoeukaryotes as a group, these sample sizes reflect the diversity in the ocean of the two groups of picophytoplankton. Picoeukaryotes are spread across 12 classes in 4 divisions while there is only one class of picoprokaryotes (Vaulot et al., 2008). In addition, it is well established that picoeukaryotes dominate picophytoplankton biomass in colder waters at latitudes above 40◦ and have similar biomass at lower latitudes, but the smaller picoprokaryotes are more restricted toward warmer (sub-)tropical ocean waters (Buitenhuis et al., 2012). We therefore suggest that the difference in temperature span between the two groups could be real.

Our results further show that the exponential fit to the optimum growth rates only of all examined strains is lower than the fit to the upper 99th quantile of their maximum growth rates. This is because the maximum growth rates of faster-growing species at sub-optimum temperatures are higher than the optima of slower growing species. The fit through the optima was initially presented as an alternative method for representing the response of the absolute maximum growth rates of a phytoplankton community to temperature by Eppley (1972, Figure 2). However, more data of picophytoplankton strains with optima at lower temperatures would need to be included to distinguish better between these two methods of deriving the absolute maximum growth rates of a phytoplankton community.

### Temperature and the Chlorophyll a to Carbon Ratio

Phytoplankton acclimate to the prevailing environmental conditions by changing their cell composition. The chlorophyll a to carbon ratio is an important variable for measuring biomass and primary production and varies between different phytoplankton groups, e.g., diatoms have higher chlorophyll a to carbon ratios compared to picophytoplankton (Geider et al., 1997). In agreement with previous studies (Eppley, 1972; Geider, 1987) we show that with increasing temperature the chlorophyll a to carbon ratio also increases for the group of picophytoplankton. We also show that this effect on the chlorophyll a to carbon ratio is caused by the increase in chlorophyll a concentration with temperature, rather than by a potential decrease of cellular carbon.

We also indicate a drop above the optimum temperature for some individual strains. This reduction in photosynthetic machinery at supra-optimal temperatures is comparable to the effect caused by photoinhibition at high light levels to reduce damage (Geider, 1987) and is thus consistent with the photosynthetic model of Baumert and Petzoldt (2008), which attributes the decrease of growth rate above TOpt to an increase in light inhibition with temperature.

### Picophytoplankton and Climate Warming

Picophytoplankton, including both groups of picoprokaryotes and picoeukaryotes, is treated as a single plankton functional type in ocean biogeochemical models (Le Quéré et al., 2015). Hence, the assumption is that it can be represented with a common set of physiological traits. Generally, there is some support for this assumption, as both groups of picophytoplankton are adapted to low nutrient and light conditions because of their high nutrient uptake and light harvesting efficiency compared to other phytoplankton groups (Raven, 1998). Both adaptations could help to explain their better success in oligotrophic (Alvain et al., 2008) and deep mixed water columns (Veldhuis et al., 2005). However, the distribution of picoprokaryotes is inversely related to that of picoeukaryotes in the natural environment (Buitenhuis et al., 2012), and these distributions are correlated with nitrogen concentration and depth of the euphotic layer (Bouman et al., 2011). In addition, temperature was also shown to be an important predictor for the realized ecological niche space of diverse phytoplankton groups (Brun et al., 2015). The temperature span at which growth was positive for Prochlorococcus sp. presented in our study is consistent with the quartile temperature span of the realized ecological niche (16– 25◦C) in the study by Brun et al. (2015) which uses observations from MAREDAT (Buitenhuis et al., 2013). Unfortunately, they were not yet able to specifically separate the realized ecological niche of picophytoplankton due to the lack of available data on a broader range of species. Our study highlights the importance of quantifying the direct impact of each temperature-related parameter for a large variety of phytoplankton strains to define fundamental ecological niches, which are required for the formulation of ocean biogeochemistry models (Le Quéré et al., 2005), and which aim to represent realized ecological niches as emergent properties (Follows et al., 2007).

With ongoing climate warming, the biomass and productivity of picophytoplankton relative to other phytoplankton could increase due to enhanced water column stratification and lower nutrient availability (Behrenfeld et al., 2006; Morán et al., 2010). The results presented here support a potential advantage for picophytoplankton as a consequence of the higher temperature dependence of their maximum growth rates compared to other phytoplankton groups. Picophytoplankton shows a stronger increase in absolute maximum growth rates with temperature with a Q<sup>10</sup> of 2.3 compared to coccolithophores with a Q<sup>10</sup> of 1.7 (Buitenhuis et al., 2008), and a mixed phytoplankton community with a Q<sup>10</sup> of 1.88 (Eppley, 1972). However, the relative advantage of the temperature dependence of the absolute maximum growth rates of picophytoplankton also needs to be considered within an ecosystem with trophic interactions in a warming climate, where the effect of temperature on the top down control by zooplankton may also alter the phytoplankton community structure.

In addition, we suggest that climate warming may also change the composition of the picophytoplankton community itself.

### REFERENCES


Even though picoprokaryotes may show a stronger increase in biomass in specific regions due to their higher Q10, they are restricted by a narrower temperature tolerance range. The sharp decrease of maximum growth rates above the optimum temperature suggest that the temperature tolerance range is also an influential parameter for the distribution of phytoplankton species and its change with climate warming. We therefore assume that picoprokaryotes will be shifted to higher latitudes or depth. This shift has already been suggested using a neural network model which defines niches of two picoprokaryotes based on temperature, PAR and nutrient availability (Flombaum et al., 2013). However, we also suggest that picoeukaryotes, in particular those of an intermediate size around 2µm, will be able to increase their contribution to phytoplankton biomass over a wider temperature span.

### AUTHORS CONTRIBUTIONS

BS conducted the laboratory experiments, analyzed the data, and is the lead author on this paper. EB and CL wrote the project proposal, acquired funding, and put forward some of the hypotheses. All authors co-wrote the manuscript.

### FUNDING

The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7 2007-2013) under grant agreements n◦ 238366 (Greencycles II) and 282672 (EMBRACE), and the Natural Environment Research Council grant n◦ NE/K001302/1(i-MarNet).

### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fmars. 2016.00164

picoeukaryotes. Limnol. Oceanogr. 53, 863–867. doi: 10.4319/lo.2008.5 3.2.0823


Koenker, R. (2006). Quantreg: Quantile Regression R Software Version 4.02.

Kulk, G., de Vries, P., van de Poll, W., Visser, R., and Buma, A. (2012). Temperature-dependent growth and photophysiology of prokaryotic and eukaryotic oceanic picophytoplankton. Mar. Ecol. Prog. Ser. 466, 43–55. doi: 10.3354/meps09898


distributions in the Atlantic Ocean. Limnol. Oceanogr. 52, 2205–2220. doi: 10.4319/lo.2007.52.5.2205

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Stawiarski, Buitenhuis and Le Quéré. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# In situ Measurements and Model Estimates of NO<sup>3</sup> and NH<sup>4</sup> Uptake by Different Phytoplankton Size Fractions in the Southern Benguela Upwelling System

J. Ffion Atkins <sup>1</sup> \*, Coleen L. Moloney <sup>2</sup> , Trevor A. Probyn<sup>3</sup> and Stewart Bernard1, <sup>4</sup>

*<sup>1</sup> Department of Oceanography, Marine Research Institute, University of Cape Town, Cape Town, South Africa, <sup>2</sup> Department of Biological Sciences, Marine Research Institute, University of Cape Town, Cape Town, South Africa, <sup>3</sup> Department of Agriculture, Forestry and Fisheries, Cape Town, South Africa, <sup>4</sup> Council for Scientific and Industrial Research, Cape Town, South Africa*

#### Edited by:

*Dag Lorents Aksnes, University of Bergen, Norway*

#### Reviewed by:

*Kyle Edwards, University of Hawaii at Manoa, USA S. Lan Smith, Japan Agency for Marine-Earth Science and Technology, Japan*

> \*Correspondence: *Ffion Atkins ffion.atkins@gmail.com*

#### Specialty section:

*This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Marine Science*

Received: *30 July 2016* Accepted: *23 September 2016* Published: *14 October 2016*

#### Citation:

*Atkins JF, Moloney CL, Probyn TA and Bernard S (2016) In situ Measurements and Model Estimates of NO3 and NH4 Uptake by Different Phytoplankton Size Fractions in the Southern Benguela Upwelling System Front. Mar. Sci. 3:194. doi: 10.3389/fmars.2016.00194* Bulk measurements can be made of phytoplankton standing stocks on a quasi-synoptic scale but it is more difficult to measure rates of production and nutrient uptake. We present a method to estimate nitrogen uptake rates in productive coastal environments. We use observed phytoplankton cell size distributions and ambient nitrogen concentrations to calculate uptake rates of nitrate, ammonium and total nitrogen by different size fractions of diverse phytoplankton communities in a coastal upwelling system. The data are disaggregated into size categories, uptake rates are calculated and these uptake rates are reaggregated to obtain bulk estimates. The calculations are applied to 72 natural assemblages for which nitrogen uptake rates and particle size distributions were measured *in situ*. The calculated values of total N uptake integrated across all size classes are similar to those of *in situ* bulk measurements (N slope = 0.90), (NH<sup>4</sup> slope = 0.96) indicating dependence of NH<sup>4</sup> and total N uptake on ambient N concentrations and cell size distributions of the phytoplankton assemblages. NO<sup>3</sup> uptake was less well explained by cell size and ambient concentrations, but regressions between measured and estimated rates were still significant. The results suggest that net nitrogen dynamics can be quantified at an assemblage scale using size dependencies of Michaelis-Menten uptake parameters. These methods can be applied to particle size distributions that have been routinely measured in eutrophic systems to estimate and subsequently analyse variability in nitrogen uptake.

Keywords: phytoplankton, diversity, allometry, nitrogen uptake, particle size distributions

### 1. INTRODUCTION

The diversity of phytoplankton communities influences the flows of carbon, nitrogen and other important elements through the marine environment. Marine ecosystem models that aim to capture this relationship represent phytoplankton diversity either by different functional groups (Follows and Dutkiewicz, 2011), cell size (e.g., Moloney et al., 1991; Baird and Suthers, 2007; Banas, 2011; Ward et al., 2012) or by both (Le Quéré et al., 2005). Our understanding of the Atkins et al. Nitrogen Uptake along Size Spectra

consequences of this diversity on global biogeochemistry is still limited (Lomas et al., 2014). In a broad ecological context, in addition to taxonomic distinction, the term diversity currently includes functionality within an environment (Tilman, 2001; McGill et al., 2006; Westoby and Wright, 2006; Litchman et al., 2007). A challenge in biogeochemical modeling is to try account for diversity among organisms and its role in nutrient flux (Follows and Dutkiewicz, 2011), plasticity in organism traits (Pahlow and Oschlies, 2009), trade-offs in energy expenditure and the relationships between physiological traits and environmental forcing (Aksnes and Cao, 2011). The most commonly used function to model nutrient uptake is the Michaelis-Menten equation and parameter values for maximum uptake rates (Vmax) and half saturation constants (Ks) are widely available in the literature (see Litchman et al., 2015), often resolved at the species level in batch/continuous cultures (e.g., Eppley et al., 1969) and see Edwards et al. (2014) and typically at a genus level from natural populations (see Collos et al., 2005). The variation in Vmax and K<sup>s</sup> within phytoplankton groups and in relation to cell size were extensively reviewed by Litchman et al. (2007) and Edwards et al. (2012), where large variation was evident between and within phylogenetic groups. K<sup>s</sup> values, for example, were found to vary over two orders of magnitude for a given group (Collos et al., 2005; Franks, 2009; Seeyave et al., 2009; Aksnes and Cao, 2011). Collos et al. (2005) found strong genus-specific differences in K<sup>s</sup> between Thalassiosira and Chaetoceros, both diatoms, under similar nutrient levels. Absolute values of Vmax and their range are highest in diatoms, whereas K<sup>s</sup> values are highest in dinoflagellates (Litchman et al., 2007; Edwards et al., 2012). The paucity of K<sup>s</sup> values to account for all genotypic diversity in natural assemblages, under variable environmental conditions, as well as computational costs, has meant that K<sup>s</sup> is often regarded a constant. The assumption that these parameter values are invariant within phylogenetic groups has been highlighted as a potential source of error when parameterizing nutrient uptake by Michaelis-Menten kinetics (Franks, 2009).

Several studies have aimed to quantify the dynamic physiological response of phytoplankton cells to changing environmental conditions (e.g., Smith and Yamanaka, 2007; Pahlow et al., 2008; Bonachela et al., 2011; Smith et al., 2011) and have improved our conceptual understanding of cellular constraints on nutrient uptake and growth. Such dynamic trait-based approaches have been incorporated into large-scale modeling studies (Arteaga et al., 2014), with improved agreement between in situ values and model output (Smith et al., 2015). In many situations, the necessary in situ data are not available to constrain the dynamic response of a diverse, natural assemblage within a realistic, local context. Relatively simple size-based models can adequately replicate large scale dynamics of nitrogen in the marine environment (Ward et al., 2012; Acevedo-Trejos et al., 2014) with the advantage of reducing the number of free parameters, and thus model uncertainty, by using size-scaling exponents (Baird and Suthers, 2007; Banas, 2011; Ward et al., 2012). The size structure of plankton assemblages and the dominant size fraction will dictate, to some degree, the pathways of nutrients and how they are transferred to higher trophic levels (Probyn et al., 1990; Moloney et al., 1991; Chisholm, 1992; van der Lingen et al., 2006). Litchman et al. (2007) found strong empirical relationships between organism size and physiological rates (Vmax and Ks) and considered cell size a master trait. Our understanding of the variability in uptake kinetic parameters in relation to community composition and environmental variability is poor, and there is a need for field-based and laboratory studies of physiological processes of phytoplankton groups (Gregg et al., 2003; Litchman et al., 2007; Allen and Fulton, 2010).

This study hypothesized that some of the variance in Michaelis-Menten parameter values can be accounted for by considering the size spectra of the phytoplankton populations. To test such an hypothesis, we used measured particle size distributions (from Beckman Coulter Counter data) to calculate sets of theoretical, size-based biomass and Michaelis-Menten parameters for different field samples. We applied ambient nitrogen concentrations from each sample to Michaelis-Menten models to estimate size-based nitrogen uptake rates and integrated these across all sizes for the sample. These calculated rates were subsequently compared to measured in situ bulk uptake rates to estimated uptake rates of NO3, NH<sup>4</sup> and total N (total N = NO<sup>3</sup> + NH<sup>4</sup> ). This research offers a tool to extend the application of pre-existing particle cell size distributions, relying on robust assumptions of the size dependence of nitrogen metabolism.

## 2. METHODS

### 2.1. In situ Data Collection

Data from three separate case studies were used, data from Lamberts Bay were taken from a fixed station (32◦ 05.020′ S, 18◦ 16.010′E) at 0 m, 3.5 km off Lamberts Bay, as daily samples during the periods 25 February–11 March 2004 and 15 March– 6 April 2005. In Saldanha Bay, sampling took place at a fixed station (33◦ 01.748′ S, 18◦ 00.888′ E) from 0, 3, 6, and 9 m, every 2 months for a period of 3 days from January 2012 to January 2013. Water samples were collected using a 5 L Niskin water sampler and stored in 20 L black buckets, which were then transported to the laboratory within 1–2 h of collection for the determinations of particle size distributions, nutrient concentrations, <sup>15</sup>N uptake and particulate nitrogen calculations. Methods employed in all three case studies were consistent, unless stipulated otherwise. Data from the different systems within the Benguela ecosystem were chosen to try obtain a good spread in biomass and uptake rate values.

### 2.1.1. Cell Size Distributions and Community Structure

Particle size distributions (PSDs) of samples were measured using a Beckman Multisizer 4 Coulter Counter. A discrete sample volume of 40 mL was used to count particles per size class and was blank corrected by 0.2 µm filtered seawater. An aperture size of 140 µm was used, with a capacity to measure particles from 2 to 86 µm. Confidence in measurements below 5 µm is significantly reduced, and thus such values are omitted from particle size spectra. Dominant species were identified using inverted microscopy following Utermohl (1958).

### 2.1.2. <sup>15</sup>N Uptake

One liter from each sample was spiked with <sup>15</sup>N-labeled NH4Cl or NaNO<sup>3</sup> (BOC Limited, isotope assay 99%) in acid-cleaned polycarbonate bottles. Spike concentrations were approximately 0.1 µmol <sup>15</sup>N L−<sup>1</sup> for NH<sup>4</sup> and varied between 0.04 and 2 µmol <sup>15</sup>N L−<sup>1</sup> for NO3, depending on estimations of in situ NO<sup>3</sup> concentrations from temperature. Incubations were carried out in situ at the corresponding depth of collection, using a custom-made rig for 4 h in Lamberts Bay and for 24 h in Saldanha Bay. The differences between the two incubation times has been accounted for by scaling the 4 h incubations to 24 h. The assumption was made that daylight was 14 h and that uptake during the night was 55% of daylight rate for NH<sup>4</sup> and 12% of daylight rate of NO<sup>3</sup> uptake, as measured at in-shore locations in Probyn et al. (1996). Incubations were terminated by filtration onto Whatman GF/F filters approximately 30 min after retrieval. Filters were rinsed with artificial seawater and Milli-Q to flush dissolved isotopes from the filter matrix and dried at 75◦C overnight before storage. Nitrogen uptake rates were calculated using post-incubation particulate N concentrations, which accounts for uptake of unlabeled nutrient sources (Dugdale and Wilkerson, 1986). Ammonium uptake rates are not corrected for isotope dilution and thus represent an underestimate. Incubations were terminated by filtration on 47 mm ashed GF/F filters, which were washed with artificial sea water and Milli-Q and then dried at 60◦C overnight. Samples were punched out of each filter (disc size depending on organic coverage) and particulate <sup>15</sup>N concentrations were measured on a Finnigan MAT mass spectrometer (Department of Archeometry, University of Cape Town). The filtrate was used for nutrient analysis of ambient concentrations at the end of the incubation.

### 2.1.3. Nutrient Analyses

Nitrogenous nutrient concentrations were measured manually after filtration through Whatman GF/F filters. All nutrient analyses were initiated immediately on return to the shore within 1.5 h of collection. Ammonium (NH4) was analyzed according to the methods described in Koroleff (1983) scaled down to 5 mL samples, and nitrate (NO3) following the procedure of Nydahl (1976).

### 2.2. Model Setup

Theoretical uptake rates were calculated from measured in situ PSDs and ambient nitrogen concentrations. Details of each step are discussed further below. In brief,


rates (ρ) of NO<sup>3</sup> and NH<sup>4</sup> in µ mol L−<sup>1</sup> h −1 for each size bin, using ambient nutrient concentrations.

3. The sums of the estimated uptake rates per size bin (ρ NO<sup>3</sup> and ρ NH3) were compared to corresponding in situ uptake measurements. The implications of the assumptions of each step are evaluated in the discussion.

### 2.2.1. Conversions to Biomass

Measured biomass of particulate nitrogen (µmol L−<sup>1</sup> ) includes all particulate matter down to a cut-off nominal size of 0.7 µm (GF filter), whereas Coulter Counter measurements have a lower limit of 3 µm. A comparison between a linear (Moloney and Field, 1989) and non-linear (Menden-Deuer and Lessard, 2000) conversion from cell volume to biomass was carried out. Cellular nitrogen content was calculated per size bin and total biomass per size bin was calculated by multiplying by cell abundance (N) within each size bin. Carbon biomass was also calculated using (Moloney and Field, 1989), as a carbon biomass is required in addition to nitrogen biomass to solve for size-dependent uptake parameters. The non-linear equation follows that of Menden-Deuer and Lessard (2000):

$$
\log \text{pgNcell}^{-1} = -0.928 + 0.849 \ast \log \text{Vol} \tag{1}
$$

Linear conversion follows (Moloney and Field, 1989) where 1 µm<sup>3</sup> = 0.071 pgC (dry) and 1 µm<sup>3</sup> = 0.0185 pgN (dry).

### 2.2.2. Uptake Parameters

Size-dependent uptake parameters, Vmax (µmolN µmolC−<sup>1</sup> h −1 ) and K<sup>s</sup> (µmolN L−<sup>1</sup> ), were calculated per size bin using general allometric equations (aVol<sup>b</sup> ) with values a and b from Ward et al. (2012) (**Table 1** and **Figure 1**). Conversions of units were carried out by normalizing to carbon, calculated using the linear conversion to carbon (Moloney and Field, 1989).

### 2.2.3. Estimating Uptake Rates

The size-dependent parameters were applied to the Michaelis-Menten equation to calculate nitrogen uptake rate for each size bin, using nitrogen biomass per size bin and ambient nitrogen concentrations. The NO<sup>3</sup> taken up by the assemblage was calculated by summing across all size bins:

$$
\rho \text{NO}\_3 = \sum^{size} \left( \frac{V\_{\text{max}} \ast PN \ast NO\_3}{NO\_3 + K\_s} \right) \tag{2}
$$

where PN is the nitrogen biomass of the cells per size bin and NO<sup>3</sup> to ambient concentration. The corresponding equation was used to calculate NH<sup>4</sup> uptake. Estimated uptake rates are compared to the relative measured in situ N uptake. The inhibition of NO<sup>3</sup> by ambient NH<sup>4</sup> concentrations was also incorporated into separate estimations of ρNO3:

$$\rho\_{\rm NO\_3} = \sum^{size} \left( V\_{\rm max\_{NO\_3}} \left( \frac{NO\_3}{NO\_3 + K\_{\rm NO\_3}} \cdot e^{\psi NH\_4} \right) \right) \tag{3}$$

Total nitrogen uptake was calculated both with and without an inhibition term, Equation (4) details total N uptake with inhibition:


*Where appropriate size-dependent uptake parameters, Vmax and K<sup>s</sup> are calculated as aVol<sup>b</sup> .*

$$
\rho N = \sum^{size} \left( V\_{\text{max}\_{NO\_3}} \left( \frac{NO\_3}{NO\_3 + K\_{sNO\_3}} \cdot e^{\psi\_{NH\_4}} \right) \right)
$$

$$
+ V\_{\text{max}\_{NH\_4}} \left( \frac{NH\_4}{NH\_4 + K\_{sNH\_4}} \right) \right) \tag{4}
$$

Further comparisons were made between measured, massspecific uptake rates (v) and non-allometric rates. Mass-specific uptake rates were calculated by dividing the bulk absolute rate by the corresponding measured nitrogen biomass (PN). The non-allometric rates were calculated using a fixed Vmax and K<sup>s</sup> value for all bins along the size spectrum. Sensitivity of the parameter values was tested by comparing the outcome of 9 combinations of realistic values for NO3: Vmax = [0.1, 0.5, 1] , Kmax = [0.5, 2, 15]; and NH4: Vmax = [0.1, 0.5, 1] and K<sup>s</sup> = [0.1, 1, 10]. All parameter units and values used are detailed in **Table 1**. Assessments were made between measured and estimated values of uptake rates of NO3, NH<sup>4</sup> and total N by using an absolute percentage difference and bias estimates (Zibordi et al., 2004).

### 3. RESULTS

### 3.1. In situ

The range of values for measured particulate nitrogen, ambient nitrogen concentrations and uptake rates vary among the three case studies (**Figure 2**). This variability reflects distinct assemblages observed in each case study. Highest values of particulate nitrogen (PN) were observed in Lamberts Bay (LB04 and LB05) relative to Saldanha Bay. LB05 was dominated by a dinoflagellate Prorocentrum triestinum with maximum particulate nitrogen reaching 146 µmol N L−<sup>1</sup> , in association with lowest ambient nitrogen concentrations. SB samples had relatively low biomass (average 10.3 µmol N L−<sup>1</sup> ), almost completely dominated by diatoms. Highest field-measured uptake rates of total nitrogen (**Figure 3A**) and nitrates (**Figure 3B**) were seen in LB04, corresponding to an assemblage dominated by a ciliate (Myrionecta rubra) and a diatom (Skeletonema spp.) with a maximum of 0.67 µmol N L <sup>−</sup>1h −1 . Rates of NH<sup>4</sup> uptake were lower on average than NO<sup>3</sup> uptake in all case studies (**Figure 3C**). The size spectra measured were highly variable per sample. **Figures 4A,C,E** show typical size distributions of a low biomass range, and **Figures 4B,D,F** show samples of high biomass, illustrating distributions of bimodality.

### 3.2. Conversions to Biomass

The two methods of conversion from cell volume to mass gave estimates of particulate nitrogen that were significantly correlated with measured in situ values (**Figure 5**). For the combined data set (SB and LB), the correlation for the non-linear conversion was r = 0.78, p < 0.005 and for the linear conversion r = 0.76, p < 0.005. The two regressions comparing measured in situ and estimated particulate nitrogen using the linear and nonlinear conversion methods were assessed by testing H0: slope = 1 (**Table 2**). The regression slopes for the linear and non-linear conversions were greater than one, but were not significantly different; linear (t0.05, <sup>72</sup> = 3.65, p = 0.99) and non-linear (t0.05, <sup>72</sup> = 3.33, p = 0.99). Both slopes provided good predictions of biomass from particle size distributions and both conversion methods. The non-linear conversion of Menden-Deuer and Lessard (2000) was used in further estimates of uptake rates.

### 3.3. Estimating Nitrogen Uptake

The ranges of estimated N uptake rates were similar to those measured in situ (**Figure 6**). Predictions of nitrogen uptake rates were significantly correlated with respective measured uptake rates: NO<sup>3</sup> (r = 0.60, p < 0.005); NH<sup>4</sup> (r = 0.61, p < 0.005) and total N (r = 0.67, p < 0.005). The slopes of the relationship between measured and estimated uptake rate values were also assessed testing H0:slope = 1 (**Table 2**). The regression slopes were not statistically different from 1 for NH<sup>4</sup> (t0.05, <sup>67</sup> = −0.26 =, p = 0.30) and total N (t0.05, <sup>72</sup> = −0.26, p = 0.40); this was not the case for NO3(t0.05, <sup>72</sup> = −3.06, p = 0.00). An inhibition term (ψ) of 1.99 µmol N−<sup>1</sup> was estimated for NO<sup>3</sup> uptake. The resulting predictions for ρNO<sup>3</sup> were similar to those of ρNO<sup>3</sup>

FIGURE 2 | Summary box plots of the in situ data from Lamberts Bay 2004 and 2005 (LB04, LB05) and Saldanha Bay (SB) for (A) particulate nitrogen, (B) total N (NO<sup>3</sup> + NH<sup>4</sup> ), (C) NO3 (D) NH4 concentrations. Boxes are medians, 25th and 75th quartiles and whiskers are extreme values not considered outliers, which are shown as crosses. SB (*n* = 52), LB04 (*n* = 9), LB05 (*n* = 11).

with no inhibition, with a increase in bias when inhibition is included (bias ρNO<sup>3</sup> = 0.03, bias ρNO<sup>3</sup> <sup>ψ</sup> = −0.72). Predictions of total N uptake do not differ greatly when an inhibition term is applied; ρN (slope = 0.97), ρNψ(slope = 1.05) (**Table 2**) but more bias is introduce with an inhibition term (ρN<sup>ψ</sup> = −0.89, bias ρN = −1.10). Estimations for ρNO<sup>3</sup> (both with and without an inhibition term) did not match those measured in situ (**Table 2**). The comparisons between measured and calculated mass-specific rates showed poor agreement, and no statistical similarity was observed between the two data sets (**Table 2**). The relationships between estimated and measured ρNH4, ρN and ρN<sup>ψ</sup> are not statistically different (**Table 2**) and are thus considered good predictions of the uptake of NH<sup>4</sup> and total N. The non-allometric rates were also compared with each other and a hypothetical 1:1 slope (**Figure 7**). Of the 9 different combinations of uptake parameters tested (H<sup>0</sup> slope = 1), one set was close to 1 but not statistically significant (slope = 0.96, p < 0.00) for NO3, and 2 sets for NH4, the closest being significantly similar to 1 (slope = 1.2, p = 0.78) (**Table 3**).

### 4. DISCUSSION

Predictions of biomass and nitrogen uptake rates were made using measured particle size distributions of natural assemblages, volume to biomass conversions (Menden-Deuer and Lessard, 2000) and size-dependent Michaelis-Menten uptake parameters (Ward et al., 2012). The in situ values used to validate the modeled values had a large range and thus a large spread existed in the data. There were good correlations between estimated and measured particulate N. This strong correlation gave necessary confidence in using particle size distributions derived from the Beckman Coulter Counter to predict the uptake rates of NH4, total N and to a lesser extent NO3. Significant correlations were found between modeled and in situ measured uptake rates and the values predicted for the uptake of NH<sup>4</sup> and total N were statistically similar to values measured in situ.

### 4.1. Conversions to Biomass

Both conversion models used to derive particulate nitrogen from particle size distributions (via non-linear or linear functions) yield similar results with a good correlation between estimated

and measured values. The regression equations used to estimate biomass were applied to all assemblages, which were most often mixed assemblages, i.e., containing dinoflagellates (LB05), ciliates (LB04), and diatoms (SB). LB05 had a high percentage of the dinoflagellate Prorocentrum triestinum at very high biomass (max. 146 µmol N L−<sup>1</sup> ), and the correlation coefficients for this particular data set are strongest. Even so, when applied to assemblages containing different taxa (ciliates or diatoms), overall the conversion factors performed well and the regression fit is close to a 1:1 relationship between measured and estimated nitrogen biomass. An even better fit may have resulted if group-specific conversion factors were used, but such empirical relationships for volume:nitrogen of the groups measured in this study were not found in the literature. It is noted that diatoms, for example, contain less carbon per unit volume than other groups, attributed to their significantly higher vacuole volume (Strathmann, 1967; Sicko-Goad et al., 1984). Cellular nitrogen content or nitrogen stores have also been observed to vary considerably between different species of phytoplankton (Parsons et al., 1961; Dortch et al., 1984).

Further errors could have been introduced by the assumptions made in deriving particle size distributions via a Coulter Counter, which assumes sphericity of cells. This could lead to underlying bias because of non-spherical groups (e.g., dinoflagellates) or particles of elongate shape, e.g., chain-forming diatoms, which are known to introduce error and can lead to an

under/overestimation of total volume (Boyd and Johnson, 1995). Furthermore, the Coulter Counter measures down to 2 µm diameter (with confidence from 5 µm) and thus omits the submicron range due to limitations in technical capabilities. Nevertheless, the Coulter Counter has been used in several studies to successfully derive volume to carbon ratios (Mullin et al., 1966; Strathmann, 1967; Montagnes et al., 1994) and the presented results provide confidence that such data can adequately represent the particulate biomass of the nitrogen inventory in natural, diverse assemblages in eutrophic systems, characterized by large cells and high biomass.

line, red line has a hypothetical slope of 1:1 such that measured = estimated

values. (• SB), (+ LB04), (x LB05).

The data presented here show that particle size distributions convert well to a measure of biomass, despite the broad scale application of a dinoflagellate volume:nitrogen conversion to mixed assemblages, the exclusion of submicron size ranges, and the assumptions of sphericity when using the Coulter counter. It has been noted that quantitative measurements of particulate carbon/nitrogen are in general lacking (Behrenfeld and Boss, 2006), and we suggest tha Coulter Counter derived PSDs can provide adequate measures of nitrogen biomass, most notably, when examining communities in eutrophic systems. Such conversions may not be as successful in oligotrophic areas, where cell size distributions are characteristically dominated by pico/nano plankton (<2 µm), but would need further investigation.

### 4.2. Estimating Uptake Rates

A significant correlation exists between the estimated and measured uptake rates of NO3, NH<sup>4</sup> and total N, for natural



*t* = *a* − *1/Standard Error (SE) where Ho: slope* = *1. DF* = *72, critical value of* t *(1.66) and alpha (*α = *0.05).*

hypothetical 1:1 slope, black line is the regression between measured and model uptake rates.

assemblages. The slopes of the regressions for the estimated vs. measured values of NH<sup>4</sup> and total N uptake were close to 1, indicating statistical similarity to what was measured in situ. The size-dependence of the Michaelis-Menten uptake parameters, Vmax and K<sup>s</sup> , used by Ward et al. (2012) proved to be adequate values and yielded comparable results of nitrogen uptake to what had been measured in situ. Several studies have called into question the adequacy of the Michaelis-Menten kinetics equation to describe nutrient uptake in phytoplankton (Droop, 1974; Pasciak and Gavis, 1974; Aksnes and Egge, 1991). These criticisms are based on the premise that the equation does not account for differences in uptake rates in limiting or non-limiting conditions (Rhee, 1974; Grover, 1991), or that internal stores of nutrients can dictate uptake based on simple diffusion limitation (Droop, 1974). Both Michaelis-Menten uptake parameters are subject to variability, not only in different species but due to differences in nutrient availability and varying environmental conditions (Lomas and Glibert, 1999; Collos et al., 2005 and references therein). Smith et al. (2009) suggest that optimal uptake kinetics, which accounts for physiological acclimation to fluctuating environmental conditions, is a superior alternative

TABLE 3 | The combination of uptake parameters (Vmax and Ks) that resulted in the regression slope closest to 1.


*t* = *a* − *1/Standard Error (SE) where Ho: slope* = *1. Critical value of t (1.66) and alpha (*α = *0.05).*

to standard Michaelis-Menten descriptions of Vmax and K<sup>s</sup> . A flexible phytoplankton functional type (FlexPFT) model (Smith et al., 2015), which resolves the dynamic response of phytoplankton communities, which was able to reproduce productivity and chlorophyll values of two contrasting time series better than when no flexible response was included. Thus, the limitations of Michaelis-Menten are recognized, more particularly in its assumption that parameter values are constant during environmental fluctuations. However, its use will most likely remain popular due its simplicity and the availability of parameter values in the literature. The variability of in situ measured uptake rates of NH<sup>4</sup> and total N is statistically matched by the variability in what was estimated using sizescaled parameters, which implies that much of the variability in Michaelis-Menten parameters, when applied at an assemblage scale, can be accounted for by simple size scaling of Vmax and Ks . The results also imply that net community rates of NH<sup>4</sup> and total nitrogen uptake are driven by ambient concentrations and cell size.

As expected, the case for NO<sup>3</sup> was more complex. Although the slope of the estimated ρNO<sup>3</sup> was positive and close to 1, statistically it was not significant and reveals the potential importance of other influencing factors, in addition to cell size and ambient concentration. The suppression of NO<sup>3</sup> uptake by NH<sup>4</sup> may explain some of the variability observed in in situ measured values that is not accounted for in the model estimates. Numerous studies have shown an interaction between NH<sup>4</sup> and NO<sup>3</sup> uptake (e.g., McCarthy et al., 1975; Muggli and Smith, 1993; Harrison et al., 1996). NH<sup>4</sup> is generally considered to suppress the uptake of NO<sup>3</sup> (Dortch, 1990) but this is observed to be a highly variable process, where NH<sup>4</sup> can have little to no effect on NO<sup>3</sup> uptake (Kokkinakis and Wheeler, 1987) or can enhance rather than inhibit NO<sup>3</sup> uptake (Dortch, 1990). The extent to which NH<sup>4</sup> will affect NO<sup>3</sup> uptake is not just speciesdependent, but is also affected by physiological state and the preconditioning nutrient concentrations (Varela and Harrison, 1999; L'Helguen et al., 2008). Equally, the concentration of NH<sup>4</sup> at which suppression of NO<sup>3</sup> uptake occurs varies between systems (Dortch, 1990; Dugdale et al., 2006, 2007; Probyn et al., 2015). The effect of incorporating an inhibition term, in this case, made little difference to the estimates of ρNO<sup>3</sup> and ρN. A range of inhibition parameter values used in other studies were also investigated, ranging from 1.5 (Kishi et al., 2007) to 4.6 (Dutkiewicz et al., 2009), with little significant change in statistical comparisons. The value of 1.99, the outcome of a best fit model to the NO<sup>3</sup> uptake values for this study, was deemed optimal for the range of values measured. Another suggestion to explain the deviations from Michaelis-Menten kinetics for NO<sup>3</sup> uptake, is the potential for "shift-up" kinetics described in Dugdale et al. (1990, 2006). It was observed that NO<sup>3</sup> uptake may not follow Michaelis-Menten kinetics consistently along the upwelling timeframe, where initial (highest) concentrations of NO<sup>3</sup> will not equate to highest uptake rates, as communities take time to respond to new injections of NO3.

The predictions did not work when measured and calculated biomass-specific rates (h−<sup>1</sup> ) were compared (**Table 2**). This is not surprising. The measured uptake rates result from an interplay between ambient nitrogen concentrations, total particulate nitrogen and the structure (size and taxa) of the phytoplankton assemblage, which will affect mass-specific rates as well as affinity for nitrogen. Mass-specific values influence physiological efficiency, with small cells having faster mass-specific rates and greater affinity for nitrogen at low concentrations than large cells. These influences of assemblage structure cannot be accounted for when dividing uptake rates by measured particulate nitrogen. Much of the uptake signal is dominated by the small fractions (<15 um) of the size spectra (**Figure 6**) and highest uptake rates are observed when the small size fractions dominate and thus biomass is low, illustrating that the successful predictions of uptake rates is not driven by high biomass. Absolute uptake rates can be considered an ecosystem metric of nitrogen dynamics, and this study shows that, in a eutrophic environment, size-scaled MM parameters can be used to predict NH<sup>4</sup> and total N uptake, keeping the numbers of parameters to a minimum and thus minimizing uncertainty associated with each parameter. Data to constrain added parameters are not available from the in situ experiments. The non-allometric predictions, which use constant Vmax and K<sup>s</sup> values across the entire spectrum resulted in a variety of regression slopes, with few matching a 1:1 relationship. The kinetic parameter values used all fall within a realistic range observed in the region, and of the nine combinations tested (**Figure 7**), no significant prediction was made for NO<sup>3</sup> (although the slope was close to 1) and one successful prediction was made for NH4. However, it would be difficult to know in advance which parameter values to use, whereas the allometric calculations produced good matches to the observations.

To conclude, a large proportion of the variability observed in uptake rates of nitrogen measured in situ, in various assemblages, was explained by ambient nutrient concentrations and cell size, in spite of several simplifications and sources of error. The case for NO<sup>3</sup> uptake was not as strong as NH<sup>4</sup> and is suggested to be due to the complex suppressive behavior of NH<sup>4</sup> on NO<sup>3</sup> uptake as well potential "shift-up" effects observed in upwelling systems. In addition, accounting for the internal storage of NO<sup>3</sup> may have improved estimations of ρNO3, but are beyond the scope of these data. Nevertheless, realistic approximations of nitrogen uptake, and thus new production (Dugdale and Goering, 1967) are achieved when using size-scaled Michaelis-Menten uptake parameters and particle size distributions. The strength of this study lies in its application to in situ measurements of cell size distributions and ambient nutrient concentration, to derive approximations of nitrogen uptake. Further research is recommended to include Dissolved Organic Nitrogen uptake rates into approximations of total N uptake, given its significant contribution to total production (Harrison et al., 1985; Probyn, 1988). This is no menial task however, given its complex kinetic behavior (Eppley et al., 1971; Bronk et al., 2004; Solomon et al., 2010) and current lack of size-scaling relationships in the literature. New production, considered to be the portion of primary production with the highest implications for carbon export or the flow of energy to higher trophic levels (Hutchings, 1992; Probyn, 1992; Dugdale et al., 2006), is a useful measurement in studies of ecosystem dynamics. In the absence of laborious and expensive <sup>15</sup>N data, the use of particle size distributions to estimate nitrogen uptake can be a useful tool in assemblage scale studies of nitrogen dynamics in productive coastal upwelling systems.

### AUTHOR CONTRIBUTIONS

2004/2005 in situ data were collected and analyzed by TP (15N, nutrient analyses) and SB (particle size distributions). 2012/2013 data were collected by both TP (15N, nutrient analyses) and FA ( <sup>15</sup>N, nutrient analyses, particle size distributions). FA designed the study, performed analyses, made the figures and wrote

### REFERENCES


the manuscript. CM contributed to model implementation and validating of methods used, discussions of the results and edited the manuscript. TP also contributed to discussions of research and edited the manuscript. SB contributed to discussions of research.

### FUNDING

This work is based on research supported in part by the National Research Foundation of South Africa (Grant Number 98967). Additional funds were from the Ma-Re Institute of the University of Cape Town, 7701, Cape Town, South Africa and the Council for Scientific and Industrial Research (CSIR), Rosebank, 7700, Cape Town, South Africa.

### ACKNOWLEDGMENTS

The authors would like to thank André du Randt and Lisa Mansfield of the Department of Agriculture, Forestry and Fisheries as well Marie Smith from the University of Cape Town for help with data collection during the several sampling periods.


supplied with nitrate, ammonium, or urea as the nitrogen source. Limnol. Oceanogr. 16, 741–751. doi: 10.4319/lo.1971.16.5.0741


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Atkins, Moloney, Probyn and Bernard. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# A Model Simulation of the Adaptive Evolution through Mutation of the Coccolithophore Emiliania huxleyi Based on a Published Laboratory Study

#### Kenneth L. Denman\*

*Canadian Centre for Climate Modelling and Analysis, Bob Wright Centre, School of Earth and Ocean Sciences, University of Victoria, Victoria, BC, Canada*

We expect the structure and functioning of marine ecosystems to change over this century in response to changes in key ocean variables associated with a changing climate. Organisms with generation times from years to decades have the capacity to adapt to changing environmental conditions over a few generations by selecting from existing genotypes/phenotypes, but it is unlikely that evolution through mutation will be a major factor for organisms with generation times of years to decades. However, phytoplankton and other microbes, with generation times of days or less, experience hundreds of generations each year, allowing the possibility for favorable mutations (i.e., those that produce organisms with fitness maxima nearer to the environmental conditions at that time) to dominate existing genotypes and survive in a changing climate. Several laboratories have grown phytoplankton cultures for hundreds to thousands of generations and demonstrated that they have changed genetic makeup. In particular Schlüter et al. (2014) grew replicates derived from a single cell of *Emiliania huxleyi*, a coccolithophorid with broad geographical and thermal range, for 3 years (∼1250 generations) at 15◦C, and then for a year at 26.3◦C, near their upper thermal limit. During the last year the intrinsic growth rate increased more or less linearly, which the authors attribute to genetic mutation. Here we simulate genetic mutation of a single trait (intrinsic growth rate), both for the control phase and the warm phase of their study. We consider sensitivities to frequency of mutation, changes with temperature in intrinsic growth rate, and use the experimental setup and results to place constraints on the way mutations occur. In particular, all numerical experiments with mutation result in a lag time ∼30–140 generations before a significant increase in realized growth rate occurs. This lag after a favorable mutation results from the number of generations required for a single favorable mutant cell to reach a significant fraction of the ∼10<sup>5</sup> cells in the culture. A numerical experiment that includes a simple plastic response formulation shows that plasticity could remove this lag and yield results more in agreement with those observed in the laboratory study.

Keywords: climate change, phytoplankton, adaptive modeling, traits, genetic mutation, plasticity

### Edited by:

*Dag Lorents Aksnes, University of Bergen, Norway*

#### Reviewed by:

*Thorsten Reusch, GEOMAR Kiel, Germany Chris J. Daniels, Independent Researcher, UK*

> \*Correspondence: *Kenneth L. Denman denmank@uvic.ca*

#### Specialty section:

*This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Marine Science*

Received: *09 June 2016* Accepted: *19 December 2016* Published: *11 January 2017*

#### Citation:

*Denman KL (2017) A Model Simulation of the Adaptive Evolution through Mutation of the Coccolithophore Emiliania huxleyi Based on a Published Laboratory Study. Front. Mar. Sci. 3:286. doi: 10.3389/fmars.2016.00286*

### INTRODUCTION

The climate has been changing and is expected to continue to change—and possibly at an increasing rate (Collins et al., 2013; Rhein et al., 2013) The oceans are intimately involved in both regulating and responding to that change, and marine ecosystems are and will continue to change in response to changes associated with a changing climate (Hoegh-Guldberg et al., 2014; Pörtner et al., 2014; Wong et al., 2014). However, coupled climate-ecosystem models that predict future changes in marine ecosystems, for the most part use fixed compartment model structures for ecosystems with minimally-adaptive parameters: mainly variable C:N ratios and a temperature dependence of some intrinsic rates such as phytoplankton growth rate (e.g., Chust et al., 2014). While we use these models to predict the future structure and function of marine ecosystems, considerable skepticism remains (e.g., Planque, 2015).

Increasing temperature is the first order environmental change affecting marine species. In response, the ranges of most species are shifting poleward, nearly 2◦ latitude per decade, ∼190 km ± 20%(SE) (e.g., Sorte et al., 2010). In particular, Emiliania huxleyi blooms in polar regions became more frequent and of greater extent in SeaWiFS satellite imagery (1997-2007) compared with CZCS imagery (1978-1986) (Winter et al., 2014). The large variability in rates of poleward shift for different species means, for example, that the species assemblage (of fishes) in a fixed region is changing (Simpson et al., 2011). Other documented changes in response to warming are in phenology: for example, open ocean and coastal zooplankton reaching their biomass maximum ∼1 month earlier over 40 years, correlated with the total number of "degree-days" above 6◦C over the spring months of March-April-May (Mackas et al., 2007).

There are three other main mechanisms of adaptation to climate-related, multi-decadal change in the ocean environment. First, there is evolutionary adaptation within existing genotypic/phenotypic variability. Guppies removed from one stream to another for several years exhibit a rate of evolution in age and size at maturity many orders of magnitude higher than rates inferred from the geological record (e.g., Reznick et al., 1997). Second, there is evolutionary adaptation through mutation that changes genotypes. Evolution by mutation in phytoplankton reared in laboratory conditions over hundreds to thousands of generations has been documented in several studies (Collins and Bell, 2004; Collins et al., 2006; Collins, 2011; Lohbeck et al., 2012; Schlüter et al., 2014). The speed of evolutionary adaptation is expected to be inversely proportional to generation time: most microbes in the ocean have generation times of a day or less, so experience thousands of generations in a decade. Hence, evolutionary adaptation would be expected to be important for these organisms on decadal and longer timescales. The third adaptive response is phenotypic plasticity: "...the capacity of a single genotype to exhibit variable phenotypes in different environments" (Whitman and Agrawal, 2009). There is still much uncertainty about the mechanisms, magnitudes, limits, heretability, and tradeoffs of plasticity, and how to distinguish it from evolutionary adaptation (e.g., Collins et al., 2014; Reusch, 2014).

The objective of this paper is to develop a model at the trait level of genetic mutation by the coccolithophorid Emiliania huxleyi based on observations taken over 4 years of laboratory culture experiments (Schlüter et al., 2014). Litchman and Klausmeier (2008) and Litchman et al. (2012) described a framework for a trait-based approach to investigate the evolutionary responses of phytoplankton to global environmental change. In a series of original papers, Norberg has explored the application of complex adaptive modeling concepts to examples of evolutionary adaptation to environmental change within existing phenotypic variability (Norberg et al., 2001, 2012; Norberg, 2004). Here, as in Norberg (2004), the single trait is the maximum growth rate of phytoplankton as a function of the environmental variable temperature. As in the laboratory experiments, the model simulates the growth of E. huxleyi at 15◦C for 3 years, and then for 1 year after the temperature is increased to 26.3◦C. The simulations explore first the response of random mutations that are equally probable across the trait space (a "flat" probability distribution function—pdf), and then of infinitesimal or incremental random mutations centered on the existing mean of the genotype distribution for various widths of a Gaussian normal pdf of mutation magnitudes. Finally, the effect of a simple formulation for phenotypic plasticity of the original genotype grown at 15◦C, then warmed abruptly to 26.3◦C, will be presented.

### MODEL DESCRIPTION

### The Coccolithophore Emiliania huxleyi

The coccolithophore E. huxleyi is widely distributed over the global ocean (e.g., Hagino et al., 2011), viable over a temperature range from 4 to 28◦C (e.g., Watabe and Wilbur, 1966; Fielding, 2013), with maximum growth rates in the temperature range 18– 25◦C (Watabe and Wilbur, 1966; Zhang et al., 2014). In general, growth rates increase with temperature, with clear differences between Arctic and Atlantic strains (Daniels et al., 2014; Zhang et al., 2014). Zhang et al. developed thermal reaction norms (TRNs) for six E. huxleyi isolates originating from the central Atlantic near the Azores, Portugal (38◦ 34′N; monthly SST range 16–22◦C), and five isolates originating from coastal waters near Bergen, Norway (60◦ 18'N; monthly SST range 6–16◦C), all kept at 15◦C in culture. The fitted growth rates for the Bergen isolates were higher in the range 7–22◦C; they were higher for the Azores isolates in the range 26–28◦C, with a crossover point near 24◦C.

While isolates of E. huxleyi from various regions around the globe have a core set of common genes, there is considerable genetic variability across its global distribution (Hagino et al., 2011; Read et al., 2013). According to Read et al., "Genome variability within this species complex seems to underpin its capacity both to thrive in habitats ranging from the equator to the subarctic and to form large-scale episodic blooms under a wide variety of environmental conditions." Thus, the cultures in Schlüter et al. (2014), originating from a single cell take from waters (∼10◦C) near Bergen, Norway, would not necessarily be expected to grow at the maximum rate observed for the species at 15◦C, even though they were apparently growing in an exponential manner.

### Experimental Background

The model is formulated to simulate, as closely as possible, the experimental protocol followed during the laboratory studies (Schlüter et al., 2014). The main trait is the growth rate (d−<sup>1</sup> ), which is a function of a single environmental variable/stressor temperature. The cultures were grown at three different pCO<sup>2</sup> levels: 400, 1100, and 2200 µatm, but in this model only the experiments at the "ambient" level, 400 µatm, are simulated. The maximum growth rate as a function of temperature has long been considered to be an important predictor of the rate of primary production, along with incoming irradiance and nutrient availability (Eppley, 1972; Bissinger et al., 2008). A recent analysis of observations of growth rate as a function of temperature specifically for E. huxleyi has been published (Fielding, 2013): non-zero growth rates have been observed over the range of temperatures from 2 to 27◦C, with a very sharp decline at ∼27◦C as also observed by Schlüter et al. (2014). The most dense range of observations are for standard temperatures 10 and 15◦C, where growth rates from near zero to the maximum at that temperature have been observed (Figure 2A from Fielding, 2013). Several fits to the 99th quantile of the data (i.e., 1% of the data points exceeded the fitted function) were carried out. We adopted the power law fit, which is the best fit according to the criteria used by Fielding. **Figure 1** shows the dependence of growth rate on temperature for the power law fit (Fielding, 2013). The red line shows the power law fit that passes through the growth rate at 15◦C observed by Schlüter et al. (2014) (1.15 d−<sup>1</sup> , black diamond), and the vertical dashed red line shows its rapid drop off near 27◦C. The dashed black line shows the dependence on temperature of the maximum growth rate observed for E. huxleyi, according to Fielding (2013).

### Model Setup

In the model, genotypes are formulated in equal intervals along the trait axis, the growth rate µ(T) (d−<sup>1</sup> ), where T is the temperature. Thus, there are potential genotypes along the trait axis from µmax = 0 to µmax ≈ 2 d−<sup>1</sup> [corresponding to a temperature ∼27◦C, where the growth rate drops precipitously to zero (Fielding, 2013; Schlüter et al., 2014, Supplementary Information)].

The model is a simple exponential growth equation for each genotype i:

$$\frac{dN\_i}{dt} = \mu\_i(T)N\_i \tag{1}$$

where: N<sup>i</sup> is the number of cells in genotype i, and µ i (T) is the growth rate of genotype i. At 15◦C the maximum possible growth rate is µmax = 1.29 d−<sup>1</sup> (**Figure 1**, Fielding, 2013) and, as shown by the solid diamond in **Figure 1**, the realized growth rate was 1.15 d−<sup>1</sup> (Schlüter et al., 2014).

During the laboratory experiments, 10<sup>5</sup> cells were transferred every 5 days from the existing batch cultures into fresh culture medium to initiate the next batch culture. In the model, the total number of cells across all genotypes N<sup>T</sup> (= P <sup>i</sup>Ni) is "normalized" to 10<sup>5</sup> every timestep (0.2 d) with the same normalization factor applied to each genotype. In the standard simulations, random mutation was allowed once each day: at 15◦C the growth rate was

1.15 d−<sup>1</sup> , so that a mutation occurred slightly more often than 1 per generation. Each mutation produced a single cell (in 10<sup>5</sup> cells). Mutations were allowed at genotypes with growth rates less than and equal to 1.15 d−<sup>1</sup> . Those mutant genotypes with growth rates less than 1.15 d−<sup>1</sup> grew less quickly than the original genotype—so were not "fixed." Because of the normalization each timestep, those mutants consisted of less than 1 cell, so were set to zero (i.e., not fixed) when they dropped to 0.1 cells. When multiple non-zero genotypes exist, the mean realized growth rate across all non-zero genotypes is given as µmean = ( P <sup>i</sup>Niµi)/NT.

According to Huertas et al. (2011), "Experimental measures of mutation rates in phytoplankton range from 10−<sup>5</sup> to 10−<sup>7</sup> mutations per cell per generation." So the rate of one mutation per 1.15 generations in a culture of 10<sup>5</sup> cells is at the high end of the published rates. We carried out sensitivity studies with mutations occurring both more or less frequently than 1 per day: generally the simulations at lower rates resulted in a slowing down of the increase in biomass of favorable mutations but without any material change in the final results.

The magnitude of each mutation (distance of mutant genotype along the growth rate trait axis from its parent genotype) was determined from a random number generator. Two cases were simulated. First, with a "flat" pdf where the new genotype was equally probable anywhere from the lowest to highest allowed growth rate for that temperature, and, second with a Gaussian normal pdf, where the width of the distribution across genotypes was changed for different simulations. The original genotype and genotypes resulting from mutations were tracked separately. For a flat pdf, only mutations from the original genotype were allowed, since the origin was not important. For the Gaussian pdf, mutations were allowed from the original genotype or from the mutant genotypes (with a probability proportional to their relative biomasses). In both cases, only one mutation was allowed per day; sensitivity simulations with more or fewer mutations per day did not materially affect the results.

To illustrate the description above without explanation until the Results section, **Figure 2A** shows an initial genotype at the start of a simulation at 15◦C, and **Figure 2B** shows a histogram of the distribution (on a logarithmic axis) of total cell biomass in each genotype—after 3 years of simulation at 15◦C. The blue bars represent the relative biomass in all non-zero genotypes; "extinct" or not "fixed" genotypes were set to 10−<sup>7</sup> as explained above.

This model considers only one trait, the maximum growth rate at a given temperature. However, two other traits were considered. First, the mortality rate µmort is considered to follow

FIGURE 2 | For the first set of simulations, at 15◦C, there were 58 genotypes (#0–#57) spaced evenly in 0.02 d−<sup>1</sup> intervals along the growth rate/trait axis <sup>µ</sup> spanning the range from 0 to 1.16 d−<sup>1</sup> . (A) Shows the initial genotype with µ = 1.15 d−<sup>1</sup> (the center value of the highest genotype). (B) Shows (for one particular simulation) the relative biomass (logarithmic scale) in each genotype after 3 years of mutations, where the probability of mutation was equal ("flat") across all genotypes. After 3 years, all genotypes except #57 (and #55, which would soon become extinct) were extinct (or not "fixed") since their simulated concentrations had become less than 1 cell (horizontal dashed line) in a culture of 10<sup>5</sup> cells. When low fitness genotypes reached 1/10 of a cell, they were determined to be extinct and set to a value of 10−<sup>7</sup> .

a power law scaling increasing as a function of temperature (Brown et al., 2004; McCoy and Gillooly, 2008; and, specifically for phytoplankton, Regaudie-de-Gioux and Duarte, 2013). However, the observations do not show any sudden drop in realized growth rate when the cultures were warmed from 15 to 26.3◦C, suggesting that this scaling is inappropriate for short term changes and more appropriate for asymptotic "steady state" conditions. Second, cell size is also a function of temperature, but calculations based on the experimental results suggest that it is a minor effect. Hence, neither mortality nor cell size are considered further.

The other important environmental variable in the study of Schlüter et al. (2014) is pCO2. While only the 400 µatm case is considered here, it is likely that higher concentrations of CO<sup>2</sup> result in a reduction in the height of the "fitness window," in analogy with the "thermal window" concept for animals (Pörtner and Farrell, 2008; Denman et al., 2011).

### Simulations

For the first 3 years, five replicates of the coccolithophore Emiliania huxleyi were grown in culture at 15◦C for each of three pCO<sup>2</sup> levels: 400, 1100, and 2200 µatm. At the end of 3 years, the temperature of the cultures was raised in intervals of 1◦C d−<sup>1</sup> to a final temperature of 26.3◦C at which they were grown for an additional 1 year. Model simulations of the laboratory experiments with pCO<sup>2</sup> concentration of 400 µatm were performed as follows:


(4) Simulations at 26.3◦C, addition of a plastic response. In all simulations in study 3, for the different values of s, there was a lag of at least 60 days or generations before µmean, the mean growth rate of the five "replicate" simulations began to increase, contrary to the laboratory results where µmean increased linearly throughout year 4 without any noticeable lag or offset when the temperature was raised from 15 to 26.3◦C (Schlüter et al., 2014). To remove this lag, a simple, but plausible, formulation of a plastic response (to be described later) was implemented.

### RESULTS

## Simulations at 15◦C

Based on arguments (Orr, 1998, 2005) critical of the concept that adaptive evolution proceeds according "micromutationism" or infinitesimal mutations as first postulated by Fisher (1930), the first set of simulations (for 3 years at 15◦C) allowed for the random mutations to obey a flat pdf over the growth rate from 0 to 1.16 d−<sup>1</sup> , the approximate observed growth rate µmean at 15◦C (**Figure 1**). There were 58 equally wide genotypes over this space (numbered from 0 to 57). Initially they were all zero except for genotype #57, representing the measured mean growth rate 1.15 d −1 , shown as the solid diamond in **Figure 1**. The initial biomass of genotype #57 in each simulation is shown as the height of the pale yellow bar in **Figure 2A**.

In the simulations at 15◦C, genotype #57 outcompeted all other mutant genotypes, all of which had lower growth rates (and hence lower fitness) than genotype #57. [We take the fitness of a mutant genotype m relative to the parent genotype p to be the ratio of their realized growth rates: Wmp = µm/µp, and of the relative fitness of mutant genotype i relative to mutant genotype j to be Wij = µi/µ<sup>j</sup> (Lenski et al., 1991; Schlüter et al., 2014). If Wmp (Wij) is greater than 1, then genotype m (i) has a higher fitness than genotype p (j).] Therefore, after 3 years, in all five replicate simulations the most abundant genotype was #57 (**Figure 2B**), with its realized growth rate of 1.15 d−<sup>1</sup> . The horizontal dashed line represents 10−<sup>5</sup> of the total biomass, i.e., 1 cell. So by the end of the simulation, almost all genotypes except that with the highest realized growth rate (i.e., genotype #57) had biomass less than 1 cell and were effectively extinct. In the particular simulation shown in **Figure 2B** (one of 5 replicates) genotype #55 also had barely more than 1 cell, but it was a very recent mutation and its biomass would have quickly dropped below 1 cell, as can be seen in **Figure 3**. **Figure 3A** shows the magnitude of all the mutations over the 3 years: they are randomly distributed evenly over all genotypes between #0 and #57.

**Figure 3B** shows the time paths of the logarithm of the biomass of genotypes 20, 55, 56, and 57. Whenever there is a mutation to genotype # 20 (blue dashed line), it quickly dies out because its fitness relative to the parent genotype #57 is small, W20 57 ∼ 0.36. Genotype #55 (green) dies out more slowly, W55 57 ∼ 0.97, and genotype #56 dies out even more slowly, W56 57 ∼ 0.98. The solid red line shows the total biomass of genotype #57, consisting mostly of the original genotype (pale yellow portion in **Figure 2B**) plus mutations to that genotype (lower blue portion), which is also shown by the solid black line in **Figure 3B**. Note that

the vertical scale in **Figures 2B**, **3B** is the logarithm of biomass, so actually only 0.016% of the biomass in genotype #57 consisted of mutant cells after 3 years (all 5 replicate simulations had a similar fraction of biomass in genotype #57 ∼0.02%. These cells have growth rates equal to the original clone, but they may have other genes that differ from the original clone, as pointed out by Schlüter et al. (2014). However, the simulations in the next section started with 10<sup>5</sup> cells of what is assumed to be the original genotype #57, which were then warmed instantaneously (in the model) to a temperature of 26.3◦C.

## Simulations at 26.3◦C with a Flat Pdf for Mutations

In the simulations described here, there are 92 genotypes (numbered 0 to 91) between a growth rate of 0 d−<sup>1</sup> and the maximum growth rate µmax at 26.3◦C (solid red line in **Figure 1**), with each genotype interval being 0.02 d−<sup>1</sup> wide as before. Thus, the highest genotype #91 is centered at 1.83 d−<sup>1</sup> with its upper limit being µmax(26.3◦C) = 1.84 d−<sup>1</sup> . Similarly, µmax(15◦C) = 1.15 d−<sup>1</sup> occurs at the center of genotype #57.

Five replicate simulations at 26.3◦C with a flat pdf of the magnitudes of random mutations all quickly ended up with mutant genotypes with the highest growth rate or relative fitness eventually dominating the culture. **Figure 4** tracks the time history of the biomass of the four highest genotypes: 88, 89, 90, and 91 for one of the 5 simulations. A mutation to #89 occurred first (on day 31), followed by one to #88 (on day 59), then one to #91 (on day 72), and lastly one to #90 (on day 219), with the four jumps afterwards indicating subsequent mutations to this genotype. These are not the only mutations to these genotypes then, just the first ones during this simulation. Note that #88 grew more slowly than #89 (because the fitness of #89 was relatively higher, but #91 outpaced them both, for the same reason. They all outcompeted the original clone #57 because of their significantly higher relative fitness. This coexistence of four mutant clones is an example of clonal interference observed in asexual populations (e.g., Muller, 1932; Gerrish and Lenski, 1998; Imhof and Schlötterer, 2001).

Given enough generations, the clone with the highest fitness will dominate the culture. Reducing the mutations from once a day (slightly greater than one generation) to every other day did not affect the end result, only marginally the rate of getting there. **Figure 5** shows time series of the growth rate for the five replicate simulations, each with a new "seed" for the random mutations. The timing and nature of the increase in growth rate also depends on how soon mutations at the higher

FIGURE 4 | Time history of relative biomasses (logarithmic scale) for different genotypes for one replicate simulation after abrupt warming from 15 to 26.3◦C. There are now 92 genotypes (#0–#91) spanning the trait range from 0 to 1.84 d−<sup>1</sup> , the latter being the maximum growth rate at 26.3◦C (solid red line, Figure 1). As before a mutation was equally probable to all genotypes ("flat" pdf). The initial genotype (representative of the culture at 15◦C) was now #57 with a growth rate of 1.15 d−<sup>1</sup> . The first large magnitude mutation, to genotype #89 on day 31, rapidly replaced the original genotype #57 because of its much greater relative fitness 1.56. However, the mutant genotype #91(magenta line) eventually replaced earlier genotypes #89 (green line) and #88 (blue line) because it had the highest relative fitness of all mutants.

genotypes occur. Regardless, in each of these simulations, there is no significant increase in growth rate in the first ∼20 days, then it rapidly increases eventually to the growth rate of the highest mutant genotype. This behavior does not follow the linear increase in µmean from 1.15 d−<sup>1</sup> at the start of the year to 1.33 d −1 (with no discernable initial lag) that was observed in the laboratory (Schlüter et al., 2014). Moreover, the asymptotic mean growth rate after 1 year in these simulations is much higher than the eventual observed mean growth rate in the laboratory experiments (shown by the blue dashed line).

## Simulations at 26.3◦C with a Gaussian Normal Pdf of Random Mutations

In the simulations with a flat pdf for random mutations, the invariable domination by mutations near the maximum possible growth rate µmax suggests that in the laboratory experiments mutations with infinitesimal magnitudes might have been more likely (as suggested by Fisher, 1930), rather than mutations with "large" magnitudes being as likely as infinitesimal mutations (as argued by Orr, 1998, 2005, and others).

In these simulations, the magnitudes of mutations follow a Gaussian normal random pdf about the parent genotype. The width of the Gaussian normal pdf of mutation magnitude about the genotype undergoing a mutation is given by s (measured in genotype intervals of 0.02 d−<sup>1</sup> ). Hence, for s = 1 the distance from the center of the parent genotype interval to the outsides of the two adjacent genotypes is ±1.5s, i.e., the probability of a mutation occurring in the parent genotype or the adjoining genotypes is 86.6%. For s = 2 the distance from the center of the parent genotype interval to the outsides of the two adjacent genotypes is ±0.75s, i.e., the probability of a mutation occurring in the parent genotype or the adjoining genotypes is reduced to 54.7%.

dashed line is the fitted line to the measured mean growth rate (of five replicate

cultures) in the experiments (Schlüter et al., 2014).

Three sets of five replicate simulations were performed, with s = 1, 2, and 3. For s = 1, the growth rates after 1 year were well below those observed and these results are not discussed further. In **Figure 6A**, for s = 2, we show the distribution of biomass among genotypes after 1 year on a logarithmic scale for the replicate with the median mean growth rate. Although there appear to be about 20 genotypes in play, a linear plot of these genotypes (**Figure 6B**) shows that only about 4 or 5 genotypes account for almost all (at least 99%) of the biomass. We have therefore allowed only the 10 highest biomass mutant genotypes to undergo mutations themselves, with a probability inversely proportional to their relative biomass. Thus, from **Figure 6B**, on the next day, a mutation would be most likely be from #63, next most likely from #61, next most likely from #64 and so on, with the magnitude of each mutation determined randomly

from a Gaussian normal pdf with s = 2. **Figure 7A** shows, for the same replicate simulation as in **Figure 6**, the time evolution of the biomasses of the original clone (#57, red) as well as the five mutant genotypes with the most biomass after 1 year: 61, 63, 64, 65, and 66, again demonstrating clonal interference, especially with #63 outcompeting #61, and with the higher fitness genotypes 64, 65, and 66 increasing each at a greater rate. **Figure 7B** shows the realized growth rate for the same simulation (heavy solid line), the mutations each day (jagged light solid line), and ± the standard deviation of the distribution of the biomasses of the active genotypes (see **Figure 6A**), along the trait or genotype axes (light dashed lines)

In this set of five replicate simulations with s = 2, the mean growth rate increased from 1.15 to 1.27 d−<sup>1</sup> after 1 year. In addition, the growth rate did not begin to increase until after ∼110 days, roughly 125 generations (**Figure 8**). In the laboratory study (Schlüter et al., 2014), the realized growth rate increased, more or less linearly without discernible lag, to a value (from their fitted line) of 1.33 d−<sup>1</sup> at the end of 1 year. Thus, the increase in realized growth rate in these

FIGURE 7 | (A) Shows, for the same replicate simulation as in Figure 6, the time history of relative biomasses for the original genotype #57 and for the five most abundant mutant genotypes (61, 63, 64, 65, and 66) 1 year after abrupt warming from 15 to 26.3◦C (similar to Figure 4). (B) Shows the time history of the mutations (light solid jagged line) about the growth rate (heavy solid line). Light dashed lines show ± one standard deviation of the distribution of biomass (Figure 6) about the growth rate/trait axis. When there are more genotypes with significant biomass, the standard deviation will be larger.

simulations was too small and the initial lag of ∼110 days was unrealistic.

Another set of five simulations was performed with s = 3. **Figure 9** shows the time path of the mean growth rate for each of the five replicate simulations (light lines), the overall mean growth rate (brown solid line) and the fitted linear increase in growth rate from the experiments (blue dashed line, Schlüter et al., 2014). After 1 year, the mean growth rate was 1.47 d −1 (range 1.39–1.69 d−<sup>1</sup> ), exceeding that in the laboratory experiment. These simulations tend to exhibit lags of ∼70–130 days followed by plateaus, especially the simulation with the highest growth rate after 1 year. In that simulation, after ∼70

Gaussian normal pfd (with s = 2) for mutations about the mean growth rate Note that the realized growth rate did not increase significantly in any simulation until after ∼110 days. The blue dashed line is as in Figure 5 (note change of scale on the vertical axis).

FIGURE 9 | Time series of the realized growth rates for all five replicate simulations with s = 3 (light broken lines), the mean growth rate for the five simulations (solid brown line), and the fitted (dashed blue) line to the experimental results as in Figures 5, 8 (again note the change of scale on the vertical axis).

days the growth rate increased steeply to a plateau ∼1.33 d−<sup>1</sup> (genotype #66), then at ∼200 days it increased again to a plateau ∼1.55 d−<sup>1</sup> (genotype #77) followed by another steep rise starting at ∼320 days. **Figure 10A** shows the distribution of genotypes after 1 year for this simulation: here there were 12 genotypes with biomasses greater than 1 cell. **Figure 10B** tracks the time history of the simulation for genotypes 66, 77, 81, 82, and 85. The first large magnitude mutation from the parent genotype #57 to genotype #66 (on day 15) is rare (3s) but possible for a Gaussian normal pdf with s = 3; the second from #66 to #77 (on day 149) is also rare but possible. **Figure 10B** again shows clonal interference, as mutants with higher relative fitness eventually out-compete less fit mutants (cf. Figures 8, 9 in Gerrish and Lenski, 1998).

To summarize the results of this set of simulations, the overall mean growth rate increased roughly linearly after about 70 days, but again among the replicate simulations there was a lag of

FIGURE 10 | Results for one of five replicate simulations with s = 3, the one with the highest growth rate (1.69 d−<sup>1</sup> ) at the end of 1 year. All other parameters are the same as in Figures 6–8. (A) Shows the relative biomass of mutations in all genotypes after 1 year. (B) Shows the time history of the original genotype #57 (solid red line) and five other genotypes (66, 77, 81, 82, and 85). Mutations with large magnitude to #66 and later to #77 each became dominant, resulting in plateaus lasting ∼60 days (see Figure 9).

∼70–130 days before the growth rate(s) start to increase, contrary to the experimental data (Schlüter et al., 2014).

### DISCUSSION

## Three-Year Simulations at 15◦C

Initially, the model was set up with 58 genotypes (each 0.02 d <sup>−</sup><sup>1</sup> wide) spanning the range of possible growth rates at 15◦C from 0 to ∼1.16 d−<sup>1</sup> (Figure 2 and Fielding, 2013). Mutations were equally probable (a "flat" pdf) to all 58 genotypes (#0 to #57) under the assumption that the original genotype #57 was the genotype with the highest possible growth rate and hence the maximum relative fitness. So only mutations to that same genotype survived or were "fixed," while mutations to other genotypes (#0 to #56), all with lower relative fitness, became extinct (or failed to be "fixed"), as shown in **Figures 2**, **3**. At the end of the 3 years, in all five replicate simulations, mutations to genotype #57 contributed ∼0.02% to the total biomass shown in that genotype. Although these cells had the same growth rate as the original clones, they presumably possessed other genes that apparently did not affect their growth rate at 15◦C.

### Time Lag in Growth Rate Response to Mutations

Simulations at 26.3◦C had 92 possible genotypes, each of width 0.02 d−<sup>1</sup> , spanning the growth rates between 0 and 1.84 d−<sup>1</sup> , the maximum possible growth rate for this clone (the value of the red line in **Figure 1** at 26.3◦C). The initial genotype was still #57, assumed to be the single genotype existing after 3 years of growing at 15◦C, ignoring the ∼0.02% of the cells that were mutants in the simulations but with the same growth rate at 15◦C. All simulations exhibited a time lag after the temperature shift from 15◦C before there was any significant increase in the realized growth rate, which was not observed in the laboratory experiments of Schlüter et al. (2014).

For a flat pdf of random mutations, the genotype created from the largest magnitude favorable mutation eventually dominated and replaced the original genotype. Usually, after 1 year the dominant genotype is #90 or #91 (**Figures 4**, **5**). **Figure 5** shows that there is typically a lag of ∼15–30 days (∼17–34 generations) before the realized growth rate starts to increase significantly. Then very quickly (over ∼20 days) the growth rate climbs rapidly to that for the highest mutant genotype, where it remains for the rest of the year unless there is a subsequent mutation to a higher genotype. This behavior, two plateaus separated by an abrupt increase from the first to the second, is completely inconsistent with, and with a much larger final growth rate than, the final fitted growth rate from the laboratory experiments.

For the flat pdf, each mutation has a 62% chance of having a relative fitness less than that of the original clone (57 of 92 possible genotypes). If the rate of mutations were to decrease by a factor of 10, then the lag time would be 10 times longer, but the time for a given favorable mutation to increase would be the same because it is a function of the generation time or growth rate.

It was concluded from these simulations that an initial lag followed by an abrupt increase in growth rate results from allowing mutations of the largest magnitude to have the same probability as mutations of the smallest magnitude. If small magnitude mutations were to have a much higher probability than large magnitude mutations, then possibly the transition to higher grow rates after increasing the temperature to 26.3◦C would be more gradual and continuous. To allow for mutations of very small magnitude, in subsequent simulations the magnitude of each mutation along the trait axis was chosen randomly from a Gaussian normal pdf, N(µmax, s) in statistical notation, centered on the growth rate of the parent genotype, with a width along the trait axis scaled by the standard deviation s (in genotype intervals).

The first set of five simulations shown here, with s = 2 genotypes wide, generated a much too small increase in mean growth rate µmean, reaching only 1.27 d−<sup>1</sup> compared with the fitted value of 1.33 d−<sup>1</sup> from the laboratory experiments. Again, the simulations show a long lag of ∼110 days before any significant increase occurred (**Figure 8**). A second set of five simulations with s = 3 was then performed (**Figure 9**). A larger number of genotypes were generated from mutations, with many of them still viable (1 cell or more) at the end of 1 year (**Figure 10**). The mean growth rate of the five replicate simulations increased more or less linearly for the latter two thirds of the year, with a slope roughly double that observed. But there still remained a lag of ∼70 days before the mean growth rate started to increase. Overall, for a larger s, i.e., larger magnitude mutations, the lag time was shorter. For s = 1, 2, and 3, the lag time was respectively ∼150, ∼120, and ∼70 days. Clearly, adaptive evolution by genetic mutations, modeled in the manner described here, cannot alone explain the laboratory results (Schlüter et al., 2014) because all simulations were characterized by initial lags upon warming to 26.3◦C.

### A "Plastic" Response to Abrupt Temperature Change?

A possible explanation for the immediate continuous increase in observed growth rate after increasing the temperature from 15 to 26.3◦C is that it was a "plastic" response of the cells to their changing environment. The idea of plasticity "buying time" for genetic adaptation to take place is central to the concept of "plastic rescue" avoiding extinction (e.g., Lande, 2009; Chevin et al., 2010; Kopp and Matuszewski, 2014). There are many definitions of plasticity: Whitman and Agrawal (2009) list 11, but perhaps their simplest is "Phenotypic plasticity" is "the capacity of a single genotype to exhibit variable phenotypes in different environments ...." According to Reusch (2014), reviewing evidence of plasticity in marine animals and plants: "Phenotypic plasticity broadly defines the adjustment of phenotypic values of genotypes depending on the environment, without genetic changes."

Most studies of plasticity compare different phenotypes of the same genotype in different environments. More relevant in our case would be studies that consider the temporal change in phenotypic properties of a given genotype in response to a change (continuous or abrupt) in its environment, but such studies are rare. And different species generally have different plastic responses to the same change in environment (different "reaction norms," (e.g., Pigliucci, 2005; Whitman and Agrawal, 2009; Reusch, 2014). There is no clear information on how plasticity might be modeled in this case, especially what ultimately limits the rate and magnitude of plastic response. Currently, both the energetic costs and limits of plasticity are research questions of considerable interest (e.g., DeWitt et al., 1998; Pigliucci, 2005).

Given that the generation time of E. huxleyi in the laboratory experiments was less than 1 day, a plastic response would have to be "transgenerational" or heritable, for which there is mounting evidence in animals (Munday, 2014; Walsh et al., 2014), in clonal plants (e.g., Latzel and Klimešová, 2010), and in phytoplankton (Schaum et al., 2013; Schaum and Collins, 2014). For asexual reproduction the hypothesized mechanism is "epigenetic inheritance" whereby an environmental change causes genes to be expressed, which continue to be expressed in succeeding generations if the environmental change continues (Latzel and Klimešová, 2010; Schaum et al., 2013; Schaum and Collins, 2014; van Oppen et al., 2015). In the laboratory experiments of Schlüter et al. (2014), it is assumed that the change in temperature from 15 to 26.3◦C caused the expression of an existing gene in essentially all cells in the culture in the first and succeeding generations which mediated a slow increase in growth rate, without the lag that would result from the favorable mutation of a single cell dividing sufficiently often to start to compete with the original population.

Here we assume that the plasticity is heritable, and model it as a first order restoring function without lag:

$$\frac{d\mu\_i(t)}{dt} = (\mu\_{\text{max}}(i) - \mu\_i(t))/T \tag{2}$$

where µi(t) is the realized growth rate and µmax(i) is the maximum growth rate, both for the initial genotype i, according to the power law fit (Fielding, 2013) through the original growth rate at 15◦C (solid red line in **Figure 1**). T (or τ ) is the "e-folding" time for the response. The assumed mechanism is that because of energy costs the plastic response of a given genotype i cannot exceed its µmax(i) value for 15◦C, even though it is now at a higher temperature. The rate at which µi(t) approaches µmax(i) decreases as it gets closer, the logic being that the larger the plastic response, the more energy that is required.

The solution to the ordinary differential Equation (2) is standard:

$$
\mu\_i(t) = (\mu\_i(0) - \mu\_{\text{max}}(i))e^{-t/T} + \mu\_{\text{max}}(i) \tag{3}
$$

This function has the form shown **Figure 11**, where the dashed curve shows the full function to its asymptote. The solid curve has a T value set to 281 d, so that the initial slope of Equation (3) at small t is equal to the slope of the linear fit to the observations over 1 year (Figure 1A in Schlüter et al., 2014). For the initial genotype, µmax = 1.29 d−<sup>1</sup> , so that the observed (fitted) growth rate after 1 year of 1.33 d−<sup>1</sup> could not be reached by means of plasticity alone. In fact for the value chosen for T, the plastic response at the end of 1 year would result in a mean growth rate of only 1.25 d−<sup>1</sup> (solid curve, **Figure 11**).

the simulations) is set to match the slope of the line fitted to the 1 year of measured growth rates from the laboratory experiments in Schlüter et al. (2014).

Three sets of five replicate simulations were then performed at 26.3◦C with s = 2, 2.5, and 3, but with a plastic response of the original genotype. Now the growth rate of the initial genotype (initially µi(0) = 1.15 d−<sup>1</sup> ) increased with time according to Equation (3). As its growth rate increased, the biomass of the original genotype was added to any in the appropriate growth rate interval that had accumulated from mutations. Due to the plastic response, the original genotype had moved from #57 to #62 on the growth rate axis after 1 year. **Figure 12A** shows the results of 1 replicate simulation with s = 2.5; in all five replicate simulations with s = 2.5, the original genotype represented most of the biomass in that interval. **Figure 12B** shows the time evolution of the five other genotypes with the most biomass after 1 year: clonal interference between genotypes 63, 64, and 66. Genotype #66, because it had the highest relative fitness, outcompeted genotypes 63, and 64, even though they had mutated earlier. **Figure 13A** shows the time history of the growth rates for all five replicate simulations, the ensemble mean growth rate (solid brown line), and the (dashed blue) line fitted to the laboratory results. The plastic response eliminated the initial lag in the increase of the growth rate, consistent with the observations. The ensemble growth rate after 1 year was 1.34 d−<sup>1</sup> (slightly greater than that of the observations, 1.33 d−<sup>1</sup> ). In **Figure 13B**, simulated random measurement error has been added to the simulated overall mean growth rate, for comparison with the observations (Figure 1A in Schlüter et al., 2014). Thus, the plastic response, as formulated, removed the lag in response present in all previous simulations, giving time for mutations to new genotypes eventually to dominate the culture toward the end of the year. In addition to the maximum growth rate, the only other trait reported on by Schlüter et al. (2014) was cell diameter. The

FIGURE 12 | Results for one simulation (with s = 2.5) that includes the plastic response (Figure 11). In (A), the vertical dotted line shows the growth rate of the original genotype and the position on the x-axis of the light yellow bar shows where the growth rate of the initial genotype (#57) has reached (genotype #62) with the growth rates shown on the upper x-axis. (B) Shows the time series of the relative biomass of the different genotypes: the original genotype (#57, solid red line), and the five most abundant genotypes at the end of 1 year (63, 64, 66, 67, and 70). Genotype #66 has become the dominant genotype (highest peak in A) due to its higher fitness relative to #57, although eventually the mutant genotype #70 would replace #66.

cell diameter was significantly smaller (∼10%) at 26.3◦C, but only for the cultures grown at the "ambient" level of pCO2: 400 µatm.

### Effects of Multiple Stressors

Schlüter et al. (2014) maintained cultures of Emiliania huxleyi, all originating from the same single cell, at three different pCO<sup>2</sup> levels for 4 years, increasing the temperature from 15 to 26.3◦C at the end of the third year. Although the growth rate at 15◦C decreased with increasing pCO2, the growth rate increase over the last year (at 26.3◦C) was greater at successive higher pCO<sup>2</sup> levels, such that the growth rates at the end of the experiment were closer together than during the first 3 years, suggesting that at the higher temperature, the cells were affected less by CO<sup>2</sup> concentration. Without some information about energy costs of adaptation, it is not clear how to model either the effects

line fitted to the experimental results (Schlüter et al., 2014). (B) shows (blue) points along the mean (brown) curve with simulated random "measurement errors," and the fit to the experimental results (solid blue line), for comparison with Figure 1A in Schlüter et al. (2014).

of mutation (or of plasticity) in response to two simultaneous stressors.

### CONCLUSIONS

Modeling even the adaptive response to abrupt change in a single environmental variable in an asexual phytoplankton population of a single trait led to unexpected results. If this model is a valid representation of the experimental results of Schlüter et al. (2014), then several conclusions pertain:

(1) The largely linear increase over 1 year in measured growth rate without an initial lag after an abrupt increase in temperature cannot be explained on the basis of genetic mutation alone. The caveat (mentioned by Schlüter et al., 2014) is that there were cells in the culture at 15◦C after 3 years, which were mutants with the same growth rate 1.15 d <sup>−</sup><sup>1</sup> but with some different genes that would possibly allow them to respond differently to the increase in temperature to 26.3◦C. In the model simulations at 15◦C, after 3 years these cells comprised only ∼0.02% of the culture, suggesting that some lag would still occur after the switch to a warmer temperature.


### AUTHOR CONTRIBUTIONS

All research and manuscript writing and preparation were carried out by the author.

### REFERENCES


### FUNDING

The author received no research funds for this work. The Canadian Centre for Climate Modelling and Analysis of Environment and Climate Change Canada and the University of Victoria provided office space and network support.

### ACKNOWLEDGMENTS

The author benefitted from discussions with other participants at the 2014 and 2016 Gordon Research Conferences on Ocean Global Change Biology, and from discussions with J. R. Christian. Y. Zhang, U. Riebesell, and T. Reusch provided their growth rate vs. temperature data and fitted thermal response functions from Zhang et al. (2014). The author wishes to thank the two reviewers for their constructive and helpful comments, which improved the manuscript immeasurably.


Plattner, M. Tignor, S. K. Allen, J. Boschung, et al. (Cambridge; New York, NY: Cambridge University Press), 255–316.


**Conflict of Interest Statement:** The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Denman. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Quantifying Tradeoffs for Marine Viruses

#### Nicholas R. Record<sup>1</sup> \*, David Talmy <sup>2</sup> and Selina Våge<sup>3</sup>

<sup>1</sup> Bigelow Laboratory for Ocean Sciences, East Boothbay, ME, USA, <sup>2</sup> Department of Earth, Atmosphere and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA, <sup>3</sup> Department of Biology, Hjort Centre for Marine Ecosystem Dynamics, University of Bergen, Bergen, Norway

The effects of viruses on marine microbial communities are myriad. The high biodiversity of viruses and their complex interactions with diverse hosts makes it a challenge to link modeling work with experimental work. In various trophic groups, trait-based approaches have helped to simplify this complexity, as traits describe organism properties in terms of taxon-transcending units, allowing for easier identification of generic, underlying principles. By predicting large-scale biogeography of different plankton functional types based on key sets of traits and their associated tradeoffs, these approaches have made major contributions to our understanding of global biogeochemistry and ecology. This review addresses the question of how a trait-based approach can make contributions toward understanding marine virus ecology. We review and synthesize current knowledge on virus traits with a focus on quantifying the associated tradeoffs. We use three case studies—virulence, host range, and cost of resistance—to illustrate how quantification of tradeoffs can help to explain observed patterns, generate hypotheses, and improve our theoretical understanding of virus ecology. Using a nutrient-susceptible-infected-virus model as a framework, we discuss tradeoffs as a link between model building (theory) and experimental design (practice). Finally, we address how insights from virus ecology can contribute back to the trait-based ecology community.

Keywords: marine virus, host, tradeoff, trait, model

### 1. INTRODUCTION

"We live in a dancing matrix of viruses"

– Thomas and Parker (1974).

Linking modeling and experimental work is an ongoing challenge in ecology. For marine viruses, ecologists are beginning to model the role of viruses in shaping biogeography, biogeochemistry, macroecology, and climate in the oceans. As bearers of life and death, viruses influence growth and mortality rates within microbial communities, mediating biogeochemical processes, and driving adaptation and evolution (Fuhrman, 1999; Brussaard, 2004; Suttle, 2007; Weitz and Wilhelm, 2012). Lytic viruses may account for up to 50% of bacterial mortality in the pelagic ecosystem (Suttle, 1994; Fuhrman and Noble, 1995; Fuhrman, 1999), and they can abruptly terminate eukaryotic algae blooms (Bratbak et al., 1993; Nagasaki et al., 1994). Lysogenic viruses, embedded in the host genome, may on the other hand have effects on hosts ranging from parasitic to mutualistic (Weinbauer, 2004). Viruses contribute to both top-down and bottom-up control of the microbial community (Weitz et al., 2016). They are thus key components of ocean ecosystem models.

#### Edited by:

Susanne Menden-Deuer, University of Rhode Island, USA

#### Reviewed by:

Kristina Dee Anne Mojica, Oregon State Univeristy, USA Urania Christaki, Ministry of Research and Higher Education, France

> \*Correspondence: Nicholas R. Record nrecord@bigelow.org

#### Specialty section:

This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Marine Science

Received: 31 July 2016 Accepted: 18 November 2016 Published: 15 December 2016

#### Citation:

Record NR, Talmy D and Våge S (2016) Quantifying Tradeoffs for Marine Viruses. Front. Mar. Sci. 3:251. doi: 10.3389/fmars.2016.00251

Virus-mediated mortality has multiple, often contrasting, and globally significant biogeochemical effects. For example, there are competing hypotheses on whether viral lysis increases or decreases carbon export from the euphotic zone. If dissolved matter from lysis is typically remineralized, this would lead to increased regenerate production in the euphotic zone (Fuhrman, 1999; Wilhelm and Suttle, 1999; Weinbauer, 2004) and reduce export by shortcutting transfer to higher trophic levels and sinking fecal pellets (De La Rocha and Passow, 2007). On the other hand, transparent exopolymeric particles released during lysis may actually enhance particle aggregation and sinking (Proctor and Fuhrman, 1991). Furthermore, by stimulating regenerate production, viruses may sustain higher microbial biomass (Weinbauer, 2004), which may affect export. Virus infection can also alter cell stoichiometry and uptake rates, thereby altering biogeochemical pathways (Weitz and Wilhelm, 2012; Jover et al., 2014).

Viruses are also important drivers of microbial diversity (Thingstad, 2000; Weinbauer, 2004; Thingstad et al., 2015). A consequence of the strong top-down control by viruses on the microbial community is selection for host cell structures and functions rendering resistance. Such structural adaptations may be physiologically costly, which allows coexistence of both susceptible and resistant hosts. Typically, structural changes are such that virus-host interactions become highly specific (Lima-Mendez et al., 2015). The result is that viruses can regulate strain diversity within species (Thingstad et al., 2014), or species diversity within microbial communities, depending on the specificity of the virus-host interactions. In a dynamic world, co-evolutionary arms races—where hosts try to escape virus infections and viruses evolve to infect resistant hosts—provide an important mechanism to build and maintain microbial diversity (Martiny et al., 2014).

The increasing recognition of the importance of viruses has motivated work to incorporate them into ecosystem models particularly those representing biogeochemical processes (Weitz et al., 2015; Middleton et al., in press). Virus ecology is complex, however, and representing the diversity of processes and interactions described above remains a challenge for modelers. Most ecosystem models approach ecological problems either at the species level or at the level of trophic groups. This strategy is reasonable, given the fundamental importance of species as a taxonomic unit and of trophic interactions. However, this approach has limitations when it comes to certain objectives. Challenges include: (1) connecting community structure with ecological function, (2) drawing causal links between organism properties and macroecological patterns, and (3) making diversity tractable in ecosystem models. Each of these challenges is key both to understanding basic ecology as well as to predicting the ocean's response to changing climate and other pressures.

An alternative to species-centric models is the trait-based approach to ecology, which has seen a recent resurgence in marine ecology (Barton et al., 2016). The trait-based approach to ecology has some early roots in marine systems (Sheldon et al., 1972), but much of the foundational work comes from terrestrial ecosystems, where global trait databases have facilitated breakthroughs (Wright et al., 2005; Violle et al., 2007; Kattge et al., 2011). The approach has gained traction in marine ecosystems over the past 10 years, primarily for phytoplankton (Follows et al., 2007; Litchman et al., 2007; Litchman and Klausmeier, 2008; Edwards et al., 2012; Barton et al., 2013), but also for zooplankton (Kiørboe et al., 2010; Litchman et al., 2013; Record et al., 2013b) and fish (Claudet et al., 2010; Marras et al., 2013; Opdal and Jørgensen, 2015; Pimentel et al., 2016). While ecologists have not agreed upon a single rigorous definition of "trait," the objective is to define characteristics of organisms that link processes at the individual level to population-, community-, or ecosystem-level processes. Traits are typically taxon-transcending properties that describe growth, ontogeny, reproduction, and defense, and ultimately determine fitness (Litchman et al., 2013). When successful, the traitbased approach can explain mechanistically the organization and function of an ecosystem (Hansen et al., 1994; Follows et al., 2007; Rose et al., 2007; Banas, 2011; Record et al., 2012, 2013a; Zhang et al., 2013; Andersen and Beyer, 2015). The notion of a trait often goes hand-in-hand with modeling, as traits can be represented as parameters in systems of dynamical equations. As such, they provide a useful link between models, which require values for these parameters, and experiments, which measure them.

Many of the parameters found in virus models have been reviewed and described in the context of traits (Weitz et al., 2016, Ch. 2). To link traits with the underlying ecology, we also require an understanding of tradeoffs associated with sets of traits. Tradeoffs occur when an increase in fitness associated with one trait comes at a fitness cost associated with another trait. Identification of tradeoffs has recently been proposed as a key step toward linking the work of modelers and empiricists (Barton et al., 2016). The concept of tradeoffs is commonly invoked in the virus literature (Bohannan et al., 2002; De Paepe and Taddei, 2006; Jessup and Bohannan, 2008; Pradeep Ram and Sime-Ngando, 2010; Keen, 2014), and with the recent reemergence of the trait-based approach in marine ecology, it is timely to review our understanding of marine virus tradeoffs in order to help incorporate it into the broader trait-based dialogue. Here we provide a review of marine virus traits and attempt to characterize and quantify the tradeoffs associated with some of the most important traits. We include viruses that infect pelagic bacteria, archaea, and eukaryotes, though there is considerably more literature on bacteriophages. We use three case studies and simple illustrative model simulations to demonstrate how quantification of tradeoffs can help to explain observed patterns, generate hypotheses, and link modeling work and empirical work.

### 2. A FRAMEWORK FOR TRAIT-BASED VIRUS MODELS

The first step in a trait-based approach to the ecology of a group of organisms is to build a framework that includes the traits involved in important tradeoffs (Litchman et al., 2013). Here we use a dynamical systems model as the core of our framework. A recent review of marine virus-host models (Middleton et al., in press) found a wide variety in model equations and state variables used to describe marine virus-host interactions. While there was some commonality among models, nearly one third did not include a state variable tracking virion abundance (e.g., Beltrami and Carroll, 1994; Chattopadhyay and Pal, 2002; Singh et al., 2004; Rhodes and Martin, 2010). This follows the convention in biogeochemical models of using a linear mortality term to capture all background mortality including viral lysis. Other notable state variables in marine virus-host models included a separate infected host population (Bratbak et al., 1998), a virus population within host cells (Siekmann and Malchow, 2008), a virus inhibitor (Thyrhaug et al., 2003), and a resistant population (Middelboe, 2000). Model design is often dictated by available data or by hypotheses, or, for marine virushost models, based on other standard forms such as susceptibleinfected-removed (SIR) models of epidemics (Kermack and McKendrick, 1927).

Following Litchman et al. (2013), we have classified virus traits based on ecological function and trait type (**Table 1**). This exercise itself illustrates some of the challenges around building a general trait-based framework for marine pelagic ecology. Some of the trait categories in the Litchman classification needed to be changed to apply to viruses. Additionally, not all of these traits convert easily into model parameters. Some traits that have been studied and reviewed (Weitz et al., 2016) translate directly to model parameters (e.g., burst size). Those that do not (e.g., size) generally have one or more underlying relationships that translate indirectly into model parameters. We constructed a set of equations based on the common components in marine virushost models (Middleton et al., in press) designed to incorporate the quantitative traits outlined in **Table 1**. The full model includes all traits discussed in this review so that the associated tradeoffs can be explored mathematically. The model can be reduced based on simplifying assumptions into various forms that are used in other modeling studies (detailed in Supplementary Material). A chemostat is simulated, where hosts are partitioned into those that are susceptible and those that are infected. Encounter between free living viruses and susceptible hosts creates infected hosts. The full model is a Nutrient-Susceptible-Infected-Virus (NSIV) model, representing virus infection of a generic host population. The equations are written:

$$\frac{dN}{dt} = \delta(N\_{in} - N) - \mu(N)(S + \gamma I) \tag{1}$$

$$\frac{dS}{dt} = \frac{1}{c}\mu (N)S - \phi SV - \alpha S \tag{2}$$

$$\frac{dI}{dt} = \chi \frac{1}{c} \mu (\text{N}) I + \phi S V - (1 - \chi) \lambda I - aI \tag{3}$$

$$\frac{dV}{dt} = \beta(1 - \nu)\lambda I - \phi SV - \psi V \tag{4}$$

where N is the nutrient concentration supplied at an input concentration Nin and dilution rate δ, S is the population of susceptible hosts, I is the population of infected hosts, and V is the population of viruses (**Table 2**). The parameter φ represents an interaction kernel between viruses and hosts, µ is a growth function for hosts, and cis the host nutrient quota. Host and virus losses, ω and ψ respectively, include losses due to dilution, as well as other forms of mortality or decay. The parameter γ determines the virulence strategy, representing the lysogenic proportion of the virus. Hosts are lysed at rate λ, and each lysis event results in β free living virions. Each parameter represents a trait explicitly or can be expressed as a function of a trait. In some contexts, a parameter can combine multiple traits, such as the interaction kernel, which includes processes like encounter (dependent upon size) as well as structure or entry mechanism. In such cases, as we understand more about these traits, we can replace the parameter with a more refined function that captures multiple traits. We will use this model, or its reduced versions (detailed in Supplementary Material), to illustrate the tradeoffs associated with the reviewed traits.

### 3. IDENTIFYING AND QUANTIFYING TRADEOFFS

Each of the traits listed in **Table 1** is hypothetically involved in one or more tradeoffs. Here we focus on four traits and their associated tradeoffs: size, virulence, host range, and resistance. For the latter three cases, we use the NSIV model framework (Equations 1–4) to evaluate the tradeoff associated with the trait and compare predictions to observations. The fourth case resistance—illustrates the interaction between virus traits and host traits.

### 3.1. Size

Ocean ecosystems are strongly size-structured. Organism size is a first-order determinant of many aspects of ecosystem structure and function, including production and metabolism (López-Urrutia et al., 2006), reproduction (Sheldon et al., 1972), predator-prey interactions (Banas, 2011; Golet et al., 2015), and species richness (Record et al., 2012) to name a few. As a trait, it is often viewed as a primary axis for describing marine ecosystems (Barton et al., 2013; Litchman et al., 2013), with a strong body of theory explaining how size structures marine ecosystems from bacteria to whales (Andersen et al., 2016). It is unknown whether these allometric relationships extend to the viruses.

### 3.1.1. Survival

Important sources of virus loss include ultraviolet light (Murray and Jackson, 1993; Wilhelm et al., 2003), grazing (Deng et al., 2014), adsorption, and genome size and density (De Paepe and Taddei, 2006). These processes have strong allometric dependencies in general, but it is an open question whether virus loss in the marine environment is strongly sizedependent.

### 3.1.2. Encounter and Infection

As non-motile entities, extracellular virus particles depend on Brownian motion for random encounter with hosts. As such, diffusive transport is likely to be a primary determinant of host-virus encounter. Larger virus particles diffuse more slowly, and are thus expected to be at a disadvantage in terms of contact rates (Murray and Jackson, 1992). Simple physical arguments may also be used to understand which hosts are more



Where the category names have been changed, the original Litchman category name is given in parentheses. Bold text indicates quantitative trait; plain text indicates categorical trait. Parameter in parentheses corresponds to how the trait is represented in Equations (1–4) or (11, 12).

#### TABLE 2 | Parameter and variable descriptions and units.


susceptible to encounter with virus particles. Probability of virus attachment is greater for larger organisms with higher surface area. Furthermore, larger organisms generally swim faster, clearing a larger volume of water and enhancing the probability of virus encounter (Murray and Jackson, 1992). Simple physical controls on encounter do not necessarily manifest in clear relations between virus particle size and the size of the host it is able to infect. For example, coccolithoviruses with capsids ∼170– 200 nm in diameter infect haptophyte Emiliania huxleyi (5–8µm diameter) (Schroeder et al., 2002), while the significantly smaller Rhizosolenia setigera-virus (∼30 nm diameter) infects the much larger diatom R. setigera (2–50µm diameter and 0.1–1 mm length) (Nagasaki et al., 2004). Furthermore, the sizes of virus and host genomes appear to be unrelated (Brown et al., 2006). While these examples do not point toward a simple, canonical virus:host size ratio, to the best of our knowledge, no one has systematically addressed this question in a broad range of marine virus-host systems.

#### 3.1.3. Virus Production

Over sufficiently large ranges, growth rate tends to decline with organism size in eukaryotes, while the opposite is true for prokaryotes (Kempes et al., 2012). Very little is known about the relation between virus particle size and production rate. Since viruses utilize host metabolic machinery for replication, virus production rate generally follows growth rates of the host and varies depending on host growth conditions and physiology (Van Etten et al., 1983; Moebus, 1996; Bratbak et al., 1998; Middelboe, 2000; Baudoux and Brussaard, 2008). On the other hand, replication rate may depend more directly on virus particle size. Virus replication rate is also likely to depend on morphological variation across diverse phylogenies. A proxy often used to infer virus accumulation rate is burst size. There is evidence that burst size is related to the ratio between host and virus genome lengths (Weitz et al., 2015), and that number of base pairs is related to capsid size (Jover et al., 2014), suggesting that a smaller virus can make more copies of itself than a large virus, all other factors being equal. However, burst size is not a direct reflection of the metabolic efficiency of virus replication. It says nothing about the time required for replication, which in part may be reflected in the duration of latent period. Few direct measurements of virus replication rates are available, making it difficult to know the allometric scaling of virus production.

### 3.2. Virulence: Tradeoffs with Lysogeny and Lysis

Pathogenic virulence influences microbial fitness in complex and interesting ways. Lysogenic viruses can enhance host fitness by increasing the growth of infected hosts (Edlin et al., 1975), and providing protection against closely related viruses (Ptashne, 1967). Lysogeny is associated with horizontal gene transfer (Chiura, 1997; Lawrence and Ochman, 1998; Ochman et al., 2000), and bacterial genomes contain a high portion of dormant or repurposed phage genes (Casjens et al., 2000; Ochman et al., 2000; Hayashi et al., 2001; Daubin et al., 2003). Due to its importance for public health and epidemiology, there is a sizeable literature on factors controlling the switch from lysogeny to lysis (Brüssow et al., 2004; Ptashne, 2004), as well as some marine examples (Paul and Jiang, 2001; Brum et al., 2016). The switch may be related to molecular interactions between host and virus (Ptashne, 2004; Zeng et al., 2010), or environmental cues that relate, for example, to host production (Koudelka et al., 1988; Wilson and Mann, 1997; Williamson et al., 2002; Weinbauer et al., 2003). Relatively few studies (Levin and Lenski, 1983; Stewart and Levin, 1984; Koudelka et al., 1988; Williamson et al., 2002; Weinbauer et al., 2003) have explored the ecological factors that may ultimately govern when and where lysogenic vs. lytic replication modes are selected. Here, we briefly review observed relationships between environmental variables and prevalence of lysogeny. We then use Equations (1–4) to explore a tradeoff that may govern observed trends.

#### 3.2.1. Temperature

Wilson and Mann (1997) concluded that the only studies relating temperature to the switch between lysogeny and lysis were with enteric hosts (Edgar and Lielausis, 1964; Gough, 1968), and that evidence in marine systems was limited. Since then, correlations between temperature and lysogeny have been found in a range of environments (Cochran and Paul, 1998; Williamson et al., 2002; Maurice et al., 2010; Payet and Suttle, 2013). The general pattern shows low temperatures favoring lysogenic phages, and high temperatures favoring lytic phages. Temperature has been used to provoke prophage induction in natural seawater samples (Jiang and Paul, 1996), but laboratory experiments testing the dependence of the switch on temperature have been equivocal (Williamson and Paul, 2006). Early in their experiments, Williamson and Paul (2006) observed elevated temperature leading to higher production rates and reduced lysogeny. Later in the experiments however, high temperature cultures reduced overall production of free phage by both lytic and lysogenic infections.

### 3.2.2. Light

Tests of the influence of light intensity on the switch between lysogeny and lysis can be divided into those that tested effects of UV radiation, and those that tested whether direct sunlight could induce lysis. In general, the results evidence that induction response to light varies among host species (possibly even at the strain level) and specific lysogens. For example, Vibrio lysogens could be induced by sunlight (Faruque et al., 2000) and Synechococcus phages could be induced by continuous, high light (McDaniel et al., 2006). In contrast, other studies failed to induce natural assemblages with sunlight (Wilcox and Fuhrman, 1994; Jiang and Paul, 1996) while UV radiation has been proven effective to revert lysogenic to lytic infections within natural assemblages (Jiang and Paul, 1996; Weinbauer and Suttle, 1996).

### 3.2.3. Nutrients

Field and laboratory observations suggest nutrient status is likely to influence the prevalence of lysogeny. There is ample evidence, from a range of studies in different oceanic regions, that the proportion of hosts in natural assemblages carrying inducible prophages varies as a function of trophic status. The abundance of hosts with lysogenic infections is often lower in more productive than in less productive waters and also lower in highly productive summer months than in low productive winter months (Jiang and Paul, 1994; McDaniel et al., 2002; Weinbauer et al., 2003; Lymer and Lindström, 2010; Payet and Suttle, 2013). Additionally, it has been empirically shown that nutrient enrichment of natural samples may induce lysogens in some bacterial assemblages (Wilson et al., 1998; Williamson et al., 2002), but not in others, e.g., Synechococcus populations (McDaniel and Paul, 2005), while nutrient starvation can lead to the establishment of lysogeny in the heterotrophic bacteria Pseudomonas aeruginosa (Kokjohn et al., 1991). Similarly, phosphate depletion in cultures of the photoautotrophic bacteria Synechococcus sp. (Wilson et al., 1996) has been shown to decrease burst size and lysis rate of infected host populations, suggesting cyanophages entered a lysogenic state in response to nutrient starvation.

### 3.2.4. The Virulence Tradeoff

There must be a tradeoff associated with the switch between lysis and lysogeny, otherwise one would always be favored over the other. In low productive systems, encounter between hosts and extracellular virus particles may be low, and insufficient to overcome losses, rendering lysogeny the favorable strategy for production. In relatively productive systems, when encounter is high, virus replication could be maximized by frequently lysing hosts. This amounts to a tradeoff with the maximum host production potential. The above literature review suggests increases in light, temperature, and nutrients are all correlated with diminished lysogeny, with arguably the strongest support for nutrient related control. We can examine this hypothesized tradeoff using the NSIV model (Equations 1–4), where the parameter γ determines the virulence strategy of the virus. When γ = 1, the virus is lysogenic. Infected hosts grow at the same rate as susceptible hosts (a simplifying assumption that can potentially be relaxed), and there is no lysis. When γ = 0, infected hosts do not grow, and lysis proceeds at rate λ. With the system solved in steady state (see Supplementary Material), we can explore two scenarios exemplifying contrasting virulence strategies. The following two expressions are the total equilibrium virus biomass when γ = 1 and when γ = 0, respectively.

$$V\_{\rm lys}^{\rm tot} = \frac{\beta \delta}{\alpha \nu} \mathcal{N}\_{\rm in} - \frac{\beta \delta}{\mu} \tag{5}$$

$$N\_{\rm lyt}^{\rm tot} = \frac{\beta \delta \mu}{c(\beta \delta \phi + \psi \mu)} N\_{\rm in} - \frac{\alpha}{\phi} \tag{6}$$

Note that these expressions assume the rate of lysis, λ, is significantly greater than other parameters in the model (Supplementary Material). The above expressions are both linear functions of the nutrient input concentration Nin (**Figure 1A**), and give a guide to when lytic replication may be favorable over lysogeny. Interestingly, the minimal nutrient input required for lytic viruses to exist is always greater than the nutrient input required for lysogenic viruses to exist:

$$N\_{in}^{lps} = \frac{c\alpha}{\mu} \tag{7}$$

$$N\_{in}^{lyt} = \frac{c\alpha}{\mu} + \frac{c\alpha\psi}{\phi\delta\beta} \tag{8}$$

Since c, ω, ψ, φ, δ, and β are all positive, we have N lys in < N lyt in . The prediction is that lytic viruses may only be present at a nutrient input concentration that is higher than that required to sustain host biomass. Thus, low nutrient supply may naturally favor lysogenic viruses, since lytic viruses may not survive as free-existing entities. If viruses are assumed to switch from lysogeny to lysis once nutrient supply is sufficient to support a free living population of viruses, then the overall prevalence of lysogeny would decrease as a function of nutrient enrichment, perhaps replaced by predominately lytic viruses (**Figure 1B**). Thus, lysogeny may be favored under low nutrient conditions, and lytic production favored under relatively high nutrient conditions (Knowles et al., 2016; Weitz et al., 2016, cf).

The analysis presented here examines the potential for lytic viruses to exist in a range of nutrient conditions, but says nothing about the biological mechanisms that directly control virus replication strategy. Host metabolic state is associated with changes in replication strategy (Ptashne, 2004; Ghosh et al., 2009), and is expected to improve as nutrient supply increases. Host metabolic state may therefore provide a direct, mechanistic link between environmental conditions and virus replication strategy. Better understanding of the transition from lysogeny to lysis thus depends on our mechanistic understanding of metabolic cues, as well as the trade-offs governing feasibility of the different strategies, shown here to include host-virus encounter, burst, virus replication rate, host, and virus mortality (Equations 5, 6, **Figure 1**).

### 3.3. Host Range: Tradeoffs with Specificity and Generality

The prevalent view of high host specificity among marine viruses has been changing recently as wide and variable host ranges are observed among marine viruses (Holmfeldt et al., 2007; Flores et al., 2011). Host ranges can be variable across host strains (DePaola et al., 1998; Liu et al., 2001; Allen et al., 2007; Holmfeldt et al., 2007; Stenholm et al., 2008; Martínez et al., 2015) as well as across host phyla (Malki et al., 2015). A broad host range (generalist) must come with some cost; otherwise we would expect no host specialists. Coexistence between generalists and specialists is a topic of broader interest in ecology (Egas et al., 2004; Ma and Levin, 2006). In other ecological contexts, tradeoffs associated with generalism versus specialism are associated with foraging strategy (Wilson, 1994), scale of temporal variability in environment or resource (Gilchrist, 1995), and habitat fragmentation (Marvier et al., 2004) to name a few. For viruses, there has been some analytical work examining possible tradeoffs (Jover et al., 2013). By revisiting data in published studies, we found evidence for possible tradeoffs with host range size, including virus genome size, burst size, and morphology (**Table 3**, data shown in Supplementary Material). There are other sources of information that suggest possible tradeoffs but without sufficient measurements to show statistical significance (e.g., Mojica and Brussaard, 2014).

### 3.3.1. Genome Size

A broader host range could imply that the virus strain has some increased ability to overcome a wider range of host defenses. The hypothesized tradeoff would be that this requires a longer genome with larger functional potential, which requires more cell resources to assemble, ultimately slowing virus population increase rates. In a diverse host community, access to a greater number of hosts would outweigh this cost for a generalist, and in less diverse host communities, the more rapid population increase rate of specialists would be favored. There is some evidence that host range size correlates positively with genome size for lytic viruses (**Table 3**). These relationships are driven by the extremes (i.e., generalists and specialists), with higher variance for intermediate host ranges. The relationship is also reversed for lysogenic viruses (**Table 3**) (e.g., Stenholm et al., 2008). In some cases there is no relationship (Comeau et al., 2006).

### 3.3.2. Burst Size

There is at least one example of evidence for a strong relationship between host range and burst size, though this relationship is based on a small sample size (**Table 3**) (Stenholm et al., 2008). The relationship is also in the reverse direction from what one would expect from a tradeoff: a higher host range is associated with a higher burst size, so generalists would hypothetically have an advantage over specialists in both cases. However, greater burst size is also associated with greater latency period (Wang, 2006), and greater burst size, as with host range, is associated with larger genomes (Brown et al., 2006; Weitz et al., 2016). A tradeoff might therefore involve more than two traits, with a greater host range requiring extra genetic machinery and longer latency time, producing a cost with the potential to offset the advantages of generalism.

### 3.3.3. Morphology

A number of morphological traits associated with size relate positively with host range size, namely head length, head diameter, and tail diameter (**Table 3**). Additionally, DePaola et al. (1998) found among Vibrio phages a distinct short-tailed, long capsid morphotype that had a markedly wider host range than the other phages examined. Again, the tradeoff would likely have to do with the extra resources required for larger sizes.

### 3.3.4. Interaction Networks

The host range trait can be categorized into generalists, specialists, and intermediate cases, and the overall prevalence of these different strategies manifest in distinct network structures (Proulx et al., 2005). Nestedness—that is, the specialist virus

FIGURE 1 | Tradeoff between lysogenic and lytic infection. (A) Lines were generated using Equations (5) and (6) with δ, µ, c, β, φ, ω, and ψ equal to 0.1, 1×10−<sup>9</sup> , 2.3×10−12, 50, 1×10−11, 0.4, 0.1, respectively. The lysogenic and lytic populations can sustain non-negative biomass when <sup>N</sup>in <sup>=</sup> <sup>N</sup> lys in , and <sup>N</sup>in <sup>=</sup> <sup>N</sup> lyt in , respectively (Equations 7, 8). Low nutrient input enables lysogeny to survive when the lytic strategy would fail. High nutrient input can lead to survival of free-existing lytic phage. (B) The model in (A) can be used to explain the relationship between fraction of hosts that are lysogenic (FLC), and fraction of hosts with lytic infections (FIC). Data are of bacterial assemblages in a range of trophic conditions, ranging from the relatively oligotrophic Mediterranean Sea, to the more productive Baltic Sea (Weinbauer et al., 2003). Total lysogenic infection was inferred by treatment with mitomycin C. The decline in FLC as a function of FIC is thought to be due to nutrient enrichment. The jagged blue line averages total lysogenic (FIC) and lytic infection (FLC) for a community of phages, each modeled with Equations (1–4) where parameters β and φ were drawn randomly from uniform distributions ±50% of the values in (A), and no tradeoffs were imposed between parameters. Each virus in the community was assumed to switch from lysis to lysogeny when Nin = N lyt in . The jagged line arises because each community member has a unique N lyt in determined by the randomly drawn β and φ. The gray shaded region is one standard deviation from the mean for FLC and FIC.

infects the host that is infected most commonly—appears to be common among closely related host-virus groups, though other configurations occur (Flores et al., 2011). Interestingly, these network structures appear limited to more closely related phylogentic host-virus networks. Broad phylogenetic groups are characterized by a nested-modular network structure, whereby nestedness only occurs in modules, and viruses within each module are generally unable to infect more distantly related hosts belonging to separate modules (Beckett and Williams, 2013). Marine viruses follow these patterns as well, though an aggregation of the reviewed data shows a disproportionately high number of generalists and specialists as compared to intermediate cases (**Figure 2A**).

#### 3.3.5. The Host Range Tradeoff

To examine the potential tradeoffs associated with host range, we use a simplified version of the NSIV model (Equations 1–4), where we consider only the lytic case without an explicit population of infected hosts (Supplementary Material Section 1.3). If we assume a nutrient replete environment, we can approximate host population growth rate with a constant α, and write the system as two equations:

$$\frac{d\mathbf{S}}{dt} = \alpha \mathbf{S} - \phi V \mathbf{S} - m\mathbf{S} \tag{9}$$

$$\frac{dV}{dt} = \phi \beta \,\text{VS} - \psi \, V \tag{10}$$

Simplifications like this allow for focusing on a single tradeoff. To understand the host range dimension, we include multiple hosts and viruses, with different combinations of infection:

$$\frac{d\mathbf{S}\_{\circ}}{dt} = \alpha\_{\circ}\mathbf{S}\_{\circ} - \sum\_{i} \phi\_{ij} V\_{i}\mathbf{S}\_{\circ} \left[\frac{\rho\_{\circ j}\mathbf{S}\_{\circ}}{\sum\_{k} \rho\_{ik}\mathbf{S}\_{k}}\right] - m\_{j}\mathbf{S}\_{\circ} \tag{11}$$

$$\frac{dV\_i}{dt} = \sum\_j \phi\_{ij} \beta\_{ij} V\_i \mathbf{S}\_j \left[ \frac{\rho\_{ij} \mathbf{S}\_j}{\sum\_k \rho\_{ik} \mathbf{S}\_k} \right] - \psi\_i V\_i \tag{12}$$

where i and j subscripts represent hosts and viruses respectively, and ρij is a binary parameter that describes whether virus j infects host i. In this configuration, different host-virus interaction matrices (Flores et al., 2011) can be input as binary matrices of ρ values.

In this system, a diversity of viruses and hosts can coexist if host range trades off with φiβi/ψ<sup>i</sup> (Jover et al., 2013). We tested a tradeoff between host range and the interaction kernel φ, which encapsulates the above reviewed traits that likely tradeoff with host range. We ran an ensemble of simulations with varying numbers of hosts and viruses, nested host range structures, and a forced tradeoff between host range and φ (**Figure 2B**). The simulation reproduced the observed bimodal pattern of higher abundance of generalists and specialists as compared to the intermediate cases (**Figure 2C**) when two conditions were met: the interaction network has a nested structure, and the tradeoff relationship (**Figure 2B**) is



The scatter plots for these correlation analyses are in the Supplement.

concave up. If the tradeoff is concave down, then increasing host range toward the extreme comes at a very high cost in terms of the interaction kernel (and vice versa), shifting the resulting distribution to a unimodal one with an intermediate host range. This example shows how the trait-based approach gives us a quantitative hypothesis about the shape of a tradeoff and its ability to describe observed patterns.

Host range is not just a function of virus traits, however. Defense mechanisms of hosts can vary across strains as well. Because the life histories of viruses and hosts are intimately coupled, tradeoffs with host range can occur across the virushost relationship. We discuss this idea more generally in the next section.

### 3.4. Resistance to Infection: Tradeoffs Relating to Host Traits

Because viruses rely on hosts for their genetic material, tradeoffs associated with virus traits can be intimately tied to host traits as well. Tradeoffs around competitive and defensive traits in hosts (in the following referred to as cost of resistance, COR) are an intriguing example of such a link between virus and host traits.

#### 3.4.1. COR in Natural Communities

Natural virus-host communities provide indirect evidence for COR. The apparent paradox between laboratory experiments, where host resistance readily evolves and eventually excludes viruses, and the large abundance of viruses in the pelagic environment (Weinbauer, 2004) gets resolved when considering COR. Specifically, resource limitation in natural environments may render expensive defense less viable. There is ample evidence of coexistence of susceptible and resistant hosts in natural communities (Waterbury and Valois, 1993; Tarutani et al., 2000; Holmfeldt et al., 2007; Middelboe et al., 2009), supporting the idea that COR prevents resistant types to outcompete susceptible types. Further support for COR is found in the observation that dominant host types tend to be both resistant (Rosenzweig, 1973; Lenski and Levin, 1985; Suttle and Chan, 1993; Waterbury and Valois, 1993; Malmstrom et al., 2004; Suttle, 2007; Middelboe et al., 2009; Campbell et al., 2011; Våge et al., 2013; Thingstad et al., 2014) and slow growing (Malmstrom et al., 2004; Suttle, 2007; Campbell et al., 2011; Samo et al., 2014; Thingstad et al., 2014). Finally, it appears that nested infection networks are widespread in natural communities (Chao et al., 1977; Flores et al., 2011; Jover et al., 2013; Koskella and Brockhurst, 2014; Martiny et al., 2014). In these networks, COR prevents defense-specialized hosts infected by generalist viruses only to outcompete competition-specialized hosts that are infected by most viruses. Supporting this idea, there is evidence that hosts infected by specialist viruses have faster growth rates than hosts infected by generalist viruses (Chao et al., 1977).

#### 3.4.2. COR in Experimental Communities

Observing COR directly in experiments can be difficult, since COR may be small and dependent on the environment (Bohannan et al., 2002). Nevertheless, a number of studies have measured COR. The most prevalent expression of COR is a reduced growth rate in resistant types, as observed experimentally in prokaryotes including Escherichia coli (Lenski and Levin, 1985; Lenski, 1988; Bohannan et al., 1999; Bohannan and Lenski, 2000; Harcombe and Bull, 2005), Pseudomonas (Lythgoe and Chao, 2003), Synechococcus (Waterbury and Valois, 1993; Lennon et al., 2007), Flavobacteria (Middelboe et al., 2009), Prochlorococcus (Avrani et al., 2011) and eukaryotic Phaeocystis pouchetti (Haaber and Middelboe, 2009) and Ochromonas tauri (Thomas et al., 2011). Besides reduced growth rates, increased susceptibility to other viruses (Avrani et al., 2011, Prochlorococcus) and reduced abilities to form biofilms (Buckling and Rainey, 2002; Brockhurst et al., 2005, Pseudomonas) are other known expressions of COR.

#### 3.4.3. Defense Mechanisms with Varying COR

Besides environmental conditions that may influence the expression of COR (Lennon et al., 2007), different defense mechanisms probably have varying COR, both in quality and quantity. Changes in surface receptors that hamper virus adsorption (Middelboe, 2000; Middelboe et al., 2001; Buckling and Rainey, 2002; Mizoguchi et al., 2003; Stoddard et al., 2007; Middelboe et al., 2009; Pagarete et al., 2009; Avrani et al., 2011; Bidle and Vardi, 2011) often hamper uptake of limiting nutrients as well, which can explain reduced growth rates in resistant hosts. On the other hand, internal defense mechanisms such as the CRISPR-Cas (Barrangou et al., 2007; Sorek et al., 2008; Levin, 2010; Makarova et al., 2011) and restriction enzymes (Wilson and Murray, 1991; Labrie et al., 2010) prevent take-over of the host by the virus after adsorption, which does not influence nutrient uptake dynamics directly. Instead, costs for these internal defense systems may arise from resource allocation and maintenance of the enzymatic machinery. It is conceivable that extending resistance to new viruses with these internal defense systems (e.g., by adding an additional recognition sequence in the CRISPR system) may be relatively inexpensive, but we lack quantitative evidence. Other mechanisms rendering resistance to various degrees, whose specific COR are poorly understood, include prophage incorporation (Stoddard et al., 2007; Martiny et al., 2014), chronic infection (Fuhrman, 1999; Thomas et al., 2011), immunization through viral lysate (Bidle and Vardi, 2011) and quorum sensing allowing a regulated expression of surface receptors (Høyland-Kroghsbo et al., 2013). The most drastic defense is abortive infection leading to induced cell death (Bidle and Vardi, 2011; Berngruber et al., 2013; Refardt et al., 2013).

#### 3.4.4. Linking Host and Virus Traits through COR

An intriguing aspect of virus ecology is the strong link between virus and host traits. A resistance trait in the host leads to adaptive and evolutionary changes in the virus to sustain infectivity. Interestingly, however, COR also affects viruses in a more direct way. In a review on marine viruses, Suttle (2007) hypothesized inverse rank-abundance distributions of hosts and their associated viruses, where the most abundant hosts are low-active and infected by rare and low virulent viruses, while the rare hosts are active and infected by abundant and highly virulent viruses. Findings of abundant low-active and defensive hosts (Rosenzweig, 1973; Lenski and Levin, 1985; Suttle and Chan, 1993; Waterbury and Valois, 1993; Malmstrom et al., 2004; Suttle, 2007; Middelboe et al., 2009; Campbell et al., 2011; Våge et al., 2013; Samo et al., 2014; Thingstad et al., 2014) and inverse rank-abundance distributions emerging in virushost interaction models when assuming COR (Våge et al., 2013; Thingstad et al., 2014) support Suttle's hypothesis. The positive correlation between host activity and virulence in this scenario provides a direct link between COR and viral infectivity.

Inverse rank abundance distributions also impose a tradeoff between host abundance and virulence, which becomes apparent when considering the model for host infection rates used earlier:

$$R = \phi\_{i\dot{j}} V\_i S\_{\dot{j}} \tag{13}$$

where R is the infection rate for S<sup>j</sup> by V<sup>i</sup> . Given inverse rankabundance distributions as described by Suttle (2007), infection rates for highly competitive hosts should be reduced due to the low host abundance, despite high adsorption coefficients of their viruses, whereas infection rates for highly defensive hosts should be reduced due to the low adsorption coefficient of their viruses, despite the high host abundance. The consequence is that highest infection rates may occur at intermediate virulence and host defensiveness (**Figure 3**). This tradeoff between host abundance and virulence of the virus can only be corroborated once we overcome the major challenge of quantifying abundances of viruses associated with defensive vs. competitive hosts (Jover et al., 2013). A step in that direction can be made through methods that identify single virus-host pairs in natural communities, such as phageFish (e.g., Martiny et al., 2014).

We also note that "host abundance" needs to be treated with care, as analysis of SSU rRNA used to quantify host abundances in the field resolves "species" level diversity, whereas virus-host interactions typically take place on the more strain-specific level. Investigations of virus-host interactions in natural communities will therefore rely on refinements in sequence-based methods, such as CRISPR spacer similarities and single-cell sequencing (Roux et al., 2016).

### 3.5. Summary

In this section, we have reviewed different virus traits and discussed quantification of potential tradeoffs by means of a dynamic NSIV model framework. We have shown that tradeoffs fundamentally influence community structure, and we have pointed out areas where more knowledge regarding tradeoffs would better inform our understanding. In the case studies we have discussed, we used trait-based tradeoffs to generate hypotheses, to explain observed patterns, and to link empirical and modeling work. In the virulence example, a steadystate analysis provided a hypothesized relationship between nutrient concentration and the fractions of hosts that are lytic and lysogenic. This hypothesis held up well to a small dataset of field measurements, and with additional support of field measurements could have important implications for the biogeography of lysogeny and lysis at basin and global scales. In the host range example, we explored a particular tradeoff between host range and interaction kernel. The simulation provided an explanation for the observed pattern where host range tends toward the extremes. Because host range can tradeoff with other traits as well (Jover et al., 2013), this is just one candidate explanation for the observed pattern, and it could be that the host range tradeoff involves multiple traits. Our review of the literature data (**Table 3**, Supplementary Material) provides strong evidence for host range tradeoffs, but no clear single trait involved in this tradeoff. In this case, analysis shows how a tradeoff can explain an observed pattern, and more experimental work is required to resolve the specifics of tradeoff and the traits involved. In these examples, the close interaction between virus traits and host traits is inescapable. Both the lysis-lysogeny switch and the host range tradeoff depend on traits such as µ-the host growth rate. The interaction between virus traits and host traits is perhaps most pronounced with COR, where this interaction can drive evolutionary dynamics and shape the rank-abundance structure of the community. Understanding these interactions and their dynamics would have value beyond virus ecology, to the field of trait-based ecology as a whole.

### 4. FUTURE DIRECTIONS

"The best theory is inspired by practice. The best practice is inspired by theory."

Knuth (1991).

One of the current challenges identified by the trait-based ecology community is bridging the gap between empiricists (i.e., practice) and modelers (i.e., theory) (Barton et al., 2016). This challenge is a common vein that runs through much of the history of science (Knuth, 1991), but has become particularly pronounced with the increased specialization required in both ecological modeling and experimentation. The quantification of ecological tradeoffs, as we have presented in this review, is an objective that provides a useful nexus of modeling and experimental work and an avenue that can cut across subdisciplines. The use of traits and tradeoffs to organize ecological information has the potential to offer a robust theory for understanding a system. Here we briefly discuss a few of the central questions in marine virus ecology, with an eye toward how the study of tradeoffs can inform these questions. We also emphasize points where the study of virus ecology can contribute new insights to trait-based ecology in general.

## 4.1. What Portion of Primary and Bacterial Production Goes to Viruses vs. to Grazers?

In some ways, viruses and grazers compete for the same resource. Additionally, virus infection could alter grazing rates. This question is key to understanding when and under what conditions production is exported or recycled (Fuhrman, 1999; Brussaard, 2004; Suttle, 2007; Weitz and Wilhelm, 2012). It is a major challenge and one for which models are indispensable (Weitz et al., 2015). To tackle this problem with models, traits that control consumption of bacteria and phytoplankton must be understood, but there is currently a lack of clarity on how to compare zooplankton traits with virus traits. For decades, zooplankton ecologists have evaluated grazing competitiveness by comparing parameters that control the shape of the curve defining zooplankton consumption as a function of prey concentration (Holling, 1959; Gentleman et al., 2003; Jeschke et al., 2004; Kiørboe, 2008; Prowe et al., 2012).

Typically, zooplankton consumption increases linearly with prey density at low prey concentrations and saturates toward a handling time limit—for example,

$$\frac{\text{g}\_{\text{max}}H}{K\_{\text{\\$}} + H} \tag{14}$$

where H is the total prey concentration and K<sup>g</sup> is the prey concentration at which predator consumption rate is half the maximal value, gmax. The parameters that define the shape of this curve, gmax and K<sup>g</sup> , can be a useful guide for zooplankton ecologists to evaluate consumption of prey biomass. This raises the question of whether virus consumption of prey biomass can be described in a comparable way and, if so, how do the different rate constants compare.

If we assume that the total concentration of prey can be approximated by the total concentration of susceptible hosts, we can write an analogous expression in terms of virus abundance and traits (Supplementary Material),

$$\frac{\lambda H}{\frac{\lambda}{\phi} + H} \tag{15}$$

Evaluating the parameters that control curve shapes may be a useful way to understand competition between viruses and grazers. To the best of our knowledge, very little work has been done to standardize and compare virus and zooplankton Holling curve parameters. Most virus models that explicitly resolve free-existing viruses assume a linear relation between virus production and host density, where the slope of the line is defined by adsorption and burst size (Thingstad, 2000; Beckett and Williams, 2013; Weitz et al., 2015). Yet, it is conceivable that at a sufficiently high host density, the burst becomes independent of encounter, and depends instead on the duration of the latent phase. Understanding tradeoffs among key parameters λ and φ will help evaluate whether losses due to viral infection saturate as a function of host cell density, with implications for transfer to higher trophic levels.

### 4.2. What Regulates Virus to Host Ratios?

Virus to host ratios have been measured as a proxy for the importance of viruses in aquatic systems for over two decades (Ogunseitan et al., 1990; Wommack and Colwell, 2000; Wigington et al., 2016). Numbers vary greatly (Wigington et al., 2016), but the ratio is typically considered to be roughly 10:1. What regulates this number still remains an important question, as the ratio has far reaching biogeochemical consequences (Fuhrman, 1999; Weinbauer, 2004; Suttle, 2007). A recent analysis of an idealized microbial food web model revealed intricate links between mechanisms within the bacterial host community and between different plankton functional types, providing a framework for how virus to host ratios may emerge in the bacterial community (Våge et al., 2016). Briefly, assuming total host abundance to be controlled by micrograzers as a result of their quick response to bacterial production (Azam et al., 1983) and assuming grazing to be non-selective, viral lysis compensates for differences in growth rates of the host strains. Virus abundance is thus positively correlated to the width of the growth rate spectrum in the host community. Interestingly, the width of the host growth rate spectrum and thus virus to bacteria ratios as well as food web structure at the level of plankton functional types are highly sensitive to COR. This suggests that mechanistically understanding and quantifying COR will be key to better understand aquatic microbial ecology and evolutionary dynamics. In trait-based ecology in general, the emphasis has been on tradeoffs within a species or trophic group, so an understanding of how traits can tradeoff between viruses and hosts has the potential to bring new knowledge to how traits can tradeoff across trophic groups more generally.

### 4.3. How Can the Trait-Based Approach Better Inform us on the Role of Marine Viruses in Regulating Climate?

Understanding climate and the cycling of carbon is one of the most pressing earth science challenges of the day. The role of marine viruses is complex and nuanced, and answering this question relies on incorporating knowledge of virus ecology into climate system models. Global and ocean scale climate models are state variable limited because of computational costs. Adding the level of complexity required to resolve food web dynamics, let alone virus ecology, is often too computationally burdensome at the global scale. Particular ecological components, if they are included at all, are typically simplified to a single state variable with fixed parameters. As computational restrictions are gradually overcome, tradeoffs offer one potentially useful technique for capturing some of the ecological complexity while minimizing state variable increases. If we relax the notion that parameter values (or traits) are fixed for species, but rather change and respond to other traits, we can capture some aspects of adaptation and diversity within modeled ecosystems. For example, virus infections can drive changes in host traits, such as growth rate, rapidly (Avrani and Lindell, 2015). By allowing parameter values to be flexible and depend on each other based on tradeoffs, we can capture some of the community dynamics without adding state variables. Virus-host dynamics are rapid enough to allow for studying these dynamics in detail and for revealing their underlying principles. Incorporating this information into climate models is a promising approach both to answer questions about the role of marine viruses in climate and to introduce ecological processes more generally into climate models.

### 5. CONCLUSION

Virus ecology and trait-based ocean ecology have new insights to offer each other. There are some ways in which trait-based approaches to ocean life can inform virus ecology. For example, the strongly size structured character of the ocean ecosystem has been explored in depth across trophic levels (cf. Andersen et al., 2016), but there is limited work on the allometry of marine viruses. A detailed investigation of the marine virus size spectrum could facilitate the incorporation of virus ecology into models. However, as we have discussed, there are ways in which virus allometry might deviate from pelagic food web allometry in general. Because of differences like this, the exchange of knowledge works in both directions: the study of virus ecology can also provide new insights to trait-based ecology. For example, the role of adaptation and evolution in altering traits dynamically has been a challenge to measure at higher trophic levels. This type of dynamic has been explored in models (Record et al., 2013a; Sauterey et al., 2014), but it is difficult to link with empirical work. The short time scales at which virus-host interactions take place makes it possible to quantify and study these dynamics, and the insights gained can help guide ecology at higher trophic levels. Along a similar vein, trait-based studies typically focus on the traits of the focal taxa, while ignoring the traits of adjacent trophic groups. The intimate interaction between virus replication and host reproduction at the genetic level forces us to consider both virus and host traits together. Because of these perspectives, virus ecology is uniquely poised to offer new insights to the broader field of trait-based ecology.

### AUTHOR CONTRIBUTIONS

NR, DT, and SV contributed equally to this manuscript.

### REFERENCES


### FUNDING

This publication was supported by the Ocean Carbon and Biogeochemistry program (NSF, NASA). NR was supported by Bigelow Laboratory institutional funds. DT was supported by NSF grant OCE-1536521 and the Gordon and Betty Moore Foundation through grant GBMF3778 to M.J. Follows. SV was supported by the University of Bergen.

### ACKNOWLEDGMENTS

This manuscript is a product of a collaboration at the "Traitbased Approaches to Ocean Life" Scoping Workshop, which was supported by the Ocean Carbon and Biogeochemistry group (NSF, NASA), the Simons Foundation, and the Gordon and Betty Moore Foundation. We thank two reviewers for their input and Joaquín Martínez Martínez for valuable comments that greatly improved the manuscript.

### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fmars. 2016.00251/full#supplementary-material


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**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Record, Talmy and Våge. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Directional and Spectral Irradiance in Ocean Models: Effects on Simulated Global Phytoplankton, Nutrients, and Primary Production

Watson W. Gregg<sup>1</sup> \* and Cécile S. Rousseaux 1, 2

*<sup>1</sup> NASA Global Modeling and Assimilation Office, Greenbelt, MD, USA, <sup>2</sup> Goddard Earth Sciences Technology and Research, Universities Space Research Association (USRA), Greenbelt, MD, USA*

The importance of including directional and spectral light in simulations of ocean radiative transfer was investigated using a coupled biogeochemical-circulation-radiative model of the global oceans. The effort focused on phytoplankton abundances, nutrient concentrations and vertically-integrated net primary production. The importance was approached by sequentially removing directional (i.e., direct vs. diffuse) and spectral irradiance and comparing results of the above variables to a fully directionally and spectrally-resolved model. In each case the total irradiance was kept constant; it was only the pathways and spectral nature that were changed. Assuming all irradiance was diffuse had negligible effect on global ocean primary production. Global nitrate and total chlorophyll concentrations declined by about 20% each. The largest changes occurred in the tropics and sub-tropics rather than the high latitudes, where most of the irradiance is already diffuse. Disregarding spectral irradiance had effects that depended upon the choice of attenuation wavelength. The wavelength closest to the spectrally-resolved model, 500 nm, produced lower nitrate (19%) and chlorophyll (8%) and higher primary production (2%) than the spectral model. Phytoplankton relative abundances were very sensitive to the choice of non-spectral wavelength transmittance. The combined effects of neglecting both directional and spectral irradiance exacerbated the differences, despite using attenuation at 500 nm. Global nitrate decreased 33% and chlorophyll decreased 24%. Changes in phytoplankton community structure were considerable, representing a change from chlorophytes to cyanobacteria and coccolithophores. This suggested a shift in community function, from light-limitation to nutrient limitation: lower demands for nutrients from cyanobacteria and coccolithophores favored them over the more nutrient-demanding chlorophytes. Although diatoms have the highest nutrient demands in the model, their relative abundances were generally unaffected because they only prosper in nutrient-rich regions, such as the high latitudes and upwelling regions, which showed the fewest effects from the changes in radiative simulations. The results showed that including directional and spectral irradiance when simulating the ocean light field can be important for ocean biology, but the magnitude varies with variables and regions. The quantitative results are intended to assist ocean modelers when considering improved irradiance representations relative to other processes or variables associated with the issues of interest.

Keywords: spectral irradiance, directional irradiance, global phytoplankton, radiative transfer, global models

#### Edited by:

*Susanne Menden-Deuer, University of Rhode Island, USA*

#### Reviewed by:

*Oliver Zielinski, University of Oldenburg, Germany Colleen Mouw, University of Rhode Island, USA*

> \*Correspondence: *Watson W. Gregg watson.gregg@nasa.gov*

#### Specialty section:

*This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Marine Science*

Received: *20 July 2016* Accepted: *04 November 2016* Published: *22 November 2016*

#### Citation:

*Gregg WW and Rousseaux CS (2016) Directional and Spectral Irradiance in Ocean Models: Effects on Simulated Global Phytoplankton, Nutrients, and Primary Production. Front. Mar. Sci. 3:240. doi: 10.3389/fmars.2016.00240*

## INTRODUCTION

Light is a critical physical influence on ocean biology. It initiates the process of photosynthesis, the first step supporting nearly all life in the oceans (Dickey et al., 2011), and altering the oxygen and carbon balances on the Earth. Light from the sun arrives at the top of the atmosphere with different intensities at different spectral bands. It comes entirely in a specific direction depending on the time of day and season, in a beam that is defined by the solar zenith angle. This beam is the direct irradiance. The atmosphere modulates this direct irradiance via spectral absorption by optically active gases and also introduces a second pathway to the oceans resulting from scattering by clouds, aerosols, and molecules. This latter process gives rise to diffuse irradiance, where the light now enters the ocean from a hemisphere encompassing the horizon to nadir. This "sky light" does not have direction specified and is in contrast to direct irradiance that arrives uninterrupted by the atmosphere. Irradiance reaching the surface is often a combination of the direct and diffuse components. The term directional refers to this difference in irradiance pathways.

Once the spectral and directional light enters the ocean, it continues its journey of absorption and scattering, now guided by optical constituents with different spectral absorption capabilities and sizes that determine their scattering effects. Now it encounters much more strongly absorbing constituents than in the atmosphere and finds its pathways blocked by a phalanx of life forms and associated byproducts, as well as inorganic substances, each of which with demands for light unheard of in the atmosphere. Its passage in the oceans differs by the constituents it encounters and the directions it is forced to take, which alters the availability and nature of light to be taken up by phytoplankton and initiate process of photosynthesis, further affecting the distribution of life at the surface and at depth.

Despite the directional and spectral nature of irradiance in the oceans, models that represent these aspects are uncommon. Most ocean biogeochemical models simulate surface bulk irradiance, typically as shortwave radiation (e.g., Maier-Reimer et al., 2005; Doney et al., 2006; Henson et al., 2010) or as photosynthetically available radiation (PAR) (Palmer and Totterdell, 2001; Zielinski et al., 2002; Marinov et al., 2010; Laufkötter et al., 2013), and then represent the transmission as a function of an attenuation term (e.g., Zhao et al., 2013). This is especially true for the global models. The attenuation term is sometimes divided into a component for water and another for phytoplankton (Jiang et al., 2003; Maier-Reimer et al., 2005; Manizza et al., 2005; Xiu and Chai, 2014), but can also represent an estimated average loss of light in the water column (e.g., Doney et al., 2006).

Recognition of the importance of directional and spectral irradiance for phytoplankton dates to Sathyendranath and Platt (1988, 1989) in investigations of phytoplankton in situ light absorption and estimates of in situ primary production. Spectral irradiance was explicitly included in a 1-dimensional regional model of the Sargasso Sea (Bissett et al., 1999), the West Florida Shelf (Bissett et al., 2005), and in 3-dimensional models of the eastern US continental shelf (Mobley et al., 2009) and North Pacific (Xiu and Chai, 2014). But spectral and especially directional irradiance have largely been ignored in global coupled biological-circulation models (with the exceptions of Gregg, 2000; Gregg et al., 2003; Gregg and Casey, 2007; Dutkiewicz et al., 2015). This is likely related to the computational load directional and spectral radiative transfer imposes on ocean models, especially globally resolved ones. But in an era of multiparallel processing, perhaps the time has come to reconsider its inclusion. Light in the natural oceans is, after all, directionally and spectrally resolved and therefore including these characteristics would enhance the realism of simulated ocean transmittance and light availability.

Our purpose here is to evaluate the importance of directional and spectral irradiance in the global oceans using an established ocean biogeochemical model and an established radiative transfer model that incorporates these aspects of light in the atmosphere and through the oceans. We limit our focus here to the effects on biological processes, specifically phytoplankton abundance, nutrient distributions, and vertically-integrated primary production. Nutrients are indirectly related to irradiance via uptake by phytoplankton. Changes in heat transfer due to ocean light absorption is important for ocean modeling as well (e.g., Gnanadesikan and Anderson, 2009), but we will defer these evaluations in the interest of brevity. Quantitative assessments can assist global modelers on how to proceed with future model improvements by quantifying the importance of these aspects and enable rational choices.

### METHODS

### Global Ocean Physical-Biogeochemical Model Configuration

The underlying biogeochemical constituents are simulated by the NASA Ocean Biogeochemical Model (NOBM; Gregg and Casey, 2007; Gregg et al., 2013) which is coupled to a global ocean circulation model, Modular Ocean Model version 4 (MOM4; Griffies et al., 2004; Gnanadesikan et al., 2006). It spans the global ocean at 1◦ horizontal resolution, with 50 vertical levels and the shallowest level at 10 m bottom depth. NOBM incorporates global coupled physical-biological processes, including six phytoplankton groups (diatoms, chlorophytes, cyanobacteria, coccolithophores, dinoflagellates, and Phaeocystis spp.). The Phaeocystis genus only includes the high latitude species, specifically Phaeocystis pouchetti (northern high latitudes) and Phaeocystis antarctica (Southern Ocean). These phytoplankton groups span much of the functionality of the global oceans. Diatoms represent high growth, fast sinking, silicate-dependent phytoplankton that have high nutrient requirements. Cyanobacteria are the functional opposite, with slow maximum growth rates, slow sinking, low nutrient requirements, and a capability for nitrogen fixation. Coccolithophores are moderate growers that sink relatively quickly due to their calcium carbonate coccoliths. They are efficient users of nitrogen, enabling them to flourish in low nutrient regions (although not as efficient as cyanobacteria). Phaeocystis spp., at least as represented here, are high latitude nanoplankton that play a role in the Earth's sulfur cycle. Unlike the other phytoplankton, they have a temperature optimum in maximum growth rate around 3◦C (Schoemann et al., 2005). Dinoflagellates are large, slow-growing phytoplankton with high nutrient requirements, but sink slowly based on the limited motility provided by flagella. Finally, chlorophytes are intended to represent the diverse functionality associated with nanoplankton, with growth rates, sinking rates, and nutrient requirements between the functional extremes and the more specialized phytoplankton. Phytoplankton-specific physiological and physical parameters are shown in Appendix Table 1.

Diatoms and chlorophytes (Arrigo and Sullivan, 1994; Arrigo et al., 1995; Robinson et al., 1998) and Phaeocystis spp. (Tang et al., 2009; Arrigo et al., 2014) have the capability to grow in sea ice. We limit irradiance in sea ice to one-tenth its value at the surface (Gregg and Casey, 2007). Biological activities in ice are modified by the percentage of sea ice present in a model grid cell.

The model also contains four nutrients (nitrate, ammonium, silicate, and dissolved iron), three detrital components (particulate organic carbon, silicate, and iron), and five carbon components: dissolved organic and inorganic carbon (DOC and DIC), alkalinity, and two new variables, particulate inorganic carbon (PIC), and chromophoric dissolved organic carbon (CDOC).

Phytoplankton growth is a function of scalar quantum irradiance, which is a measure of the photons impacting phytoplankton cells from all directions, expressed as units of µmol photons m−<sup>2</sup> s −1 (Kirk, 1992). Variable carbon to chlorophyll ratios are utilized, that depend on the light history (Gregg and Casey, 2007).

PIC is produced by coccolithophores as detached coccoliths and is lost via sinking and dissolution. PIC is produced as a fraction (25%) of the coccolithophore growth rate (Gregg and Casey, 2007) minus respiration. The PIC sinking rate is represented here as an exponential function of concentration, assuming that large concentrations of PIC are associated with larger coccolith size

$$\mathbf{w}\_{\mathbf{s}}(\text{PIC}) = \mathbf{a}\_{\mathbf{o}} \exp(\mathbf{a}\_{\mathbf{l}} \,^{\ast} \text{PIC}) \tag{1}$$

where w<sup>s</sup> is the PIC sinking rate (m d−<sup>1</sup> ), PIC is in units of µgC l −1 , a<sup>0</sup> = 0.1 m d−<sup>1</sup> and a<sup>1</sup> = 1.0 l µgC−<sup>1</sup> . Dissolution follows Buitenhuis et al. (2001), except that no dissolution is allowed for depths shallower than the calcium carbonate compensation depth, which we define as 3500 m.

CDOC represents the biogeochemical constituent necessary for the simulation of absorption by aCDOC(λ), the absorption coefficient, which is an optical quantity. It has two sources in the model: phytoplankton excretion and river discharge. Phytoplankton excretion assumes a DOC:CDOC production ratio of 0.7. It is destroyed by the absorption of photons, assuming a quantum yield for CDOC

$$
\varphi \text{ CDOC} = \frac{\mu \text{ mol CDOC destroyed}}{\mu \text{ mol photons absorbed}} \tag{2}
$$

and the quantum absorption of available spectral irradiance in the water column by CDOC

$$\mathbf{Q}\_a = \int\_{200}^{800} a\_{\rm CDOC}(\lambda) \left[ Q\_d(\lambda) + Q\_s(\lambda) + Q\_u(\lambda) \right] d\lambda \tag{3}$$

where Q<sup>a</sup> is the absorbed quanta by CDOC (µmol photons m−<sup>3</sup> s −1 ). Q denotes irradiance expressed as quanta with subscripts d, s, and u representing direct downwelling, diffuse downwelling, and diffuse upwelling components (µmol photons m−<sup>2</sup> s −1 ), respectively, and aCDOC is the absorption coefficient of CDOC (m−<sup>1</sup> ).

The photolysis of CDOC is then

$$\frac{d\text{CDOC}}{dt} = \text{CDOC} - \varphi\_{\text{CDOC}} \ast \text{Qa} \tag{4}$$

There is regional information on defining ϕCDOC (e.g., Reader and Miller, 2012, 2014), but we seek a global spectrally integrated solution for computational reasons. In this case, we iterate model runs with various values of ϕCDOC, using global distributions of data from MODIS-Aqua (Maritorena et al., 2010) as a target. After several dozen model runs, we derive ϕCDOC = 1.0E-6 (µM/µmol photons absorbed m−<sup>3</sup> ) for results in reasonable agreement with MODIS-Aqua data, which we use in this simulation.

This approach ignores photo-bleaching of CDOC, which is sometimes assumed to be an intermediate condition on the path to photolysis (photo-oxidation) (Del Vecchio et al., 2009). Photo-bleaching is a milder form of degradation, where the slope of the CDOC absorption curve, SCDOC (see Equation 18) declines (i.e., spectral-dependence becomes weaker) with exposure to irradiance. However, keeping track of various states of photo-bleaching is difficult for a prognostic tracer and requires multiple tracers with different absorption curve slopes to be realistic. Dutkiewicz et al. (2015) approach the problem by defining a CDOM-like tracer that is photo-bleached as a function of PAR. Like here, Xiu and Chai (2014) ignored variability of SCDOC (and thus photo-bleaching). Bissett et al. (1999) also photolyzed CDOC, bypassing photo-bleaching. However, photolysis degradation products were reverted to the DOC pool rather than the DIC pool. The spectral slope SCDOC may also change by water type (Stedmon et al., 2011) but is also not considered here.

River inputs of nutrients and some carbon components are included in the model, but amounts are not differentiated individually by river source. Nitrate and silicate concentrations at river mouths are assumed to be 10 µM, while dissolved iron is 1 nM. DOC is specified at 100 µM, while DIC and alkalinity are assumed to be the same as the nearby ocean discharge locations. CDOC is assumed to be 750 µM at the river mouths. Here we make an exception for northern high latitudes (>70◦N) where concentrations are set to 300 µM because the higher concentrations led to complete irradiance extinction, which is not supported by data.

### OCEAN-ATMOSPHERE SPECTRAL IRRADIANCE MODEL

NOBM is coupled to the Ocean-Atmosphere Spectral Irradiance Model (OASIM; Gregg and Carder, 1990; Gregg, 2002; Gregg and Casey, 2009) to simulate the propagation of downward spectral irradiance in the atmosphere and oceans and the upwelling irradiance/radiance in the oceans. The irradiance pathways for OASIM are shown in **Figure 1**. The atmosphere and ocean portions of the irradiance are implemented at variable spectral resolution over the range 200 nm–4 mm, depending upon the major atmospheric and oceanic absorbing sources. There are 33 spectral bands, which account for >99% of the total solar extraterrestrial irradiance. For the PAR spectral region (defined here as 350–700 nm following historical precedent) the model utilizes 25 nm spectral resolution (**Figure 2**), with band centers located at the bands shown. The 350 nm band represents the beginning of the first band and 700 nm the end of the last band, making them approximately half the width of the other bands (Gregg, 2002).

The atmospheric component of OASIM tracks irradiance through cloudy and clear skies (see **Figure 1**), accounting for spectral absorption and scattering of atmospheric gases, clouds, and aerosols. Biases and uncertainties in the atmospheric component of OASIM have been characterized for clear sky high spectral resolution (1 nm; Gregg and Carder, 1990) and under mixed cloudy and clear skies for 25 nm spectral resolution (Gregg and Casey, 2009). We elaborate here on the ocean optical calculations.

Ocean radiative transfer uses a "three-stream" method based on the Aas (1987) two stream approximation, modified for an explicit direct downwelling component by Ackleson et al. (1994)

$$\begin{aligned} \frac{d\mathbf{E}\_{\mathbf{d}}(\lambda)}{d\mathbf{z}} &= -\mathbf{C}\_{\mathbf{d}}(\lambda)\mathbf{E}\_{\mathbf{d}}(\lambda) \end{aligned} \tag{5}$$

$$\begin{aligned} \text{d}E\_{\text{a}}^{\text{s}}(\lambda) &= -\text{C}\_{\text{s}}(\lambda)\text{E}\_{\text{s}}(\lambda) + \text{B}\_{\text{u}}(\lambda)\text{E}\_{\text{u}}(\lambda) + \text{F}\_{\text{d}}(\lambda)\text{E}\_{\text{d}}(\lambda) \end{aligned} \text{(6)}$$

$$\begin{aligned} \text{d}\mathbf{E}\_{\mathfrak{n}}(\lambda) &= -\mathbf{C}\_{\mathfrak{n}}(\lambda)\mathbf{E}\_{\mathfrak{n}}(\lambda) - \mathbf{B}\_{\mathfrak{k}}(\lambda)\mathbf{E}\_{\mathfrak{k}}(\lambda) - \mathbf{B}\_{\mathfrak{d}}(\lambda)\mathbf{E}\_{\mathfrak{d}}(\lambda) \tag{7} \end{aligned}$$

where Ed(λ) is the spectral downwelling direct irradiance at the bottom of a model layer, Es(λ) is the downwelling diffuse irradiance, and Eu(λ) is the upwelling diffuse irradiance. The attenuation terms C<sup>x</sup> (where x is an indicator for the irradiance pathway d for direct downwelling, s for diffuse downwelling, and u for diffuse upwelling), backscattering terms Bx, and forward scattering F<sup>x</sup> differ for each of the irradiance pathways because of different shape factors (Aas, 1987; Ackleson et al., 1994) and mean cosines

$$\mathbf{C\_d(\lambda) = [a(\lambda) + b(\lambda)]/\underline{\mu}} \tag{8}$$

$$\mathbf{C}\_{\mathbf{s}}(\lambda) = \left[ \mathbf{a}(\lambda) + \mathbf{r}\_{\mathbf{s}} \mathbf{b}\_{\mathbf{b}}(\lambda) \right] / \underline{\mu}\_{\mathbf{s}} \tag{9}$$

$$\mathbf{C}\_{\mathbf{u}}(\lambda) = \mathbf{p}^{\mathbf{b}}(\lambda) / \overline{\mathbf{r}}^{\mathbf{u}} \tag{11}$$

$$\mathbf{B}\_{\mathbf{d}}(\lambda) = \mathbf{p}^{\mathbf{b}}(\lambda) / \overline{\mathbf{r}}^{\mathbf{u}} \tag{12}$$

$$\mathbf{B}\_{\mathbf{s}}(\lambda) = \mathbf{r}\_{\mathbf{s}} \mathbf{p}^{\mathbf{p}}(\lambda) / \underline{\mu}\_{\mathbf{s}} \tag{12}$$

$$\mathbf{B}\_{\mathbf{u}}(\lambda) = \mathbf{r}\_{\mathbf{u}} \mathbf{b}\_{\mathbf{b}}(\lambda) / \underline{\mu}\_{\mathbf{u}} \tag{13}$$

$$F\_{\mathbf{d}}(\lambda) = (1 - \mathbf{b}\_{\mathbf{f}}^{\mathsf{P}}) \mathbf{b}(\mathbf{y}) / \overline{\mathbf{h}}^{\mathsf{q}} \tag{14}$$

where a is the absorption coefficient, b is the total scattering coefficient, b<sup>b</sup> is the backscattering coefficient, b′ b is the ratio of backscattering to total scattering, and µ is the mean cosine (constant for diffuse irradiance, but varies with solar zenith angle for direct irradiance). The shape factors are indicated by the r<sup>x</sup> terms, and are specified as in Ackleson et al. (1994). Equation 5 can be solved a priori, which can then be used as a boundary condition, greatly simplifying the solution of the coupled Equations 6, 7.

OASIM is used in 5 different Ocean General Circulation Models (OGCM): NASA Global Modeling and Assimilation Office (GMAO) Poseidon (Gregg, 2000; Gregg and Casey, 2007; Rousseaux and Gregg, 2015), GMAO MOM4 (present effort), NASA Goddard Institute for Space Studies (GISS) HYCOM (Romanou et al., 2013, 2014), NASA GISS Russell (Romanou et al., 2014), and Massachusetts Institute of Technology (MIT) OGCM (Dutkiewicz et al., 2015). It is used in the coupled oceanatmosphere models of NASA/GMAO-GEOS-5 and NASA/GISS ModelE-H and -R.

### Optical Properties of Ocean Constituents

The coupled NOBM-OASIM model includes optically active constituents, including water, phytoplankton, detritus, PIC, and CDOC each with unique spectral characteristics (**Figure 3**). All are prognostic state variables, with individual sources and sinks. The optical properties of each constituent are taken from various efforts in the peer reviewed literature.

#### Water

The spectral absorption and scattering properties of water have been re-evaluated several times in the past 3 decades. Originally

direct downwelling irradiance, Es is diffuse downwelling, ρ is surface reflectance, Eu is diffuse upwelling irradiance, and LwN is normalized water-leaving radiance. All irradiances and radiances are spectrally resolved at 25 nm for Ed, Es, and Eu for the range 350–700 nm, and at variable resolution for the remainder of the 200 nm–4 um. Size of arrows approximates relative contributions.

reported by Smith and Baker (1981) for the 200–800 nm spectral domain, the data was revised by Pope and Fry (1997) for the range 380–720 nm. Morel et al. (2007) derived new data for absorption and scattering for the spectral range 300– 500 nm using information in the clearest ocean waters of the South Pacific. Finally, Lee et al. (2015) reported new absorption coefficients in the range 350–550 nm.

Water absorption data used here are from Smith and Baker (1981) for 200–300 nm and 730–800 nm, Morel et al. (2007) for 300–350 nm, Lee et al. (2015) for 350–550 nm, Pope and Fry (1997) for 550–720 nm, Circio and Petty (1951) for 800 nm–2.5 µm, and Maul (1985) for 2.5–4 µm. Water scattering are from Smith and Baker (1981) for the range 200–350 nm and 500–800 nm, and Morel et al. (2007) for the spectral range 350–500 nm. We assume no scattering by water for wavelengths longer than 850 nm. The backscattering-to-total scattering ratio ˜bbw for water is 0.5.

#### Phytoplankton

Phytoplankton optical properties are obtained from various sources. Chlorophyll-specific absorption coefficients a<sup>∗</sup> p (λ) are derived by taking reported spectra and normalizing to the absorption at 440 nm [a<sup>∗</sup> p (440)]. Normalized specific absorption spectra [a<sup>∗</sup> p (λ)]N are computed for each of the five phytoplankton groups: diatom and chlorophyte [a<sup>∗</sup> p (λ)]N are taken from Sathyendranath et al. (1987), cyanobacteria from Bricaud et al. (1988), coccolithophores from Morel and Bricaud (1981), and dinoflagellates from Ahn et al. (1992). Then the specific spectral a<sup>∗</sup> p (λ) values are derived using mean values at 440 nm. Diatom a<sup>∗</sup> p (440) represents the mean of 5 observations containing 4 different spp., chlorophytes 6 observations from 4 spp., cyanobacteria 5 observations from 3 spp., coccolithophores 3 observations of 1 sp., and dinoflagellates 1 sp., all from the references listed above. Phaeocystis spp. specific spectral absorption coefficients are taken from Stuart et al. (2000) measurements for the Arctic species Phaeocystis pouchetti.

Phytoplankton specific scattering coefficients b<sup>∗</sup> p (λ) are obtained from measurements at 590 nm and extended to the entire spectrum from specific attenuation coefficients (Bricaud et al., 1988). Diatom and chlorophyte specific scattering coefficients at 590 nm, b<sup>∗</sup> p (590) and b<sup>∗</sup> p (590), are the mean of 5 observations and 6 observations, respectively, from Morel (1987), Bricaud and Morel (1986) and Bricaud et al. (1988). Cyanobacteria b<sup>∗</sup> p (590) is the mean of 8 observations from Morel (1987), Bricaud and Morel (1986), Bricaud et al. (1988) and Ahn et al. (1992). Coccolithophore b<sup>∗</sup> p (590) is derived from the mean of 3 observations from Bricaud and Morel (1986), Bricaud et al. (1988), and Ahn et al. (1992). Dinoflagellate b<sup>∗</sup> p (590) is derived from a single observation by Ahn et al. (1992). We have been unable to locate spectral scattering properties for Phaeocystisspp., so we assume the specific scattering coefficients are the same as diatoms.

We assume no spectral dependence in the backscattering-tototal scattering ratio ˜bbp. Ahn et al. (1992) suggested a spectral dependence for cyanobacteria but generally none for the other groups. Reported values for ˜bbp are 0.002 for diatoms (Morel, 1988), 0.00071 for chlorophytes (Ahn et al., 1992), 0.0032 for cyanobacteria (Ahn et al., 1992), 0.00071 for coccolithophores, 0.0029 for dinoflagellates (both from Morel, 1988), and 0.002 for Phaeocystis spp. (assumed same as diatoms). Some of these values have been questioned based on non-sphericity of many natural phytoplankton populations (Vaillancourt et al., 2004; Whitmire et al., 2010). Based on these results, we increased ˜bbp

for chlorophytes and coccolithophores by a factor of 10, but kept them as reported for diatoms, cyanobacteria, dinoflagellates, and Phaeocystis spp.

### Detritus

Detritus both absorbs and scatters light (**Figures 2**, **3**). Absorption is typically considered an exponential function of wavelength (Roesler et al., 1989; Gallegos et al., 2011)

$$\mathbf{a}\_{\mathbf{d}}(\lambda) = \mathbf{D} \mathbf{a}\_{\mathbf{d}}^{\*} \exp[-\mathcal{S}\_{\mathbf{d}}(\lambda - 440)] \tag{15}$$

where D is the concentration of detritus µg C l−<sup>1</sup> , ad(λ) is the absorption coefficient of detritus (m−<sup>1</sup> ), S<sup>d</sup> = 0.013 nm−<sup>1</sup> (Gallegos et al., 2011) and a∗<sup>d</sup> is the mass-specific absorption coefficient of detritus, which is set to 8.0E-5 m<sup>2</sup> mg−<sup>1</sup> for small detritus as typically found in oceanic waters (Gallegos et al., 2011). Only organic carbon detritus in the model is used for detrital optics.

Detritus scattering is also taken from Gallegos et al. (2011)

$$\mathrm{p\_{q}(\lambda)} = \mathrm{Dp\_{q}^{\*}}(550/\lambda)^{0.5} \tag{16}$$

where b<sup>d</sup> is the total scattering coefficient, b<sup>∗</sup> d is the massspecific scattering coefficient. The scattering coefficient is set as 0.00115 m<sup>2</sup> mg−<sup>1</sup> and the backscattering-to-total scattering ratio ˜bbd is 0.005, as in Gallegos et al. (2011).

#### PIC

PIC optical properties have been evaluated by Gordon et al. (2009). We adopt this formulation for our simulation. PIC scatters irradiance but does not absorb

$$\mathbf{b}\_{\rm PIC}(\lambda) = \text{PLC}\,\mathbf{b}\_{\rm PIC}^\*(\lambda) \tag{17}$$

where PIC is the concentration of PIC (mgC m−<sup>3</sup> ) and b<sup>∗</sup> PIC(λ) is PIC-specific spectral scattering coefficient from Gordon et al. (2009) in units of m<sup>2</sup> mgC−<sup>1</sup> . The backscattering-to-total scattering ratio ˜bbpic is from Balch et al. (1996), using their lower bound of 0.01.

### CDOC

As a dissolved component, CDOC only absorbs and does not scatter. Its spectral absorption is similar to detritus but with a different slope

$$\mathbf{a}\_{\rm CDOC}(\lambda) = \mathbf{a}\_{\rm cdoc}^\* \exp[-\mathbf{S}\_{\rm CDOC}(\lambda - 443)] \tag{18}$$

where a<sup>∗</sup> cdoc is the mass-specific absorption coefficient of CDOC, SCDOC = 0.014 nm−<sup>1</sup> (Bricaud et al., 1981, 2010). SCDOC is in the low end range of observations in surface waters of the Equatorial Atlantic (Andrew et al., 2013) but only slightly lower than those observed in the Mediterranean Sea (Organelli et al., 2014). There are few reports of the mass-specific absorption coefficient of CDOC a<sup>∗</sup> cdoc. We have found three observations in the literature (Carder et al., 1989; Yacobi et al., 2003; Tzortziou et al., 2007). The more recent two are in agreement at 2.98 × 10−<sup>4</sup> m<sup>2</sup> mg−<sup>1</sup> in 4 rivers in Georgia, USA (Yacobi et al., 2003) and 2.78 × 10−<sup>4</sup> m<sup>2</sup> mg−<sup>1</sup> as the mean of 4 stations in the Rhode River, Maryland, USA (Tzortziou et al., 2007). Carder et al. (1989) reported a mean over about nearly an order of magnitude lower in the Gulf of Mexico (4.74 × 10−<sup>5</sup> m<sup>2</sup> mg−<sup>1</sup> ). We choose Yacobi et al. (2003) for our simulation.

### Model Setup

The model is integrated for 30 years from an initial state using climatological atmospheric forcing and atmospheric absorbing gases from Modern-Era Retrospective Analysis for Research and Applications (MERRA; Rienecker et al., 2011). The initial state for nitrate and silicate is taken from the National Centers for Environmental Information World Ocean Atlas (Conkright et al., 2002), dissolved iron is from Fung et al. (2000), and ammonium is arbitrarily set to 0.5 µM. All phytoplankton concentrations are initialized to 0.5 mg m−<sup>3</sup> and the new variables PIC and CDOC initialized to 0 Concentrations (µg l−<sup>1</sup> and µM, respectively). Alkalinity and dissolved inorganic carbon are initialized using Global Data Analysis Project (GLODAP; Key et al., 2004) and dissolved organic carbon is initialized as 0 µM. Cloud and aerosol optical properties for surface irradiance are obtained from MODIS-Aqua. Diurnal variability is represented at the model 30-min time step, but atmospheric optical components are monthly climatologies.

### Error Characterization of the Model

The biological and optical constituents of the NOBM-OASIM model are compared to in situ and/or satellite (MODIS) data where and when available, in order to quantify the bias and uncertainty. Satellite chlorophyll data are compared with the surface level of the model which is 10 m. Phytoplankton groups are compared to in situ data while total chlorophyll, PIC, and aCDOC are compared to satellite estimates. The statistics are aggregated over the 12 basins of the global oceans, mean differences (biases) computed, and then correlations computed over the basins. This provides an estimate of large scale correlations and is very stringent considering the low number of observations. The major ocean basins are divided into 3 main regions, high latitudes (poleward of 40◦ latitude): North Atlantic and Pacific and Southern Ocean, mid-latitudes (between 40◦ and 10◦ latitude): North Central Atlantic and Pacific, South Atlantic, Pacific and Indian, and North Indian, and tropical basins (between ±10◦ latitude): Equatorial Atlantic, Pacific, and Indian.

Phytoplankton groups are represented as relative abundances, and are compared to in situ data on relative abundances. The in situ data is a compilation described by Gregg and Casey (2007) and is available at http://gmao.gsfc.nasa.gov/ research/oceanbiology/data.php. Some changes to the error characterization of Gregg and Casey (2007) include (1) removal of data obtained in the sub-polar tropical Pacific basins during El Niño-Southern Oscillation (ENSO) events and (2) removal of chlorophyte data poleward of 40◦ latitude. ENSO events change the phytoplankton relative abundances, sometimes drastically, as noted in in situ (Bidigare and Ondrusek, 1996; Karl et al., 2001), satellite (Uitz et al., 2010; Masotti et al., 2011; Bricaud et al., 2012), and satellite data assimilation studies (Rousseaux and Gregg, 2012). Regarding the removal of high latitude chlorophyte data, we note that little of the data in our data base have explicitly identified chlorophyte relative abundances. Instead, we assume that all reports of intermediate phytoplankton, e.g., nanoplankton, nano-eukaryotes, etc. are compatible with the role played by chlorophytes in the model. While this assumption still holds, it is likely that such a categorization includes Phaeocystis spp. in the high latitudes, which are common here. Since we now explicitly represent these polar species Phaeocystis, we do not need to use chlorophytes as a proxy for nanoplankton and can avoid the misrepresentations between data and model in the high latitudes that we previously accommodated.

We have been unable to find relative abundance data for Phaeocystis spp., so we use absolute abundances from the MARine Ecosytem DATa (MAREDAT) project (Vogt et al., 2012). The data are reported as µg C l−<sup>1</sup> , which was converted to mg chl m−<sup>3</sup> as reported in the model using a carbon:chlorophyll ratio of 50 g g−<sup>1</sup> . Phaeocystis globosa data are removed from the comparison because our characterization is strictly for polar species of Phaeocystis. We also remove data reported prior to 1975 due to suspect quality. Abundances are logtransformed prior to statistical analysis. We have not been able to obtain global data on dinoflagellate relative abundances and there is not yet a database from MAREDAT, so we are unable to quantify model error statistics on this phytoplankton group.

There is no available satellite data for CDOC that we are aware of, but a satellite product called aCDM (absorption coefficient of Chromophoric Dissolved and Particulate Organic Matter at 443 nm) is available (Garver and Siegel, 1997; Maritorena and Siegel, 2005; Maritorena et al., 2010). We use the products from MODIS-Aqua in this effort. This product represents the absorption of both CDOM and detritus (hence the usage of CDM to minimize confusion about its nature). Siegel et al. (2002) estimated the detrital contribution as (12%). This difference in dissolved organic detrital representations contributes to the low model estimates relative to data reported here, as well as possibly inadequate phytoplankton production of CDOC and/or excessive photolysis. However, the regional correlation in **Table 1** is likely more robust.

Model total chlorophyll is also substantially lower than satellite data (**Table 1**). This is driven by the uneven seasonal sampling of satellites, resulting in little or no coverage in local winter, when chlorophyll concentrations are very low. By observing the oceans only in seasons of higher growth, satellite data overestimates global median chlorophyll.

Satellite primary production data is from the Vertically Generalized Production Model (Behrenfeld and Falkowski, 1997). Data shown in **Table 1** is a climatology from MODIS-Aqua from 2003–2013.

The atmospheric portion of OASIM has been quantitatively evaluated against in situ data (Gregg and Carder, 1990; Gregg and Casey, 2009), so no further analysis is done here. Spectrallyintegrated surface irradiance from OASIM had root mean square (RMS) difference = 20.1 Wm−<sup>2</sup> (about 11%), bias = 1.6 W m−<sup>2</sup> (about 0.8%), regression slope = 1.01 and correlation coefficient = 0.89, when compared to 2322 in situ observations

TABLE 1 | Bias and correlation of major model variables with data sources.


*NS indicates non-significant correlation, P* < *0.05 indicates statistical significance at 95% probability. Values are for basins, where data are averaged over each of the 12 basins prior to comparison, producing N* = *12. Bias is model minus in situ/satellite data. NA indicates no data for comparison found.*

under mixed cloudy and clear skies (Gregg and Casey, 2009). Under clear skies the model has demonstrated a 6.6% RMS with in situ surface observations at 1 nm spectral resolution (Gregg and Carder, 1990).

The ocean component of OASIM has been shown to improve the representation of the deep chlorophyll concentration maximum (Dutkiewicz et al., 2015). Dutkiewicz et al. (2015) also provided maps comparing computed upwelling radiances with some of the MODIS-Aqua bands. Here we present a quantitative comparison of global OASIM normalized upwelling spectral radiances compared to MODIS-Aqua accompanied by statistical characterization. In this evaluation we utilize a different global ocean model (Poseidon; Schopf and Loughe, 1995) with nearly identical NOBM configuration (i.e., not including dinoflagellates and Phaeocystis spp.), and assimilate total chlorophyll, PIC, and aCDM(443) (Maritorena et al., 2010) from MODIS-Aqua. This novel use of data assimilation ensures consistency in underlying optical constituents with observations. This enables us to isolate the OASIM calculations of spectral radiance. The simulation/assimilation/satellite data year for the comparison is 2007. The reason for the ocean circulation model switch is that data assimilation has not yet been developed for GEOS-5 MOM4-NOBM and it is essential for isolating the radiative transfer model evaluation. The normalized upwelling radiance calculation is described in Appendix 1. For this evaluation, we utilize 1 nm spectral resolution data for surface irradiance and ocean optical properties. The 1 nm bands chosen for comparison align with the band centers for MODIS-Aqua. This enables us to match to MODIS bands and reduce impacts of model/data band misalignment in the error characterization.

### Evaluation Scenarios for Spectral and Directional Irradiance

The model is run an additional 10 years of simulation after the initial spinup under different scenarios of irradiance treatment in the water column to evaluate the effects of spectral and directional irradiance. Ten years is sufficient to achieve stability for most of the scenarios (defined as <1% change in global nitrate, chlorophyll, and primary production per year), but the more different the scenario from the control, the longer it can take to achieve this level of stability. This extended run was required only for the test of direct irradiance, which required 20 years to stabilize.

All scenarios are evaluated against a control run, which is the spun-up model with full treatment of directional and spectral irradiance. Each scenario of directional and spectral irradiance is evaluated against this directionally and spectrallyresolved model. We focus here strictly on the changes in ocean biology, specifically nitrate, total chlorophyll, phytoplankton composition, and net primary production.

In all cases the surface irradiance enters the ocean as fully differentiated directionally and spectrally using the atmospheric component of OASIM, which accounts for absorption and scattering by atmospheric constituents (clouds, aerosols, gases) and penetration through the atmosphere-ocean boundary as a function of surface roughness (**Figure 1**). We evaluate the importance of the irradiance nature in the oceans using the ocean component of OASIM (the three-stream model described above, Equations 5–14) by simulating irradiance transmittance involving one of the aspects of the irradiance at a time.

First, directional irradiance is evaluated. All of the surface irradiance, and its spectral quality is conserved. In this case, the light is transmitted through the oceans as purely direct irradiance. The surface diffuse irradiance is added into the direct path as

$$\mathbf{E}\_{\mathbf{d}}(\lambda, \mathbf{0}^{-}) = \mathbf{E}\_{\mathbf{d}}(\lambda, \mathbf{0}^{-}) + \mathbf{E}\_{\mathbf{s}}(\lambda, \mathbf{0}^{-}) \tag{19}$$

and is then zeroed out

$$E\_s(\lambda, 0^-) = 0\tag{20}$$

The irradiance is tracked in the three-stream model as strictly direct irradiance (Equation 5). This enables us to understand the importance of the nature of the light and its effects if treated in the oceans strictly as direct irradiance, without changing the total irradiance entering.

The test of diffuse irradiance is similar, with the roles reversed, i.e., surface direct irradiance is added to the diffuse, and is then zeroed out

$$E^{\mathfrak{z}}(\mathsf{y}, \mathsf{0}^{-}) = E^{\mathfrak{q}}(\mathsf{y}, \mathsf{0}^{-}) + E^{\mathfrak{z}}(\mathsf{y}, \mathsf{0}^{-}) \tag{21}$$

$$E\_{\rm d}(\lambda, 0^{-}) = 0 \tag{22}$$

Now the radiative transfer is computed using Equations 6 and 7, where the terms containing E<sup>d</sup> are zero.

The scenarios thus treat the pathways of light in the oceans differently and are attenuated differently, despite containing the same total irradiance at the surface. The spectral nature of the irradiance is preserved in these scenarios so that we are strictly observing the effects of light direction.

The spectral irradiance scenarios preserve the directional nature of the surface irradiance, with direct and diffuse components explicitly computed in the water column by the OASIM three-stream model. This time, however, we compute only the attenuation (absorption and scattering) of a single spectral band. This is somewhat complex because it is difficult to decide which individual band to select a priori. Thus we test several wavelengths spanning the range of PAR individually. Specifically, we sum all of the irradiance in all the PAR bands into the 400 nm band, then use the attenuation characteristics of 400 nm, i.e., spectral absorption and scattering of water, phytoplankton, detritus, PIC, and CDOC at 400 nm

$$\mathrm{E\_d(400)} = \int\_{350}^{700} \mathrm{Ed}\left(\lambda\right) \,\mathrm{d}\lambda \tag{23}$$

$$\text{E}\_{\text{s}}(400) = \int\_{350}^{700} \text{Es}\left(\lambda\right) \,\text{d}\lambda \tag{24}$$

Then we repeat the process at 450 nm, 500 nm, 550 nm, 600 nm, and finally 650 nm, again moving all the surface spectral irradiance into the band of interest and tracking attenuation in that band. We evaluate changes in ocean biology based on the individual band attenuation compared to the full spectral nature of natural irradiance. In this and the other spectral scenarios, directionality is treated as in the control, i.e., fully resolved from surface inputs including monthly climatological clouds and aerosols.

Finally we evaluate the combined effect of directional and spectral irradiance by choosing the band that most agrees with the control and assuming only diffuse irradiance. The total irradiance entering the ocean is conserved as in all the preceding scenarios.

### RESULTS

### Model Error Characterization

Comparisons of major constituents in NOBM with various in situ and satellite data sets are summarized in **Table 1**. In situ and satellite data sets were available for most of the model tracers, but some, like detritus and dinoflagellates, were not. Bias was represented by the global difference (model minus data, usually expressed as percent) and uncertainty was represented by correlation with significance testing. The model variables were taken from year 30 of the 30-year spinup.

OASIM normalized upwelling radiances were compared with the radiances available from MODIS-Aqua. This was a different circulation model coupled to NOBM in a configuration that has the capability to assimilate satellite data, but was otherwise nearly identical to NOBM used here with MOM4 (i.e., not including dinoflagellates and Phaeocystis spp.). The assimilation ensures that we have evaluated the radiative transfer model, rather than convolving differences in underlying optical constituents. We are characterizing the error of the radiative model here, and it is essential to utilize optical constituent distributions that more closely resemble nature than a free-run model does. We achieve this through a novel use of data assimilation. The global mean bias for the band composite was −0.6 mW cm−<sup>2</sup> µm−<sup>1</sup> sr−<sup>1</sup> (−8.0%) and the correlation was 0.68 (P < 0.05). Bias and correlation for normalized upwelling radiances compared to the 6 MODIS visible bands are provided in **Table 2**.

TABLE 2 | Statistics on the comparison of global normalized water-leaving radiances LwN(λ) from the NOBM-OASIM model and radiances from MODIS-Aqua for 2007.


*SIQR is the semi-interquartile range.*

### Directional Irradiance

When all surface irradiance was assumed to be direct, and light transmittance followed Equation 5, global nitrate concentrations increased >200% (**Table 3**). This was accompanied by a large decline in global net primary production of more than −80% compared to the directionally and spectrally resolved simulation (**Table 3**). Global annual median chlorophyll, however, was only modestly affected by the change in light stream, falling only by −8.3% (**Table 3**).

When all surface irradiance was assumed to be diffuse, and irradiance was computed using Equations 6, 7, global surface nitrate concentrations decreased by nearly 19% and global median chlorophyll concentrations decreased similarly, by 21% (**Table 3**). Regional distributions showed that the

TABLE 3 | Global annual mean nitrate concentrations, global annual median chlorophyll concentrations and global net primary production as a function of directional irradiance.


*Shown are the fully directional (and spectral) model, transmittance in the oceans using only direct irradiance, and transmittance using only diffuse irradiance.*

changes were largest in the sub-tropical and tropical regions, defined here as equator-ward of 40◦ latitude (**Figure 4**). Global net primary production increased slightly in a diffuseonly representation of irradiance (**Table 3**). Phytoplankton relative abundances changed considerably more than PP and nitrate for some groups (**Figure 5**). Chlorophyte relative abundance declined while cyanobacteria, coccolithophores, and dinoflagellates increased. Diatoms and Phaeocystis spp. remained nearly constant regardless of whether the irradiance was treated as directional or as diffuse only.

### Spectral Irradiance

Treatment of irradiance attenuation as non-spectral produced differences with the full spectral model that depended upon the choice of attenuation band (**Figure 6**). Using 400 nm, mean global nitrate concentrations were much lower than the full spectral calculation, a pattern that persisted for the shorter wavelengths through 500 nm. For wavelengths >500 nm, nitrate concentrations were much higher, ranging from 104% at 550 nm to >200% for 600 nm and 650 nm. Global median chlorophyll concentrations tracked nitrate through 550 nm, with lower concentrations than the full spectral model for 400–500 nm, then higher at 550 nm (**Figure 6**). At longer attenuation wavelengths than 550 nm, global median chlorophyll and global mean nitrate diverged, with nitrate higher than control and chlorophyll lower than the control. Attenuation at 500 nm produced the closest

FIGURE 4 | Changes in regional nitrate and chlorophyll as a function of radiative transfer in the oceans tracking only the diffuse component. Changes are relative to the directionally-spectrally resolved model. The high latitudes are poleward of 40◦ latitude (i.e., the North Atlantic, North Pacific, and Southern Ocean). The tropical and sub-tropical basins are in the middle, with the tropical/sub-tropical delineation at 10◦ .

approximation to full spectral treatment for both global nitrate and chlorophyll.

Phytoplankton relative abundances were also sensitive to nonspectral irradiance transmittance in the oceans (**Figure 7**). As with nitrate, chlorophyll and primary production, transmittance at 500 nm was closest to the spectral calculation. But even here there were departures from the spectrally-resolved model: chlorophytes were almost half their relative abundance in the full spectral solution, while coccolithophores and cyanobacteria increased their relative abundances by about 3% each. Diatoms were relatively steady in their proportion of the phytoplankton community regardless of the choice of attenuation. Other than diatoms there were major changes in phytoplankton for attenuation choices greater than 500 nm.

Global net primary production as a function of spectral transmittance exhibited inverse patterns to global annual median chlorophyll (**Figure 8**). Transmittance at 500 nm compared the most favorably to the spectral primary production. Transmittances at wavelengths shorter than 500 nm showed increased primary production, while those longer showed smaller production, with declines well over 50% for 600 nm and above.

### Combined Effect of Directional and Spectral Irradiance

The combined effect of utilizing only diffuse and non-spectral irradiance for estimation of the underwater light field was larger than the individual representations of diffuse only and transmittance at 500 nm (the best case for non-spectral attenuation). Global surface nitrate concentrations were lower (−33.6% compared to the directionally and spectrally-resolved model) as was global surface median chlorophyll (−16.4%) (data not shown). Comparisons with in situ and satellite data (**Figures 9**, **10**) reinforced these results as well. In contrast, total primary production was quite similar to the directionally and spectrally-resolved simulations. Global net primary production was within 2.4 Pg C y−<sup>1</sup> or about 5%, with the non-resolved model higher (data not shown).

### DISCUSSION

Here we have attempted to clarify the effects of neglecting directional and spectral irradiance in simulations of global ocean biological variables, specifically nitrate, total chlorophyll, phytoplankton relative abundances, and net primary production. Beginning with an ocean radiative transfer model that resolves both directional and spectral irradiances, and a companion atmospheric radiative transfer model that represents directional and spectral irradiance deriving from the sun and local atmospheric conditions, including absorbing gases, clouds, and aerosols, we sequentially remove the directional and spectral components, all the while ensuring that the exact same total irradiance begins at the surface, and then report the changes in the above described biological constituents in the oceans.

The results show consequential, but not drastic changes in global ocean biology from not resolving directional irradiance and treating all irradiance as diffuse: approximately 20% reductions in global annual mean nitrate and global annual median chlorophyll. Global net primary production changes are essentially negligible at 4%. However, there are important changes in the phytoplankton relative abundances, with cyanobacteria and coccolithophores increasing their relative abundances from 31 to 40% of the total combined while chlorophytes fall from 16% of the community (second highest behind diatoms) to 4% (second lowest next to Phaeocystis spp.) (**Figure 5**).

The changes in nitrate and chlorophyll due to simulation of exclusively diffuse irradiance are much larger in the tropics (between −10◦ and 10◦ latitude) and sub-tropics than in the high latitudes (poleward of 40◦ latitude). For example, the changes in nitrate and total chlorophyll in the Equatorial Pacific are −80 and −43%, respectively, compared to the Southern Ocean, where changes of −10 and −3%, respectively, are found (**Figure 4**). This is because in the high latitudes surface irradiances is already dominated by diffuse irradiance due to the presence of persistent clouds. Treating all the irradiance as diffuse here has less effect than in the lower latitudes, since there is already less direct irradiance to begin with.

We note that nitrate and total chlorophyll decline (approximately −20% each) while primary production increases by 4% in the diffuse-only scenario (**Table 3**). Diffuse-only transmittance produces more total irradiance in the water column, which increases primary production and diminishes surface nitrate through uptake. These relationships have been noted by Kim et al. (2015) in a study on the effects on CDOM on biology in the global oceans. Higher total irradiance results in higher community metabolic activity in the surface, especially grazing, which has the net effect of reducing both nitrate (through increased uptake) and surface chlorophyll (through grazing). Higher irradiance also produces higher carbon:chlorophyll ratio, further depressing surface chlorophyll.

In this diffuse-only scenario the increase in primary production is partially due to the fact that in the merger of direct and diffuse solar irradiance (Equations 25, 26) the spectral quality of the direct irradiance is retained. This means the full solar spectrum, most relevantly the shorter (blue) wavelengths from the formerly direct irradiance are added to the diffuse stream in the interest of conserving total irradiance at the surface. These blue spectra (both from the diffuse and the additional direct converted to diffuse) photolyze CDOC, reducing its concentration, and consequently stimulate primary production by enhancing the availability of blue irradiance for photosynthesis. This also suggests that diffuse pathways in the oceans provide more ambient light than the multiple angles of the direct irradiance each day. Although this may seem counter-intuitive because clouds are the most important cause of diffuse irradiance, it is important to remember that clouds also cause a reduction in total irradiance, whereas here the full direct+diffuse irradiance is conserved in the simulation, with the

bands, each beginning with the same total surface irradiance as the spectrally-resolved model.

FIGURE 8 | Global net primary production using non-spectral transmittance of irradiance compared to the spectrally-resolved model. Included is the contribution of each phytoplankton component to the total.

FIGURE 9 | Global distribution of nitrate from the directionally and spectrally-resolved model, in situ data and the diffuse-only, 500 nm non-spectral simulation and the difference. Statistics on global distributions compared to *in situ* data are shown in the plots. The correlation for both models is statistically significant at *P* < 0.05.

clear-sky direct added to the cloudy and clear diffuse. This is clearly unreasonable in nature but here we are testing modeling approaches for representing the ocean light field. A model that does not consider irradiance directionality but is given the correct total surface irradiance would be susceptible to the scenario described here.

Ocean biological concentrations and primary production are sensitive to the nature of spectral irradiance. The magnitude of the behavior of ocean biology to simulations using non-spectral radiative transfer is dependent upon which wavelength is selected. The shorter (bluer) wavelengths are associated with higher primary production and consequently lower nitrate and chlorophyll (**Figure 6**). The changes to nitrate and chlorophyll track one another for non-spectral transmittance in these bands. The best comparison with the fully spectrally-resolved model occurs at 500 nm, but even here there are substantial changes in phytoplankton composition, with reductions in the relative abundance of chlorophytes compensated by increases in cyanobacteria and coccolithophores (**Figure 7**). This suggests, however, that there is potentially an optimal choice for nonspectral transmittance, at least for global representations, and it likely lies near 500 nm. This in turn suggests support for use of diffuse attenuation coefficient for PAR, which is derived from the attenuation coefficient at 490 nm (Kd490) (Morel et al., 2007) or using Kd490 itself (e.g., Lee et al., 2005).

Non-spectral radiative transfer using bands higher than 550 nm show much larger impacts on primary production, nitrate, and chlorophyll. Here the association between nitrate and chlorophyll diverges, with nitrate increasing with increasing wavelength and chlorophyll decreasing.

Relative abundances of phytoplankton are highly sensitive to non-spectral choices of transmittance wavelength (**Figure 7**). To understand why, we refer to **Figure 3**, which shows the spectral dependences of the ocean optical constituents. The shorter (blue) wavelengths are where CDOC absorption is strongest, and using these bands for non-spectral attenuation maximizes the absorption by this constituent. It also maximizes the photolysis of CDOC (Equations 3, 4, and **Figure 3**), which in turn leads to more blue light available for phytoplankton absorption and growth. CDOC global concentrations for the 400 nm transmittance scenario are 46% lower than the spectrallyresolved case (data not shown). This explains the elevated primary production observed in this spectral region (**Figure 8**). The remaining blue to green light available after absorption by CDOC favors cyanobacteria and coccolithophores, which have strong specific spectral absorption in this region (**Figure 3**), facilitating their growth and increased relative abundances compared to chlorophytes. This explains the changes observed in relative abundances (**Figure 7**). As we approach longer wavelengths, water absorption dominates, extinguishing available light for all phytoplankton and leading to high nutrient availability due to reduced primary production. Additionally, CDOC increases because it is a poor absorber in red light and consequently its photolysis is reduced, further exacerbating the irradiance deficit. In this case, the phytoplankton groups with the fastest growing capabilities in nutrient-replenished conditions are advantaged over the other types such as cyanobacteria and coccolithophores, which are better suited for utilizing nutrients at low concentrations.

The combined diffuse-only/non-spectral simulation with 500 nm as the attenuation wavelength does not show compensation, but rather exacerbation of the differences observed in the individual diffuse and spectral scenarios. Nitrate differences exceed −30% (non-directional/spectral low) and chlorophyll is lower by −16%. Global chlorophyll even loses significance in the correlation with satellite data, in contrast to the directionallyspectrally-resolved model (**Figure 10**). Primary production is only modestly higher at 5.1%. Chlorophytes are the most impacted, dropping their relative abundances from 15.6% in the resolved model to only 2.3%, while cyanobacteria and coccolithophores increase. This suggests that changes in irradiance simulation excluding diffuse/direct differentiation and full spectral behavior spur a community functional switch from light-limitation to nutrient limitation, shifting phytoplankton groups from the high nitrate users like chlorophytes to the efficient users like cyanobacteria and coccolithophores. Although diatoms are the most demanding for nitrate, they are relatively unaffected by changes in the light fields by omitting directional and spectral light, because they are most abundant in the nutrient-rich regions to begin with (e.g., high latitudes and upwelling regions).

We emphasize that the differences using non-directional and non-spectral simulations compared to the three-stream model and optical characterizations used here does not imply that the resolved model is correct. The OASIM model and characterizations have been evaluated in several contexts, as explained in the Methods, but we have not and most likely cannot evaluate the model in all scenarios. We do assert that it is more comprehensive in its representations of directional and spectral irradiance and therefore technically more realistic than models that do not incorporate these characteristics. Natural irradiance is directional and spectral. A model that accounts for these characteristics of light is therefore at least nominally representative. However, this does not necessarily mean the model here is accurate or even complete. There are several optical constituents in the real oceans that are not considered here, such as suspended sediments/minerals, viruses and bacteria (Balch et al., 2002; Stramski et al., 2004), suspended desert dust (Wozniak and Stramski, 2004), and mycosporine-like amino acids (Moisan and Mitchell, 2001), as well as unaccounted effects such as polarization, bi-directionality among others.

We are unable to directly compare the model described here with more typical PAR/shortwave-diffuse attenuation coefficient models because of our inclusion of CDOC. The majority of models using diffuse attenuation coefficient only represent attenuation by water and phytoplankton, which are sometimes taken as climatologies from satellite ocean color. There is growing recognition of the importance of CDOC for ocean biological modeling (e.g., Xiu and Chai, 2014; Dutkiewicz et al., 2015; Kim et al., 2015), building on the pioneering work of Bissett et al. (1999). In our representation, CDOC not only affects the irradiance availability but is also photolyzed by spectral irradiance. Any comparison with other types of models requires us to make significant assumptions about how to handle CDOC photolysis and production. The assumptions themselves would likely be a more important consideration than the presence or absence of directionally and spectrally-resolved radiative transfer.

Our purpose here is to assist modelers in understanding and quantifying the advantages and disadvantages of explicitly incorporating directional and spectral effects of radiative transfer in models of ocean biology. Many models use a representation of PAR or shortwave radiation at the surface, and propagate irradiance as a function of an empirical or analytical diffuse attenuation coefficient using Beer-Lambert's law or another nonspectral, non-directional approach. This is especially true of the global models. It is true that many of these models also obtain very good representations of ocean biology and primary production (e.g., Moore et al., 2004; Dunne et al., 2013). It may be that the parameterization of the models and the radiative transfer implicitly incorporate the dominant effects required for simulation of ocean biology. However, it is also possible that missing explicit directional and spectral aspects of oceanic radiative transfer may impact our ability to simulate climate change scenarios where, for example, changes in clouds may lead to changes in direct and diffuse composition of surface irradiance, thereby affecting evaluations of future phytoplankton and carbon representations and feedbacks. This effort is intended to help modelers quantitatively evaluate the importance of the complexity of ocean radiative transfer and help inform decisions on future model developments.

### REFERENCES


### AUTHOR CONTRIBUTIONS

All authors listed, have made substantial, direct and intellectual contribution to the work, and approved it for publication.

### ACKNOWLEDGMENTS

We thank the NASA/MERRA Project, the MODIS Ocean Color and Atmosphere Processing Teams, the MAREDAT data project, and the algorithm developers for PIC and aCDM. We thank Venetia Stuart, Bedford Institute of Oceanography, for providing Phaeocystis spp. spectral absorption coefficient data. We thank two reviewers for comments and suggestions. This work was supported by NASA PACE, S-NPP, and MAP Programs.

### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fmars. 2016.00240/full#supplementary-material


dissolved organic carbon. Limnol. Oceanogr. 59, 182–194. doi: 10.4319/lo.2014. 59.1.0182


darkness and freezing. Proc. R. Soc. B Biol. Sci. 276, 81–90. doi: 10.1098/rspb. 2008.0598


of light quantity. Proc. R. Soc. Lond. 227, 367–380. doi: 10.1098/rspb.19 86.0027


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The reviewer CM and handling Editor declared their shared affiliation, and the handling Editor states that the process nevertheless met the standards of a fair and objective review.

Copyright © 2016 Gregg and Rousseaux. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Copepod Life Strategy and Population Viability in Response to Prey Timing and Temperature: Testing a New Model across Latitude, Time, and the Size Spectrum

#### Neil S. Banas <sup>1</sup> \*, Eva F. Møller <sup>2</sup> , Torkel G. Nielsen<sup>3</sup> and Lisa B. Eisner <sup>4</sup>

*<sup>1</sup> Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK, <sup>2</sup> Department of Bioscience, Arctic Research Center, Aarhus University, Roskilde, Denmark, <sup>3</sup> Section for Ocean Ecology and Climate, National Institute of Aquatic Resources, Technical University of Denmark, Charlottenlund, Denmark, <sup>4</sup> NOAA Fisheries, Alaska Fisheries Science Center, Seattle, WA, USA*

#### *Edited by:*

*Dag Lorents Aksnes, University of Bergen, Norway*

#### *Reviewed by:*

*Øyvind Fiksen, University of Bergen, Norway Nicholas R. Record, Bigelow Laboratory for Ocean Sciences, USA*

> *\*Correspondence: Neil S. Banas neil.banas@strath.ac.uk*

#### *Specialty section:*

*This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Marine Science*

*Received: 03 June 2016 Accepted: 27 October 2016 Published: 15 November 2016*

#### *Citation:*

*Banas NS, Møller EF, Nielsen TG and Eisner LB (2016) Copepod Life Strategy and Population Viability in Response to Prey Timing and Temperature: Testing a New Model across Latitude, Time, and the Size Spectrum. Front. Mar. Sci. 3:225. doi: 10.3389/fmars.2016.00225* A new model ("Coltrane": Copepod Life-history Traits and Adaptation to Novel Environments) describes environmental controls on copepod populations via (1) phenology and life history and (2) temperature and energy budgets in a unified framework. The model tracks a cohort of copepods spawned on a given date using a set of coupled equations for structural and reserve biomass, developmental stage, and survivorship, similar to many other individual-based models. It then analyzes a family of cases varying spawning date over the year to produce population-level results, and families of cases varying one or more traits to produce community-level results. In an idealized globalscale testbed, the model correctly predicts life strategies in large *Calanus* spp. ranging from multiple generations per year to multiple years per generation. In a Bering Sea testbed, the model replicates the dramatic variability in the abundance of *Calanus glacialis/marshallae* observed between warm and cold years of the 2000s, and indicates that prey phenology linked to sea ice is a more important driver than temperature *per se*. In a Disko Bay, West Greenland testbed, the model predicts the viability of a spectrum of large-copepod strategies from income breeders with a adult size ∼100 µgC reproducing once per year through capital breeders with an adult size >1000 µgC with a multiple-year life cycle. This spectrum corresponds closely to the observed life histories and physiology of local populations of *Calanus finmarchicus*, *C. glacialis*, and *Calanus hyperboreus*. Together, these complementary initial experiments demonstrate that many patterns in copepod community composition and productivity can be predicted from only a few key constraints on the individual energy budget: the total energy available in a given environment per year; the energy and time required to build an adult body; the metabolic and predation penalties for taking too long to reproduce; and the size and temperature dependence of the vital rates involved.

Keywords: zooplankton, copepod, life history, diversity, biogeography, modeling, community ecology, Arctic

### 1. INTRODUCTION

Calanoid copepods occupy a crucial position in marine food webs, the dominant mesozooplankton in many temperate and polar systems, important to packaging of microbial production in a form accessible to higher predators. They also represent the point at which biogeochemical processes, and numerical approaches like NPZ (nutrient–phytoplankton–zooplankton) models, start to be significantly modulated by life-history and behavioral constraints. The population- and community-level response of copepods to environmental change (temperature, prey availability, seasonality) thus forms a crucial filter lying between the biogeochemical impacts of climate change on primary production patterns and the food-web impacts that follow.

Across many scales in many systems, the response of fish, seabirds, and marine mammals to climate change has been observed, or hypothesized, to follow copepod community composition more closely than it follows total copepod or total zooplankton production. Examples include interannual variation in pollock recruitment in the Eastern Bering Sea (Coyle et al., 2011; Eisner et al., 2014), interdecadal fluctuations in salmon marine survival across the Northeast Pacific (Mantua et al., 1997; Hooff and Peterson, 2006; Burke et al., 2013), and long-term trends in forage fish and seabird abundance in the North Sea (Beaugrand and Kirby, 2010; MacDonald et al., 2015). These cases can be all be schematized as following the "junk food" hypothesis (Österblom et al., 2008) in which the crucial axis of variation is not between high and low total prey productivity, but rather between high and low relative abundance of large, lipid-rich prey taxa.

Calanoid copepods range in adult body size by more than two orders of magnitude, from <10 to >1000µg C. Lipid content is likewise quite variable (Kattner and Hagen, 2009), even among congeneric species in a single environment (Swalethorp et al., 2011). Many but not all species enter a seasonal period of diapause in deep water, in which they do not feed and basal metabolism is reduced to ∼1/4 of what it is during active periods (Maps et al., 2014). Reproductive strategies include both income breeding (egg production fueled by ingestion of fresh prey during phytoplankton blooms) and capital breeding (egg production fueled by stored lipids in winter), as well as hybrids between the two strategies (Hirche and Kattner, 1993; Daase et al., 2013). Generation lengths vary from several weeks to several years.

These life-history traits (generation length, diapause, reproductive strategy, and annual routine more generally) constitute the mechanistic link between environment and the quality of the copepod community as prey (i.e., body size and composition). Lipid storage, coupled to diapause in deep water, is a strategy for surviving the winter in environments where winter foraging is not cost-effective energetically; and just as important, it provides energetic free scope for optimizing reproductive timing relative to prey availability (Falk-Petersen et al., 2009; Varpe et al., 2009). Lipid storage is tied to climate via temperature (which determines the rate at which an animal burns through its reserves during winter and rates of ingestion, growth, and development year-round) and phenology (i.e., timing of the copepods phytoplankton and protist prey: Mackas et al., 2012). This logic provides a route by which the energetics of fish, seabird, and mammal foraging are tied to temperature and phytoplankton phenology via the tradeoffs governing copepod life history.

There is likely a gap, then, between the focus of conventional oceanographic plankton models—total productivity by functional group—and the copepod traits of greatest importance to predators. A number of dynamical-modeling studies have attempted to fill this gap by modeling the copepods species by species in relation to climate forcing, often in an individualbased-model (IBM) framework (Miller et al., 2002; Ji et al., 2012; Maar et al., 2013; Wilson et al., 2016). There are two key limitations to the species-by-species approach, however. First, it is difficult to see how it can scale or generalize to the community level, given that our empirical information on the physiology and life history of the copepods is a patchwork, and realistically will always remain so. Second, it does not address the question of adaptation, either on the individual or species level. As individuals make use of their phenotypic plasticity in behavior, physiology, and life cycle, and as natural selection acts on existing species and subpopulations, it is likely that shifts in the biogeography of copepod traits such as size, lipid content, and life history pattern will not move in lockstep with the biogeography of existing species (Barton et al., 2013). Indeed, subpopulations of individual copepod species display so much life-history and physiological diversity (Heath et al., 2004; Daase et al., 2013) that it is not clear what the basic units of a general species-based model would even be. Observations of hybridization among species (Parent et al., 2015) only underscore this problem.

This paper presents a proof-of-concept for a trait-based, as opposed to species-based, copepod IBM, intended for eventual use in problems linking planktivores to climate and environment on global or regional scales. Record et al. (2013) presented a copepod community IBM in which explicit competition via a genetic algorithm was used to pick community assemblages out of a trait-based metacommunity along a latitudinal gradient. That study was concerned mainly with the emergent behavior of a very complex model system (predation-structured competition along with the interacting effects of six variable traits). In contrast, we have included as few explicitly variable traits as possible, guided by a strategic set of heuristic and quantitative comparisons with data (**Figure 1**). The balance point we have sought in this phase of work is the lightest-weight representation of diversity and plasticity that allows the model to (1) generate a realistic landscape of competitors in a single environment, (2) correctly predict fitness fluctuations in one population as a function of habitat, and (3) give sensible results over a wide biogeographic range.

The first of these criteria, captured by a Disko Bay, West Greenland model experiment (**Figure 1**, Section 3.4) is central to the goal of eventually allowing climate-to-copepod model studies to replace hand-picked sets of fixed types with a trait continuum. The second and third criteria (captured by a Bering Sea hindcast experiment and an heuristic, idealized biogeographic experiment: **Figure 1**, Sections 3.2, 3.3) provide complementary constraints on the parameterization of individual energetics, and help

distinguish the effects of temperature and prey seasonality. As we will show, these initial experiments suggest a general hypothesis: that the viability of the calanoid community, at least near its highlatitude limit, is much more sensitive to prey abundance and phenology than to temperature.

## 2. MODEL DESCRIPTION

### 2.1. General Approach

The model introduced here is "Coltrane" (Copepod Life-history Traits and Adaptation to New Environments) version 1.0. Matlab source code is available at https://github.com/neilbanas/coltrane. An overview of the model structure is shown in **Figure 2**.

Like many individual-based models, Coltrane represents the time-evolution of one cohort of a clonal population, all bearing the same traits and spawned on the same date t0, with a set of ODEs. The state variables describing a cohort are relative developmental stage D, where D = 0 represents a newly spawned egg and D = 1 an adult; survivorship N, the fraction of initially spawned individuals that remain after some amount of cumulative predation mortality; structural biomass per individual S, and "potential" or "free scope" ϕ, which represents all net energy gain not committed to structure, or equivalently, the combination of internal energy reserves and eggs already produced. Combining reserves and eggs into one pool in this way lets us cleanly separate results that depend only on the fundamental energy budget (gain from ingestion, loss to metabolism, and energy required to build somatic structure) from results that depend on particular assumptions about egg production (costs, cues, and strategies). An alternate form of the model explicitly divides ϕ into internal reserves R and egg production rate E: the simpler model without this distinction will be called the "potential" or ϕ model and the fuller version the "egg/reserve" or ER model.

The ϕ and ER models take different approaches to generating population-level results from this cohort model, as explained in detail below (Section 2.4). In both cases, the logic changes from the simple forward time-integration at the cohort level: one runs the cohort model for all possible spawning dates t0, retroactively determines which spawning dates would prove optimal or sustainable, and considers the cohort time series from those t<sup>0</sup> values, appropriately weighted, to constitute the model solution (Section 2.4). The biological logic here is similar to the backwards-in-time dynamical optimization method frequently used in studies of optimal annual routines (Houston et al., 1993; Varpe et al., 2007), although our solving method is quite different and less exact. This is a compromise with the eventual goal of coupling Coltrane to oceanographic models as a spatially explicit IBM.

Communities are generated in Coltrane 1.0 simply by running families of cases of the population-level model that vary one or more traits. Treating coexisting populations as uncoupled vastly simplifies the interpretation of the landscape of viable strategies in a given environment, or the fundamental niche of a particular trait combination, our primary modes of analysis. At the same time, it tightly restricts our choices regarding the formulation of predation mortality. In reality, coupling through shared predators can rival bottom-up effects as a determinant of community structure (Holt et al., 1994; Chesson, 2000; Record et al., 2013, 2014), and we expect that many potential applications of this model would require that this be better represented. In the present study, we have taken the minimalist, incrementalist approach of imposing the simplest possible form of predation mortality—a linear function, with scalings that closely mirror the growth and development functions (Section 2.2)—and restricting

the terms of analysis. In particular, we will describe model output in terms of trait correlations, optimality, and viability, but not in terms of absolute copepod biomass or abundance. Likewise, while some plankton models resolve the process of adaptation explicitly (Clark et al., 2013), we address it only in the indirect sense of mapping the viable and optimal regions of the strategy landscape. This approach is less mechanistic but also helpfully agnostic about whether adaptation in the copepods arises through individual plasticity, species composition shifts, or natural selection per se.

An environment in Coltrane 1.0 is defined by annual cycles of three variables, total concentration of phytoplankton/microzooplankton prey P, surface temperature T0, and deep temperature Td. At present, these annual cycles are assumed to be perfectly repeatable, so that a "viable" strategy can be defined as a set of traits that lead to annual egg production above the replacement rate, given P, T0, and T<sup>d</sup> as functions of yearday t. The level of predation mortality (Section 2.2.4) might also be viewed as an environmental characteristic.

## 2.2. Time Evolution of One Cohort

#### 2.2.1. Ontogenetic Development

Calanoid copepods have a determinate developmental sequence, comprising the embryonic period, six naupliiar stages (N1–6), five copepodid stages (C1–5), and adulthood (C6). Similar to Maps et al. (2012), conversions between relative developmental stage D and the actual 13-stage sequence have been done using relative stage durations for C. finmarchicus from Campbell et al. (2001), which appear to be appropriate for other Calanus spp. with the proviso that C5 duration is particularly variable and strategy-dependent. Development in the model follows

$$\frac{dD}{dt} = u, \ D \le 1 \tag{1}$$

where developmental rate u is

and

$$
\mu = a \, q\_d \, \sigma \, u\_0 \tag{2}
$$

$$q\_d \equiv Q\_d^{T/10^\circ \text{C}} \tag{3}$$

$$T = a \ T\_0 + (1 - a) \ T\_d \tag{4}$$

$$
\sigma = \frac{P}{K\_s + P} \tag{5}
$$

All variables and parameters are defined in **Table 1**. Activity level a is, in this version of the model, a two-state switch calculated at each time step, 1 during active feeding and 0 during diapause. The temperature-dependent factor q<sup>d</sup> describes a power-law response with a Q<sup>10</sup> of Qd, where temperature is assumed to be T<sup>0</sup> during active feeding and T<sup>d</sup> during diapause. We use the Q<sup>10</sup> functional form for convenience: the differences between this and the leading alternatives (Belehrádek, Arrhenius: ˇ Forster et al., 2011; Record et al., 2012) appear to be small compared with interspecies differences in this study (Banas and Campbell, 2016). Prey saturation σ is a simple Michaelis–Menten function with half-saturation K<sup>s</sup> . The parameter u0, the development rate corrected to 0◦C, was found by Banas and Campbell (2016) to be the primary trait responsible for differences in adult body size among Calanus spp. and other calanoids >50 µg C adult size, although not at a broader scale of diversity. It represents the aspect of development-rate variation that we interpret to be a strategy choice as opposed to a physiological or thermodynamic constraint.

#### 2.2.2. Energy Gain and Loss

The two energy stores S (structure) and ϕ (reserves/potential) follow

$$\frac{d\mathcal{S}}{dt} = f\_{\mathcal{S}} \mathcal{G} \tag{6}$$

$$\frac{d\varphi}{dt} = (1 - f\_s)G\mathcal{S}\tag{7}$$

where G is net energy gain (ingestion minus metabolic losses). When net gain is positive, it is allocated between structure and potential according to the factor f<sup>s</sup> , which commits net gain entirely to structure before a developmental point D<sup>s</sup> , entirely to potential during adulthood, and to a combination of them in between:

$$f\_s = \begin{cases} 1, & D < D\_s \\ \frac{1 - D}{1 - D\_s}, & D\_s \le D \le 1 \\ 0, & D = 1 \end{cases} \tag{8}$$

When G ≤ 0, the deficit is taken entirely from reserves: f<sup>s</sup> = 0.

Before the first feeding stage (D < D<sup>f</sup> ) we assume G = 0 for simplicity. After feeding begins,

$$G = r\_a I - M\tag{9}$$

where ingestion I and metabolic loss M are given by

$$I = \; a \; \sigma \; q\_{\emptyset} \; I\_0 \; S^{\theta - 1} \tag{10}$$

$$M = a^\star \, r\_m \, q\_\p \, I\_0 \, \mathcal{S}^{\theta - 1} \tag{11}$$

and r<sup>a</sup> is an assimilation efficiency. Ingestion follows a Kleiber's Law-like dependence on structural body mass S, with θ = 0.7 (Kleiber, 1932; Saiz and Calbet, 2007). I<sup>0</sup> is specific ingestion rate at saturating prey concentration, T = 0 ◦C, and S = 1 µg C. This is modulated by the activity switch a and prey saturation σ as in Equation (2), and a power-law temperature response for growth

$$q\_{\mathfrak{g}} = \mathcal{Q}\_{\mathfrak{g}}^{T/10^{\circ}\mathcal{C}} \tag{12}$$

which is parallel to that for development (qd) but with a different Q10. Q<sup>10</sup> values have been found to vary among copepod species but Banas and Campbell (2016) argue that common values derived from a fit across community-level data are more appropriate for comparing species near their thermal optima. We use Q<sup>g</sup> = 2.5 and Q<sup>d</sup> = 3.0, as an approximation to the best-fit complex allometric curves reported by Forster et al. (2011).

Energy loss to metabolism M follows the same temperature and size scalings. The factor r<sup>m</sup> is the ratio of metabolism to ingestion when prey is saturating. Unlike development and ingestion, which are assumed zero during diapause, M during diapause is nonzero but reduced to a basal fraction r<sup>b</sup> ≈ 1/4 (Maps et al., 2014):

$$a^\star = r\_b + (1 - r\_b)a \tag{13}$$

Note that in this formalism, gross growth efficiency ǫ becomes

$$
\epsilon = \frac{G}{I} = r\_a - \frac{r\_m}{\sigma} \tag{14}
$$

when a = 1. We have set r<sup>m</sup> = 0.14 such that ǫ = 0 when P = 1/4 K<sup>s</sup> .

#### 2.2.3. Starvation

Potential ϕ is allowed to run modestly negative, to represent consumption of body structure during starvation conditions. A cohort is terminated by starvation if

$$
\varphi < -r\_{star}\mathcal{S} \tag{15}
$$

where in this study rstarv = 0.1. A convenient numerical implementation of this scheme is to integrate S implicitly so that it is guaranteed > 0, and to integrate ϕ explicitly so that it is allowed to change sign, with no change of dynamics at ϕ = 0.

#### 2.2.4. Predation Mortality

Predation mortality is assumed to have the same dependence on temperature and body size as ingestion, metabolism, and net gain (Hirst and Kiørboe, 2002). Survivorship N is set to 1 initially and decreases according to

$$\frac{d(\ln N)}{dt} = -m\tag{16}$$

(it is convenient to calculate the numerical solution using ln N rather than N as the state variable, since values become extremely small). The mortality rate m is

$$m = a \, q\_{\text{g}} \, \text{S}^{\theta - 1} \, \text{m}\_0 \tag{17}$$

#### TABLE 1 | Parameter values and other symbols used in the manuscript.


such that that predation pressure relative to energy gain is encapsulated in a single parameter m0. In practice m<sup>0</sup> is a tuning parameter but we can solve for the value that would lead to an approximate equilibrium between growth and mortality. The condition

$$\frac{1}{\text{NS}} \frac{d(\text{NS})}{dt} = 0 \tag{18}$$

is equivalent, by Equations (6) and (16), to

$$m = f\_s G \tag{19}$$

and with a = 1 this becomes

$$\frac{m\_0}{I\_0} = (r\_a \sigma - r\_m) f\_s \tag{20}$$

Averaging f<sup>s</sup> over the maturation period 0 ≤ D ≤ 1 with D<sup>s</sup> = 0.35, and assuming σ ≈ 2/3 on average for an organism that has aligned its development with the productive season, gives m<sup>0</sup> ≈ 0.2 I0. This is the default level of predation in the model except where otherwise specified.

#### 2.2.5. Activity Level and Diapause

Modulation of activity level a has been treated as simply as possible, using a "myopic" criterion that considers only the instantaneous energy budget, rather than an optimization over the annual routine or lifetime (Sainmont et al., 2015). Furthermore, we treat a as a binary switch—diapause or full foraging activity—although intermediate overwintering states have been sometimes observed, e.g., C. glacialis/marshallae on the Eastern Bering Sea shelf in November (Campbell, personal communication). In the present model, we set a = 0 if D > Ddia (the stage at which diapause first becomes possible) and the environment is such that total population energy gain

$$\frac{d}{dt}(\varphi + \mathcal{S})N = \text{(GS)}N\tag{21}$$

would be higher under diapause. We can derive an expression for the threshhold at which this occurs by maximizing population energy gain as a function of a. When d/da of GSN is positive, active foraging a = 1 is the optimal instantaneous strategy and when it is negative, a = 0 is optimal. The threshhold

$$\frac{d}{da}(\text{GSN}) = 0\tag{22}$$

can be rearranged to give a critical prey-saturation level

$$
\sigma\_{crit} = \frac{r\_m(1 - r\_b)}{r\_a} + \frac{C\_{dia}}{r\_a} \frac{m\_0}{I\_0} \tag{23}
$$

where Cdia = 1 + ϕ/S. The first term in Equation (23) can be derived more simply by setting dG/da = 0, a criterion based on ingestion and metabolism alone. The second term adjusts this criterion by discouraging foraging at marginal prey concentrations when predation is high. A third, temperaturedependent term has been neglected. The second, mortalitydependent term tends to produce unrealistic, rapid oscillations in which the copepods briefly "top up" on prey and then hide in a brief "diapause" to burn them. It is unclear whether this model behavior is a mathematical artifact—a limitation of combining actual lipid reserves and potential egg production into a single state variable—or whether it suggests that under some conditions the optimal level of foraging is intermediate between full activity and none. Incorporating a more mechanistic treatment of optimal foraging (Visser and Fiksen, 2013) and allowing a to vary continuously would address this. In this study, we have eliminated the phenomenon by approximating Cdia as

$$C\_{dia} = \max\left[0, \ 1 + \min\left(r\_{\varphi}^{\max}, \frac{\varphi}{S}\right)\right] \tag{24}$$

where r max <sup>ϕ</sup> = 1.5.

### 2.3. Eggs and Potential Eggs

The evolution equations above Equations (1), (6), (7), (16) specify the development of one cohort in the ϕ model. If this model is elaborated with an explicit scheme for calculating total egg production over time E(t), then it is possible to define R(t), individual storage/reserve biomass, and interpret R as a state variable and ϕ as a derived quantity. The relationship between the two is

$$\frac{dR}{dt} = (1 - f\_s)GS - E \tag{25}$$

$$
\varphi(t) = R(t) + \int\_{t\_0}^{t} E(t') \, dt' \tag{26}
$$

Thus, ϕ tracks the reserves that an animal would have remaining if it had not previously started egg production. This is a useful metric for optimizing reproductive timing, as we will show (Section 2.4).

Any explicit expression for E(t) allows Equation (25) to replace Equation (7). In one model experiment below (Section 3.4), we use the following scheme: E(t) is the sum of income egg production Einc and capital egg production Ecap, which are 0 until maturity is reached (D = 1) and an additional timing threshhold has been passed (t > tegg ). Past those threshholds, they are calculated as

$$\begin{array}{ll} E\_{\text{inc}} = G, & G > 0 \\ E\_{\text{cap}} = E\_{\text{max}} - E\_{\text{inc}}, \; D > 0 \end{array} \tag{27}$$

where Emax is a maximum egg production rate which we assume to be equal to food-saturated assimilation:

$$E\_{\text{max}} = r\_a \, q\_\text{g } \, I\_0 \, \text{S}^\theta \tag{28}$$

Thus, the trait tegg determines whether egg production begins immediately upon maturation (if tegg is prior to the date on which D reaches 1) or after some additional delay. Instead of tegg , expressed in terms of calendar day, one could introduce the same timing freedom through a trait linked to light, an ontogenetic clock that continues past D = 1, or a more subtle physiological scheme. However, since we run a complete spectrum of trait values in each environmental case, it is not important to the results how the delay is formulated, provided we only compare model output, rather than actual trait values, across cases.

### 2.4. Population-Level Response

A population-level simulation (**Figure 2**) consists of integrating either the ϕ model (Equations 1, 6, 7, 16) or ER model (Equations 1, 6, 16, 25) for a full annual cycle of spawning dates t0, and then identifying optimal and viable values of t<sup>0</sup> in terms of the egg fitness F, future egg production per egg (Varpe et al., 2007). Calculating a time series of F in the ϕ model requires an estimate of individual egg biomass W<sup>e</sup> in order to convert ϕ(t) from carbon units into a number of eggs, and a similar issue arises in the ER population model. Thus, a digression on the determination of W<sup>e</sup> is required.

#### 2.4.1. Egg and Adult Size

The problem of estimating W<sup>e</sup> can be replaced by the problem of estimating adult size W<sup>a</sup> using the empirical relationship for broadcast spawners determined by Kiørboe and Sabatini (1995):

$$
\ln W\_e \approx \ln r\_{ea} + \theta\_{ea} \ln W\_a \tag{29}
$$

where rea = 0.013, θea = 0.62 (In the ER model, W<sup>a</sup> ≡ S + R at D = 1, but in the ϕ model we approximate it as S alone for simplicity). Adult size itself is an important trait for the model to predict, but the controls on it are rather buried in the model formulation above. Banas and Campbell (2016) describe a theory relating body size to the ratio of development rate to growth rate based on a review of laboratory data for copepods with adult body sizes 0.3–2000 µgC. In our notation, their model can be derived as follows: if we approximate Equations (6), (7) in terms of a single biomass variable as

$$\frac{dW}{dt} = \epsilon^{\prime} \, q\_{\S} \, I\_{0} \, \, W^{\theta}, \,\, D \ge D\_{f} \tag{30}$$

then integrating from spawning to maturation gives

$$\frac{1}{1-\theta} W^{1-\theta} \Big|\_{D=0}^{D=1} = \left(1 - D\_f\right) \epsilon' \left. q\_\xi \right|\_0 \frac{1}{\mu} \tag{31}$$

since u is the reciprocal of the total development time. Growth rate has been written in terms of I<sup>0</sup> and an effective growth efficiency over the development period ǫ ′ . If we assume that egg biomass W<sup>e</sup> = W|D=<sup>0</sup> is much smaller than W<sup>a</sup> = W|D=1, then combining Equation (31) with Equation (2) gives

$$W\_a \approx \left[ (1 - \theta) \left( 1 - D\_f \right) \; \epsilon' \left( \frac{Q\_\mathcal{g}}{Q\_d} \right)^{T/10^\circ \text{C}} \frac{I\_0}{\mu\_0} \right]^{\frac{1}{1 - \theta}} \tag{32}$$

Properly speaking, both ǫ ′ and T in Equation (32) are functions of t<sup>0</sup> since they depend on the alignment of the development period with the annual cycle. Since we are trying to use Equations (29), (32) to optimize t0, we have a circular problem. Record et al. (2013) derive an expression similar to Equation (32) and apply it iteratively because of this circularity. Some applications of Coltrane might require the same level of accuracy, but in the present study we take the expedient approach of simply assuming that T is the annual mean of T<sup>0</sup> and that ǫ ′ ≈ 1/3: i.e., that aftert<sup>0</sup> is optimized, some diapause/spawning strategy will emerge that aligns the maturation period moderately well with a period of high prey availability. This assumption eliminates the need to run the model before estimating W<sup>e</sup> via Equations (29), (32).

#### 2.4.2. Optimal Timing in the ϕ Model

With a method for approximating W<sup>e</sup> in hand, we can define egg fitness F as a function of ϕ. If a cohort spawned on t<sup>0</sup> were to convert all of its accumulated free scope ϕ—all net energy gain beyond that required to build an adult body structure—into eggs on a single day t1, the eggs produced per starting egg would be

$$F(t\_0 \to t\_1) = \frac{\varphi(t\_1)}{W\_\varepsilon} N(t\_1) \tag{33}$$

This expression condenses one copepod generation into a mapping F similar to the "circle map" of Gurney et al. (1992). Once the ODE model has been run for a family of t<sup>0</sup> cases, this mapping can be used to quickly identify optimal life cycles of any length. The optimal one-generation-per-year strategy is the t<sup>0</sup> that maximizes F<sup>1</sup> = F(t<sup>0</sup> → t<sup>0</sup> + 365). The optimal one-generation-per-two-years strategy has t<sup>0</sup> that maximizes F1/<sup>2</sup> = F(t<sup>0</sup> → t0+ 2·365). The optimal two-generation-peryear strategy has spawning dates t0, t<sup>1</sup> that maximize the product F<sup>2</sup> = F(t<sup>0</sup> → t1)· F(t<sup>1</sup> → t<sup>0</sup> + 365); and so on. A viable strategy is a combination of spawning dates and model parameters that give F ≥ 1.

#### 2.4.3. Optimal Timing in the ER Model

In reality, of course, copepods are not free to physically store indefinite amounts of reserves within their bodies and then instantaneously convert them into eggs when the timing is optimal. If a scheme for calculating egg production over time E(t) is added to the model as in Section 2.3, then the per-generation mapping represented by F takes a different form. First, for each cohort, we use the assumption that the environmental annual cycle repeats indefinitely to convert the time series of EN egg production discounted by survivorship—to a function of yearday, by adding the value on days 365+i, 2·365+i, ... to the value on day i (in practice we discretize the year into 5 d segments rather than yeardays per se). Next, we construct a matrix V whose rows are the year-long time series of EN/W<sup>e</sup> for each spawning date t0. V is thus a transition matrix with spawning date in generation k running down rows and spawning date in generation k+1 running across columns. Given a discrete annual cycle n<sup>k</sup> of eggs spawned in generation k, one can calculate the expected annual cycle of egg production in the next generation as n<sup>k</sup> <sup>+</sup> <sup>1</sup> = V · n<sup>k</sup> , where n is given as a column vector.

The first eigenvector of V gives a seasonal pattern of egg production that is stable in shape, with the corresponding eigenvalue λ giving one plus the population growth rate per generation:

$$n\_{k+1}(t) = V \cdot n\_k(t) = \lambda n\_k(t) \tag{34}$$

$$\frac{n\_{k+1}(t) - n\_k(t)}{1 \text{ generation}} \approx \lambda - 1\tag{35}$$

A strict criterion for strategy viability would then be λ ≥ 1, although this criterion is unhelpfully sensitive to predation mortality. A more robust criterion (which we use in Section 3.4 below) is to consider a strategy viable if it yields lifetime egg production above the replacement rate: if E(t0;t) and N(t0;t) are the time series of egg production and survivorship for a cohort spawned on t0, and n(t0) is a normalized annual cycle of egg production,

$$\int\_{0}^{365} \int\_{0}^{\infty} n(t\_0) \, \frac{E(t\_0; t) \mathcal{N}(t\_0; t)}{W\_\varepsilon} \, dt \, dt\_0 \ge 1 \tag{36}$$

Thus, in the ER version of the model, as in the ϕ version, we have an efficient method that describes the long-term viability of a trait combination under a stable annual cycle, along with the optimal spawning timing associated with those traits in that environment; and these methods only require us to explicitly simulate one generation.

### 2.5. Assembling Communities

Community-level predictions in Coltrane take the form of bounds on combinations of traits that lead to viable populations in a given environment (**Figure 2**). There are many copepod traits represented in the model that one might consider to be axes of diversity or degrees of freedom in life strategy: u0, I0, θ, D<sup>s</sup> , Ks , We/Wa, and even m<sup>0</sup> to the extent that predation pressure is a function of behavior (Visser et al., 2008). Record et al. (2013) allowed five traits to vary among competitors in their copepod community model. We have taken a minimalist approach, where in the ϕ model we allow only one degree of freedom: variation in u<sup>0</sup> from 0.005 to 0.01 d−<sup>1</sup> . Banas and Campbell (2016) showed from a review of lab studies that u<sup>0</sup> variations appear to be the primary mode of variation in adult size among large calanoids (W<sup>a</sup> > 50 µgC) including Calanus and Neocalanus spp., with slower development leading to larger adult sizes. That study also suggests that variation in I<sup>0</sup> is responsible for copepod size diversity on a broader size or taxonomic scale (e.g., between Calanus and small cyclopoids like Oithona). However, variation in I<sup>0</sup> (energy gain from foraging) probably only makes sense as part of a tradeoff with predation risk or egg survivorship (Kiørboe and Sabatini, 1995) and we have left the formulation of that tradeoff for future work. We therefore expect Coltrane 1.0 to generate analogs for large and small Calanus spp. (∼100–1000 µgC adult size) but not analogs for Oithona spp. or even small calanoids like Pseudocalanus or Acartia.

Choices regarding reproductive strategy require another degree of freedom. In the ϕ model, this does not require additional parameters, because the difference between, e.g., capital spawning in winter and income spawning in spring is simply a matter of the time t at which F is evaluated in postprocessing: each model run effectively includes all timing possibilities (Equation 33). In the ER model, however, diversity in reproductive timing must be made explicit. Under the simple scheme for egg production specified above (Section 2.3), this takes the form of running a family of cases varying tegg for each t<sup>0</sup> and u0.

### 2.6. Model Experiments

This study comprises three complementary experiments (**Table 2**). The first of these is an idealized global testbed which addresses broad biogeographic patterns. The second is a testbed representing the Eastern Bering Sea shelf, which addresses time-variability in one population in one environment. The last is a testbed representing Disko Bay, West Greenland, which addresses trait relationships along the size spectrum in detail. The first two are evaluated entirely in terms of the ϕ model, while in the Disko Bay case we use the ER model to allow more specific comparisons with observations.

The global testbed consists of a family of idealized environments in which surface temperature T<sup>0</sup> is held constant, and prey availability is a Gaussian window of width δt ′ centered on yearday 365/2:

$$P(t) = \text{(10 mg chl m}^{-3}\text{)} \exp\left[-\left(\frac{t - \frac{365}{2}}{\delta t'}\right)^2\right] \tag{37}$$

We compare environmental cases in terms of T<sup>0</sup> and an effective season length

$$
\delta t = \int\_0^{365\text{ d}} \sigma \, dt \tag{38}
$$

which rescales the δt ′ cases in terms of the equivalent number of days of saturating prey per year. We assume that deep, overwintering temperature T<sup>d</sup> = 0.4 T0. The ratio 0.4 matches results of a regression between mean temperature at 0 and 1000 m in the Atlantic between 20 and 90◦N, or 0 and 500 m in the Northeast Pacific over the same latitudes (World Ocean Atlas 2013: http://www.nodc.noaa.gov/OC5/woa13/). Over the same data compilation, the mean seasonal range in temperature is approximately 5◦C at the surface (and approximately zero at 500– 1000 m); an alternate formulation of the testbed that models T<sup>0</sup> as an annual sinusoid with this range gives results that are somewhat noisier but heuristically very similar to those shown in Section 3.2 below.

The Bering Sea testbed considers interannual variation in temperature, ice cover, and the effect of ice cover on in-ice and pelagic phytoplankton production (Stabeno et al., 2012b; Sigler et al., 2014; Banas et al., 2016). Variation between warm, low-ice years and cold, high-ice years has previously been linked to the relative abundance of large zooplankton including C. glacialis/marshallae (Eisner et al., 2014), and we test Coltrane predictions against 8 years of C. glacialis/marshallae observations from the BASIS program. Seasonal cycles of T0, Td, and P are parameterized using empirical relationships between ice and phytoplankton from Sigler et al. (2014) and a 42-year physical


#### TABLE 2 | Setup of model experiments.

*All other parameters are as in Table 1.*

hindcast using BESTMAS (Bering Ecosystem Study Ice-ocean Modeling and Assimilation System: Zhang et al., 2010; Banas et al., 2016). Details are given in the Appendix in Supplementary Material .

The Disko Bay testbed represents one seasonal cycle of temperature and phytoplankton and microzooplankton prey, based on the 1996–1997 time series described by Madsen et al. (2001). We use this particular dataset not primarily as a guide to the current or future state of Disko Bay but rather as a specific circumstance in which the life-history patterns of three coexisting Calanus spp. (C. finmarchicus, C. glacialis, C. hyperboreus) were documented (Madsen et al., 2001). Details are given in Section 3.4 and the Appendix in Supplementary Material.

### 3. RESULTS

### 3.1. An Example Population

One case from the global experiment with u<sup>0</sup> = 0.007 d−<sup>1</sup> , T<sup>0</sup> = 1 ◦C, and δt = 135 is shown in detail in **Figure 3** to illustrate the analysis method described in Section 2.4.2. In this case, out of cohorts spawned over the full first year, only those spawned in spring reached adulthood without starving (**Figure 3B**, blue– green lines; non-viable cohorts not shown). The fitness function F (Equation 33) declines during winter diapause and rises during the following summer when prey are available. There is no equivalent peak during the third summer, indicating that by this time cumulative predation mortality is so high that there is no net advantage to continuing to forage before spawning.

The maximum value of F for most cohorts (<sup>∗</sup> , **Figure 3C**) comes at ∼1.5 year into the simulation, at the peak in prey availability following maturation. This point in the annual cycle, however, does not fall within the window of spawning dates at which maturation is possible (compare year 2 in **Figure 3C** with year 1 in **Figure 3B**), and thus is an example of "internal life history mismatch" (Varpe et al., 2007), the common situation in which the spawning timing that maximizes egg production by the parent is not optimal for the offspring. The long-term egg fitness corresponding to stable 1-year and 2-year cycles is marked for each cohort (**Figure 3C**, red, orange circles). Some but not all of the cohorts that reach maturity are able to achieve F > 1, egg production above the replacement rate, in these cyclical solutions (solid circles). The best 1-year and 2-year strategies achieve similar maximum fitness values (red vs. orange solid dots), although they require slightly different seasonal timing.

Note that although F can be described as the egg-fitness function, the lines in **Figure 3C**—time series of F for particular spawning dates t0—are not the same as the seasonal curve of egg fitness that results from a backwards-in-time dynamic optimization (e.g., Figure 6F in Varpe et al., 2007). Rather, each curve of F(t0;t) in our approach gives a series of possible values for egg fitness at t<sup>0</sup> depending on what future strategy is taken. The forwards and backwards calculations converge (at least qualitatively) once the internal life-history mismatch is resolved and a stable long-term cycle is found (red and orange circles, **Figure 3C**). As expected (Varpe et al., 2007), these stable values of egg fitness peak, for each generation length, somewhat prior to the bloom maximum (**Figure 3C**).

### 3.2. Global Behavior

In the global experiment, populations like that shown in **Figure 3** were run for a spectrum of u<sup>0</sup> values, across combinations of T<sup>0</sup> and δt from −2 to 16◦C and 0 to 310 d (the latter corresponding to δt ′ from 0 to 150 d). Across these cases, at a given u0, the model predicts a log-linear relationship between adult size and temperature, which is not much perturbed by variation in prey availability (**Figure 4**). The slope of this relationship is equivalent to a Q<sup>10</sup> of 1.8–2.0, consistent with that predicted by Equation (32):

$$\left(\frac{Q\_d}{Q\_\emptyset}\right)^{\frac{1}{1-\theta}} \approx 1.84\tag{39}$$

Field observations of size in relation to temperature in C. finmarchicus and C. helgolandicus across the North Atlantic show a similar relationship (Q<sup>10</sup> = 1.65, Wilson et al., 2015, with prosome length converted to carbon weight based on Runge et al., 2006). Somewhat surprisingly, even wide variation in prey conditions (clusters of gray dots, **Figure 4**) has only minor effects on this slope.

The intercept of the size-temperature relationship depends on u<sup>0</sup> (**Figure 4**), with u<sup>0</sup> = 0.005–0.01 d−<sup>1</sup> corresponding to the

year 1. (A) Prey availability over time. (B) Developmental stage *D* for cohorts that reach maturity (*D* = 1) without starving: the blue–yellow color scale corresponds to spawning dates *t*0 over the viable period from pre-bloom to bloom maximum. (C) Fitness *F* over time for the cohorts shown in (B), i.e., the expected value (eggs egg−<sup>1</sup> ) of converting all free scope ϕ to eggs on a given date. Curves of *F* begin when maturity is reached (*D* = 1) and egg production becomes possible. Open and solid circles mark the value of *F* on the 1-year (orange) and 2-year (red) anniversaries of the original spawning date. Solid circles mark cohorts that achieve a fitness above the replacement rate.

range of adult size from C. finmarchicus to C. hyperboreus at the cold end of the temperature spectrum (Disko Bay, ∼ 0 ◦C: Swalethorp et al., 2011). It is not always fair, however, to associate a particular u<sup>0</sup> value with a particular species over the full range of temperatures included. As Banas and Campbell (2016) discuss further, the temperature response of an individual species is often dome-shaped, a window of habitat tolerance (Møller et al., 2012; Alcaraz et al., 2014), whereas Coltrane 1.0 uses the monotonic, power-law response observable at the community level (Forster et al., 2011). C. finmarchicus, for example, is fit well by u<sup>0</sup> = 0.007 d−<sup>1</sup> at higher temperatures (4–12◦C), whereas near 0◦C in Disko Bay, it has been observed to be considerably smaller than extrapolation along the u<sup>0</sup> = 0.007 d−<sup>1</sup> power law would predict. Past studies have also found C. finmarchicus growth and ingestion

to be suppressed at low temperatures, i.e., to show a very high Q<sup>10</sup> compared with the community-level value (Campbell et al., 2001; Møller et al., 2012).

With this caveat on the interpretation of u0, we can observe a sensible gradation in life strategy along the u<sup>0</sup> axis (**Figure 5**). From u<sup>0</sup> = 0.01 d−<sup>1</sup> (C. finmarchicus-like at 0◦C) to u<sup>0</sup> = 0.005 d −1 (C. hyperboreus-like), the environmental window in which multi-year life cycles are viable (F1/<sup>2</sup> ≥ 1) expands dramatically. This window overlaps significantly with the window of viability for 1-year life cycles (F<sup>1</sup> ≥ 1; **Figure 5**, black vs. gray contours). In all u<sup>0</sup> cases, there is a non-monotonic pattern in maximum fitness as a function of either temperature or prey (**Figure 5**, color contours), as environments align and misalign with integer numbers of generations per year or years per generation.

The overall gradient from high to moderate F with increasing temperature (**Figure 5**) is largely an artifact of displaying F normalized to generation as opposed to per calendar year. In general, these results should not be taken as a quantitative prediction of annual production rates: the linear mortality closure that simplifies the analysis also omits the role of density dependence in stabilizing growth rates. Accordingly, in what follows, we consider only whether F in a given circumstance exceeds replacement rate, not whether it exceeds it modestly or dramatically.

The number of generations per year in the timing strategy that optimizes F for each (T0, δt) habitat combination is shown in **Figure 6** for u<sup>0</sup> = 0.007 d−<sup>1</sup> . This u<sup>0</sup> value corresponds in adult size to Arctic C. glacialis and temperate C. marshallae populations in the Pacific (**Figure 4**), species which coexist and are nearly indistinguishable in the Bering Sea. In the lowest-prey conditions, no timing strategy is found to be viable. As prey and temperature increase, the model predicts bands proceeding monotonically from multiple years per generation to multiple generations per year. Validating these model predictions requires parameterizing places (in terms of T<sup>0</sup> and δt) in addition to parameterizing their inhabitants, and thus the meaning of either success of failure is ambiguous. Still, we can observe the following. Ice Station Sheba in the high Pacific Arctic (**Figure 1**) falls in the non-viable regime (**Figure 6**), consistent with the conclusion of

Ashjian et al. (2003) that Calanus spp. are unable to complete their life cycle there. Disko Bay falls on the boundary of 1 and 2-year generation lengths, consistent with observations of C. glacialis there (Madsen et al., 2001). At Newport, Oregon, near the southern end of the range of C. marshallae, the model predicts multiple generations per year, consistent with observations by Peterson (1979).

### 3.3. A High-Latitude Habitat Limit in Detail: The Eastern Bering Sea

These idealized experiments (**Figures 5**, **6**) suggest that very short productive seasons place a hard limit on the viability of Calanus spp., regardless of size, temperature, generation length, or match/mismatch considerations (although these factors affect where exactly the limit falls). A decade of observations in the Eastern Bering Sea provide a unique opportunity to resolve this viability limit with greater precision. This analysis takes advantage of the natural variability on the Southeastern Bering Sea shelf described by the "oscillating control hypothesis" of Hunt et al. (2002, 2011): in warm, low-ice years, the spring bloom in this region is late (∼ yearday 150; Sigler et al., 2014) and the abundance of large crustacean zooplankton including C. glacialis/marshallae is very low, while in colder years with greater ice cover, the pelagic spring bloom is earlier, ice algae are present in late winter, and large crustacean zooplankton are much more abundant. The task of replicating these observations serves to test the Coltrane parameterization, and situating them within a complete spectrum of temperature/ice cover cases also allows the model to provide some insight into mechanisms.

Mean surface temperature T<sup>0</sup> was used to index annual cycles of surface and bottom temperature on the Eastern Bering Sea middle shelf (Appendix in Supplementary Material; insets in **Figure 7**). Date of ice retreat tice was likewise used to index phytoplankton availability over each calendar year (Appendix in Supplementary Material; insets in **Figure 7**). Coltrane was run for each (T0, tice) combination with u<sup>0</sup> = 0.007 d−<sup>1</sup> , thus consistent with **Figure 6** except for the more refined treatment of

environmental forcing, and an adjustment to K<sup>s</sup> to match results of Bering Sea feeding experiments (Campbell et al., in press). The maximum egg fitness F for a one-generation-per-year strategy is shown as a function of T<sup>0</sup> and tice in the main panel of **Figure 7**. Coltrane predicts that one generation per year is the optimal life cycle length everywhere in this parameter space

except for the cold/ice-free and warm/high-ice-cover extremes (white contours), combinations which do not occur anywhere in a model hindcast of middle-shelf conditions back to 1971 (**Figure 7**, red and blue dots).

Late summer measurements of C. glacialis/marshallae abundance (individuals m−<sup>2</sup> ), averaged over the middle/outer shelf south of 60◦N, are shown in **Figure 7** for 2003–2010 (n = 364 over the 8 years; Eisner et al., 2014, 2015). Both these observations and the predicted maximum F from Coltrane show a dramatic contrast between the warm years of 2003–05 (tice = 0) and the cold years of 2007–2010 (tice = 100–130), with the transitional year 2006 harder to interpret. Eisner et al. (2014) found that there was less contrast between cold year/warm year abundance patterns on the northern middle/outer shelf, consistent with the model prediction that all hindcast years on the northern shelf fall within the "viable" habitat range for C. glacialis/marshallae (**Figure 7**, blue dots).

The viability threshhold that the Southeastern Bering Sea appears to straddle is qualitatively similar to that in the more idealized global experiment (**Figures 5**, **6**), primarily aligned with the phenological index (horizontal axis) rather than the temperature index (vertical axis). The threshhold in the Bering Sea experiment (tice ≈ 90–100) falls somewhat beyond the dividing line imposed in the experiment setup between early, ice-retreat-associated blooms and late, open-water blooms (tice = 75: see Appendix in Supplementary Material, Sigler et al., 2014). This gap (whose width depends on the mortality level m0: not shown) indicates that some period of ice algae availability is required by C. glacialis/marshallae in this system, in addition to a favorable pelagic bloom timing.

### 3.4. Coexisting Life Strategies in Detail: Disko Bay

The experiments above test the ability of Coltrane 1.0 to reproduce first-order patterns in latitude and time but do not provide sensitive tests of the model biology. A model case study in Disko Bay, where populations of three Calanus spp. coexist and have been described in detail (Madsen et al., 2001; Swalethorp et al., 2011), allows a closer examination of the relationships among traits within the family of viable life strategies predicted by Coltrane.

The model forcing (**Figure 8**) describes a single annual cycle, starting with the 1996 spring bloom. This represents a cold, highice state of the system, compared with more recent years in which the spring bloom is earlier (e.g., 2008, **Figure 8**, Swalethorp et al., 2011) and the deep layer is warmed by Atlantic water intrusions (Hansen et al., 2012). This particular year was chosen because measurements of prey availability and Calanus response by Madsen et al. (2001) were particularly complete and coordinated. A simple attempt to correct the prey field for quality and Calanus preference was made by keeping only the >11 µm size fraction of phytoplankton and adding total microzooplankton, in µg C. The measured phytoplankton C:chl ratio was used to convert the sum to an equivalent chlorophyll concentration, and this time series was then slightly idealized for clarity (**Figure 8**, Appendix in Supplementary Material).

Sensible results were only possible after tuning the predation mortality scale coefficient m0. It is likely that our simple mortality scheme introduces some form of bias, compared with the reality in this system of predation by successive waves of visual and non-visual predators, which will be considered in a separate study. Still, a sensitivity experiment using the ϕ model shows that varying m<sup>0</sup> has, as intended, a simple, uniform effect on fitness/population growth (**Figure 9**) that leaves other trait relationships along the size spectrum unaffected. The ϕ model predicts that copepods similar to C. finmarchicus in size have much greater fitness at a generation length of 1 year than at 2 years or more; that C. hyperboreus would be unable to complete its life cycle in 1 year, but is wellsuited to a 2-year cycle; and that C. glacialis falls in the size range where 1- and 2-year life cycles have comparable fitness value. These results are consistent with observations (Madsen et al., 2001) and more general surveys of life strategies in the three species (Falk-Petersen et al., 2009; Daase et al., 2013).

These results naturally raise the question of whether even lower values of u0—further reductions in development rate would produce even larger copepods with even longer life cycles in this environment. C. hyperboreus has been reported to have a life cycle of up to 5 years in other systems (Falk-Petersen et al., 2009) and so the question is more than theoretical. In this version of Coltrane, the lower limit on development rate (and thus the upper limit on adult size) are set by the assumption that modulation of this rate is spread uniformly across the developmental period, rather than concentrated in late copepodid stages, as might be more realistic (Campbell et al., 2001). The largest viable adults in the Disko experiment are those that barely reach D = D<sup>s</sup> , the start of reserve accumulation, before a first diapause is required.

For greater specificity, we switched from the ϕ to the ER model version, running a spectrum of tegg cases (earliest possible eggproduction date: see Section 2.5) along with a spectrum of u<sup>0</sup> (development rate) cases. The predicted "community," then is the set of all combinations of u<sup>0</sup> and tegg that lead to a viable level of lifetime egg production. An analog for each of the three Calanus spp. is constructed by averaging model results over the set of viable (u0, tegg ) cases that predict an adult size within 30% of the average measured adult size for that species. The ER model imposes additional constraints on the model organisms—e.g., they are no longer allowed an infinite egg production rate—and to compensate we reduced m<sup>0</sup> from 0.08 d−<sup>1</sup> to 0.06 d−<sup>1</sup> .

The relationship between generation length and adult size across all (u0, tegg ) combinations is shown in **Figure 10**. Results are consistent with the ϕ model (**Figure 9**) only a 1-year life cycle is viable for C. finmarchicus in this environment, only a 2-year or longer cycle is viable for C. hyperboreus, and C. glacialis again lies near the boundary where the two strategies are comparable. Note that the model allows for a continuum of intermediate cases in the C. finmarchicus–C. glacialis size range, consistent with the observation of hybridization between these species (Parent et al., 2015).

The ER model also predicts a time series of egg production associated with each trait combination, which we can compare with observations for each species. The model predicts that C. finmarchicus analogs spawn in close association with the spring bloom, that C. hyperboreus spawns well before the spring bloom, and that C. glacialis is intermediate (**Figures 11**, **12A**). These patterns are all in accordance with Disko Bay observations (Madsen et al., 2001; Swalethorp et al., 2011), although the absolute range is muted: Madsen et al. (2001) report C. hyperboreus spawning as early as February. As one would expect from these timing patterns, the model predicts a significant trend between size and the capital fraction of total egg production Ecap/(Einc + Ecap) (**Figure 12C**). Again, the pattern is qualitatively correct but muted: Coltrane predicts 80% income breeding at the size of C. finmarchicus (a pure income breeder in reality) and 80% capital breeding at the size of C. hyperboreus (a pure capital breeder in reality). More notable than the error is how much of the income/capital spectrum can apparently be reproduced as a consequence of optimizing reproductive timing alone Varpe et al.

(2009), without imposing the physiological difference between the two strategies as an independent trait (Ejsmond et al., 2015).

The model predicts (**Figure 12B**) that the largest model organisms, with the longest generation lengths, enter their first diapause near the boundary between copepodite stages C4 and C5 (D ≈ 0.75), whereas smaller organisms enter first diapause well into stage C5. Madsen et al. (2001) found that both C. glacialis and C. hyperboreus diapause as C4, C5, and adults in Disko Bay, suggesting that the model is biased toward fast maturation. The discrepancy could also be related to intraspecific variation in the real populations or nonequiproportional development in the late stages, i.e., a variable conversion scale between actual developmental stage and D.

Finally, the ER version of Coltrane allows an estimate of the fraction of individual carbon in the form of storage lipids R/(R + S) (**Figure 12D**). Averaging each model population from the first diapause-capable stage D = Ddia through adulthood, weighted by survivorship N, yields an overall range that compares well with the species-mean wax ester fractions measured by Swalethorp et al. (2011): ∼30% for C. finmarchicus to ∼60% for C. hyperboreus. In the middle of the size spectrum, reserve fraction is highly variable across viable 2-year strategies, a warning that the success of this final model prediction may be partly fortuitous. Still, taken as a whole, this experiment has yielded a striking result: that a small set of energetic and timing contraints is able to correctly predict, a priori, that Disko Bay should be able to support a spectrum of calanoid copepods from income breeders with an adult size ∼100 µg C, a 1-year life cycle, and a wax ester fraction ∼30% to capital breeders with an adult size ∼1000 µg C, a two-or-more-year life cycle, and a wax ester fraction ∼60%.

### 4. DISCUSSION

### 4.1. Temperature and Timing

In the results above, whether prey availability is treated simply (**Figures 5**, **6**) or with site-specific detail (**Figure 7**), it appears that the viability of the calanoid community near its highlatitude limit is more sensitive to prey abundance and phenology than to temperature. This result is heuristically similar to the conclusions of Ji et al. (2012) and Feng et al. (2016), although the exact physiological mechanisms differ. Alcaraz et al. (2014) suggested based on lab experiments that C. glacialis reaches an bioenergetic limit near 6◦C, and Holding et al. (2013) and others have hypothesized that thermal limits will produce ecosystemlevel tipping points in the warming Arctic. Our results, in contrast, suggest that thermal tipping points, even if present at the population level, do not generalize to the community level in copepods. Rather, the model predicts complete continuity between the life strategy of Arctic C. glacialis and temperate congeners like C. marshallae (**Figure 6**). It also suggests that even on the population level in the Bering Sea, warm/coldyear variation in prey availability is a sufficient explanation of variability in the abundance of C. glacialis/marshallae (**Figure 7**), without the invocation of a thermal threshhold.

Both the global and Bering experiments suggest, furthermore, that increasing water temperature per se is not necessarily a stressor on copepod communities, even high-latitude communities. In both cases, the low-prey viability threshhold actually relaxes (i.e., is tilted toward lower prey values) as temperature increases, indicating that in these testbeds, the positive effect of temperature on growth and maturation rate actually outweighs the effect of temperature on metabolic losses and overwinter survival (This result may be reliant on the model assumption that the stage of first diapause is highly plastic). In cases where deep, overwintering temperatures increase faster than surface temperatures (Hansen et al., 2012) this balance may not hold, and in the real ocean changes in temperature are highly confounded with changes in phytoplankton production and phenology. Still, it is notable that the model predicts that warming temperatures will have a non-monotonic effect on copepod populations (∂F/∂T<sup>0</sup> ≷ 0, **Figures 5**, **6**) even when metabolic thermal threshholds sensu Alcaraz et al. (2014) and changes in prey availability are not considered. These results are a caution against overly simple climate-impacts projections based on temperature alone.

### 4.2. Uncertainties and Unresolved Processes

The biology in Coltrane could be refined in many ways, but two issues stand out as being both mechanistically uncertain

*Ecap*/(*Einc* + *Ecap*). (D) Mean reserve fraction of individual biomass *R*/(*R* + *S*), compared with wax esters as a fration of total body carbon for three *Calanus* spp. from Swalethorp et al. (2011) (open circles).

and sensitive controls on model behavior. These correspond to the two parameters that it was necessary to tune among model experiments (**Table 2**) the obstacles to formulation of a fully portable scheme that could produce accurate results across the full range of environments considered here with a single parameterization.

The first of these is the perennial problem of the mortality closure. We modeled predation mortality as size-dependent according to the same power law used for ingestion and metabolism, a choice which is mathematically convenient and makes the effect of top-down controls, if not minor, then at least simple and easy to detect (**Figure 9**). This size scaling is consistent with the review by Hirst and Kiørboe (2002) but that study also shows that the variation in copepod mortality not explained by allometry spans orders of magnitude (cf. Ohman et al., 2004). Indeed, in some cases one might posit exactly the opposite pattern, in which mortality due to visual predators like larval fish increases with prey body size (Fiksen et al., 1998; Varpe et al., 2015). This latter pattern is one hypothesis for why in reality C. hyperboreus is confined to high latitudes, whereas the model predicts no southern (warm, high-prey) habitat limit to C. hyperboreus analogs based on bottom-up considerations (**Figure 5**). Merging Coltrane 1.0 with a light- and size-based predation scheme similar to Varpe et al. (2015) or Ohman and Romagnan (2015) would allow one to better test the balance of bottom-up and top-down controls on calanoid biogeography.

Second, our experience constructing the Bering Sea and Disko Bay cases suggests that the greatest uncertainty in the model bioenergetics is actually not the physiology itself empirical reviews like Saiz and Calbet (2007), Maps et al. (2014), Kiørboe and Hirst (2014), and Banas and Campbell (2016) have constrained the key rates moderately well—but rather the problem of translating a prey field into a rate of ingestion. Within each of our model testbeds, the prey time series P remains subject to uncertainty in relative grazing rates on ice algae, large and small pelagic phytoplankton, and microzooplankton, despite a wealth of local observations and a history of work on this problem in Calanus specifically (Olson et al., 2006; Campbell et al., 2009, in press). The precision of each testbed, and even moreso the ambition of generalizing across them, is also limited by uncertainty in the shape of the functional response (Frost, 1980; Gentleman et al., 2003), here represented by a halfsaturation coefficient, which has not been found to be consistent across site-specific studies (Campbell et al., in press; Møller et al., 2016) or well-constrained by general reviews (Hansen et al., 1997). This ambiguity is perhaps not surprising when one considers that ingestion as a function of chlorophyll or prey carbon is not a simple biomechanical property, but in fact a plastic behavioral choice. Accordingly, it might well be responsive not only to mean or maximum prey concentration but also to the prey distribution over the water column, the tradeoff between energy gain and predation risk (Visser and Fiksen, 2013), prey composition and nutritional value, and the context of the annual routine. These issues are fundamental to concretely modeling the effect of microplankton dynamics on mesozooplankton grazers. Addressing them systematically in models will require novel integration between what could be called oceanographic and marine-biological perspectives on large zooplankton.

### 5. CONCLUSION

Coltrane 1.0, introduced here, is a minimalist model of copepod life history and population dynamics, a metacommunity-level framework on which additional species- or population-level constraints can be layered. Many present and future patterns in large copepods might well prove to be sensitive to species-specific constraints that Coltrane 1.0 does not resolve, such as thermal adaptation, physiological requirements for egg production, or cues for diapause entry and exit. Nevertheless, the model experiments above demonstrate that many patterns in latitude, time, and trait space can be replicated numerically even when we only consider a few key constraints on the individual energy budget: the total energy available in a given environment per year; the energy and time required to build an adult body; the metabolic and predation penalties for taking too long to reproduce; and the size and temperature dependence of the vital rates involved.

Results of the global and Bering experiments (**Figures 5**–**7**) suggest that timing and seasonality are crucial to large copepods, but not because of match/mismatch (Edwards and Richardson,

### REFERENCES

2004) the model organisms are free to resolve timing mismatches with complete plasticity. Rather, these results highlight the role of seasonality in the sense of total energy available for growth and development per year, or the number of weeks per year of net energy gain relative to the number of weeks of net deficit. The simplicity of this view means that the model scheme and results may generalize far beyond copepods with only minor modification.

The exercise of parameterizing the Bering Sea and Disko Bay cases, and of attempting to map real environments onto an idealized parameter space in the global experiment (**Figure 6**), highlighted that the real limit on our ability to predict the fate of copepods in changing oceans may not be our incomplete knowledge of their physiology, but rather our incomplete knowledge of how their environments appear from their point of view. How do standard oceanographic measures of chlorophyll and particulate chemistry relate to prey quality, and how much risk a copepod should take on in order to forage in the euphotic zone? How do bathymetry, the light field, and other metrics relate to the predator regime? Further experiments in a simple, fast, mechanistically transparent model like Coltrane may suggest new priorities for field observations, in addition to new approaches to regional and global modeling.

### AUTHOR CONTRIBUTIONS

NB designed the model, performed the analysis, and led the writing of the manuscript. EM and TN helped formulate and interpret the Disko Bay case study, and LE the Bering Sea case study. All authors contributed to revision of the manuscript.

### FUNDING

This work was supported by grants PLR-1417365 and PLR-1417224 from the National Science Foundation.

### ACKNOWLEDGMENTS

Many thanks to Bob Campbell, Thomas Kiørboe, Øystein Varpe, Dougie Speirs, and Aidan Hunter for discussions that helped shape both the model and the questions we asked of it. Thanks as well to Nick Record, Carin Ashjian, and ØF, whose comments much improved the manuscript.

### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fmars. 2016.00225/full#supplementary-material

Alcaraz, M., Felipe, J., Grote, U., Arashkevich, E., and Nikishina, A. (2014). Life in a warming ocean: thermal thresholds and metabolic balance of arctic zooplankton. J. Plankton Res. 36, 3–10. doi: 10.1093/plankt/fbt111

Ashjian, C. J., Campbell, R. G., Welch, H. E., Butler, M., and Van Keuren, D. (2003). Annual cycle in abundance, distribution, and size in relation to hydrography of important copepod species in the western Arctic Ocean. Deep Sea Res. Part I 50, 1235–1261. doi: 10.1016/S0967-0637(03) 00129-8


Georges Bank: 1994–1999. Deep Sea Res. Part II 53, 2618–2631. doi: 10.1016/j.dsr2.2006.08.010


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The reviewer ØF and handling Editor declared their shared affiliation, and the handling Editor states that the process nevertheless met the standards of a fair and objective review.

Copyright © 2016 Banas, Møller, Nielsen and Eisner. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Spatial Modeling of Calanus finmarchicus and Calanus helgolandicus: Parameter Differences Explain Differences in Biogeography

Robert J. Wilson\*, Michael R. Heath and Douglas C. Speirs

*Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland*

The North Atlantic copepods *Calanus finmarchicus* and *C. helgolandicus* are moving north in response to rising temperatures. Understanding the drivers of their relative geographic distributions is required in order to anticipate future changes. To explore this, we created a new spatially explicit stage-structured model of their populations throughout the North Atlantic. Recent advances in understanding *Calanus* biology, including U-shaped relationships between growth and fecundity and temperature, and a new model of diapause duration are incorporated in the model. Equations were identical for both species, but some parameters were species-specific. The model was parameterized using Continuous Plankton Recorder Survey data and tested using time series of abundance and fecundity. The geographic distributions of both species were reproduced by assuming that only known interspecific differences and a difference in the temperature influence on mortality exist. We show that differences in diapause capability are not necessary to explain why *C. helgolandicus* is restricted to the continental shelf. Smaller body size and higher overwinter temperatures likely make true diapause implausible for *C. helgolandicus*. Known differences were incapable of explaining why only *C. helgolandicus* exists southwest of the British Isles. Further, the fecundity of *C. helgolandicus* in the English Channel is much lower than we predict. We hypothesize that food quality is a key influence on the population dynamics of these species. The modeling framework presented can potentially be extended to further *Calanus* species.

Keywords: copepods, zooplankton, modeling, biogeography, diapause

### 1. INTRODUCTION

Zooplankton communities are now reorganizing throughout the North Atlantic (Beaugrand et al., 2009; Chust et al., 2013). Rising temperatures are causing species to expand at the northern edge of their distribution, while they are retreating at the southern edge (Beaugrand, 2012). As a consequence, communities are changing and many species are being replaced by their southern congenerics (Beaugrand et al., 2002).

Changes in communities dominated by the calanoid copepods Calanus finmarchicus and C. helgolandicus are among the most well-studied (Wilson et al., 2015). C. finmarchicus is an oceanic

#### Edited by:

*Dag Lorents Aksnes, University of Bergen, Norway*

#### Reviewed by:

*Jan Marcin Weslawski, Institute of Oceanology of the Polish Academy of Sciences, Poland Nicholas R. Record, Bigelow Laboratory for Ocean Sciences, USA*

> \*Correspondence: *Robert J. Wilson robert.wilson@strath.ac.uk*

#### Specialty section:

*This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Marine Science*

Received: *22 June 2016* Accepted: *19 August 2016* Published: *09 September 2016*

#### Citation:

*Wilson RJ, Heath MR and Speirs DC (2016) Spatial Modeling of Calanus finmarchicus and Calanus helgolandicus: Parameter Differences Explain Differences in Biogeography. Front. Mar. Sci. 3:157. doi: 10.3389/fmars.2016.00157* species that is found from the Gulf of Maine to the North Sea (Melle et al., 2014). In contrast, C. helgolandicus is a shelf species that lives from the North Sea to the Mediterranean Sea (Bonnet et al., 2005). Both species are now moving north, which has caused C. helgolandicus to replace C. finmarchicus as the dominant calanoid copepod in the North Sea (Reid et al., 2003). Future temperature rises will likely cause this to be repeated further north (Villarino et al., 2015). We must therefore understand differences in the impacts of climate change on congeneric zooplankton species, so that we can anticipate changes in communities and their consequences.

A key test of our understanding of the interspecific differences in demography of these species is whether we can simulate their population dynamics in such a way that the relative geographic distributions of both species are a result of the differences in biology. An inability to do this can highlight important knowledge gaps that must be filled to make projections of the impact of climate change on Calanus communities more biologically credible.

In this spirit, we tested the ability of known interspecific differences to explain the geographic distributions of both species by creating a new unified model. We created a stage-structured model which represents each life stage of C. finmarchicus and C. helgolandicus, and that represents body size by dividing each stage into a set of size classes. This work is based on the previous model of C. finmarchicus in the North Atlantic of Speirs et al. (2005, 2006). Continuous Plankton Recorder survey data was used to parameterize the model and simulated annual cycles of abundance and fecundity were compared with empirical time series in a number of North Atlantic locations.

Recently, an increasing number of researchers have taken a trait-based approach to understanding zooplankton communities (Barton et al., 2013; Litchman et al., 2013). Key traits such as body size, development rate and fecundity are identified, and the functional role of species in ecosystems is thus thought to be a function of their positions within trait-space. A trait-based approach has previously been used to model copepod communities in Cape Cod Bay, Massachusetts (Record et al., 2010). We used this approach to understand the biogeography of two species, under the assumption that where species lie in trait-space is the fundamental determinant of relative biogeography.

Our underlying philosophy is that the equations describing the population dynamics of both species should be identical, but with potential differences in parameters. This constraint will arguably result in suboptimal models for each species when viewed separately. However, it enables us to more clearly understand the biological differences that drive the large-scale differences in distribution. Fundamentally, this work is based on the assumption that if knowledge of key interspecific differences is sufficient, then known interspecific differences are all that is needed for a model to reproduce the geographic distributions of both species. The only known difference between the species that could influence population dynamics is the response of ingestion rate, and thus growth, development and fecundity, to temperature (Wilson et al., 2015). We therefore begin with the hypothesis that this difference alone can explain most of the differences in geographic distribution.

## 2. MODEL

### 2.1. Model Background and Framework

We present an extension of the previous work by Speirs et al. (2005, 2006), who modeled the population dynamics of C. finmarchicus over the entire North Atlantic. This extension took two key forms. First, we incorporated recent developments in our understanding of Calanus biology. Second, we modified the model of Speirs et al. (2006) so that it could represent the population dynamics of both C. finmarchicus and C. helgolandicus. Full mathematical details of the model, along with relevant parameters, are given in Appendix 1 (Supplementary Material). Here we will summarize the modeling framework of Speirs et al. and then the extensions to it.

The model of Speirs et al. was discrete in time and space. It covered the entire North Atlantic, ranging from 30 to 80°N and 80°W to 90°E. The population of C. finmarchicus was distributed over a regular grid of cells of size 0.5°longitude by 0.25°latitude. They had two update processes. First, the population of each cell was updated to account for development, reproduction and mortality. After these updates, the population is redistributed between cells to account for physical population transport. A separate physical model was used to create the flow-field and temperature drivers for the relevant biological and physical update. The annual cycle of food in each cell was estimated by deriving phytoplankton carbon fields from satellite sea-color observations. 1997 was used as the target year for simulations because this was the year when the Trans-Atlantic Study of Calanus (TASC) collected a large number of time series of C. finmarchicus abundance in the North Atlantic. The framework of Speirs et al. was as follows. Surface developers are made up of eggs (E), naupliar stages (N1 to N6), and copepodite stages (C1 to C5). Finally, there are diapausers (C5d) and adults (C6).

Calanus development follows the equiproportional rule, that is relative stage duration is independent of temperature (Campbell et al., 2001). Development from egg to adult can therefore be divided into a fixed number of steps, with each having identical time duration under identical environmental conditions (Gurney et al., 2001). In total, there were 57 development steps, which cover the 13 stages of Calanus development.

This framework allows the entire population to be updated simultaneously, and for the entire population to be simulated with high computational efficiency (Speirs et al., 2006). However, modeling the populations of C. finmarchicus and C. helgolandicus required one modification.

We began with the hypothesis that differences in the response of growth and development to temperature are sufficient to explain the geographic distributions of both species. In other words, all equations and parameters would be the same, except for those related to growth and development. This could not be satisfactorily achieved in the original framework. Large-scale patterns of fecundity are not only the result of the effects of environmental conditions, but also of body size. Further, the ability of animals to diapause is strongly influenced by size (Wilson et al., 2016). We therefore incorporated body size into the framework. Large-scale patterns of fecundity and diapause duration could therefore be represented as the combined effects of body size and the environment, and did not require the introduction of interspecific differences. The geographic domain used by Speirs et al. covers all regions of high C. helgolandicus abundance (Bonnet et al., 2005), and was therefore maintained.

### 2.2. Biological Processes: A New View of Calanus Biology

The following biological processes are represented in our model: development, egg production, diapause and mortality. In each case, we modified the model of Speirs et al. to account for recent developments in the understanding of Calanus biology.

A recent review of the differences between the two species found that the only known relevant difference was the influence of temperature on ingestion, and thus growth, development and fecundity (Wilson et al., 2015). We therefore constrained the model by making a number of assumptions about the differences between the species based on this review. These assumptions were as follows:


Further, we take the following assumptions and simplifications about the biology and ecology of both species.


The key modeled relationships between body size, development time, egg production rate and diapause duration with temperature are shown in **Figure 1**.

There are no apparent interspecific differences in body size, and large-scale geographic patterns of body size are largely driven by temperature (Wilson et al., 2015). We therefore modeled body size under the simplified assumption that it is determined by temperature experienced at birth for all development classes (**Figure 1A**). This assumption is derived from the fact that egg size is determined by temperature (Campbell et al., 2001) and that the existence of an exo-skeleton likely greatly constrains size over all development classes. The temperature-prosome length relationship of Campbell et al. (2001) was used with a multiplier, which was fitted based on the relationship between predicted and observed female prosome length. Prosome length reduces linearly with increasing temperature. This approach contrasts with Speirs et al., which did not represent size.

Egg-adult development time was assumed to be influenced purely by temperature and food concentration. The relationship between egg-adult development time and temperature under food-saturated conditions is assumed to follow that derived by the model of Wilson et al. (2015). Development time saturates at high food levels, and we use the relationship between food concentration and development time of Campbell et al. (2001). There is a U-shaped response of development time to temperature (**Figure 1B**), which contrasts with the monotonically decreasing form used by Speirs et al. The computational approach is that of Gurney et al. (2001) and uses dynamic time-step constraints. This is the same approach as in Speirs et al. (2005, 2006) and it is effective in minimizing numerical diffusion (Gurney et al., 2001; Record and Pershing, 2008).

Fecundity was related to temperature, food concentration and body size. We assumed that egg production and growth are equivalent (McLaren and Leonard, 1995). Egg laying females have stopped growing and we therefore assume that carbon previously directed to growth will be used to make eggs. The growth rate equation of Wilson et al. (2015) forms the basis of our egg production rate (EPR) model for both species, with the food saturation component taken from Hirche et al. (1997). EPR therefore has a dome-shaped response to temperature (**Figure 1C**). Further, EPR has a saturating response to food concentration and we use a conventional allometric relationship between EPR and carbon weight, i.e., EPR ∼ carbon weight0.75 . This contrasts with Speirs et al., who represented EPR as a monotonically increasing function of temperature, but using the same food response as we have assumed. We assume that 50% of adults are female.

A recent modeling study, which synthesized empirical findings, showed that maximum potential diapause duration is largely determined by prosome length and overwintering temperature (Wilson et al., 2016). We therefore modeled diapause duration using the maximum potential diapause duration equation from that study (**Figure 1D**). Diapause duration declines at higher temperature because of increased metabolic rates, and is shorter at smaller prosome lengths because of lower relative lipid levels and higher relative metabolic costs. We assumed that a fraction of the C5 population enters diapause at the end of the C5 stage. This fraction is dependent on growth rate, with it increasing at lower growth rates, so that more animals diapause when development conditions are poor. In the model, animals exit diapause at the end of their potential diapause duration. This differs from Speirs et al., who assumed that diapause exit was triggered by a photoperiod cue.

Mortality is modeled using a stage-dependent background rate, alongside a starvation and density dependent term. Field studies indicate that mortality in both species is stage-dependent (Eiane et al., 2002; Ohman et al., 2004; Hirst et al., 2007). These estimates of stage-dependent mortality include all sources of mortality. However, we need to distinguish between different sources of mortality to properly represent population dynamics. We therefore used a fraction of the stage-specific mortality rates calculated by Eiane et al. (2002) as the background mortality rate, with additional temperature, starvation and density dependent terms. Starvation dependent mortality was modeled in the same

way for both species by assuming that it relates to growth rate; with starvation mortality only occurring below a threshold growth rate and increasing as growth rate decreases. Background mortality is temperature dependent, with mortality increasing with temperature and the relationship taking the form mortality ∼ (T/8)<sup>z</sup> . Density dependent mortality is assumed to be proportional to total biomass. Mortality was represented the same way as in Speirs et al., with the exception of starvationdependence. Speirs et al. represented this purely as a function of food concentration. However, the differences in ingestion rate between the two species (Møller et al., 2012) show that C. helgolandicus is likely to face much greater starvation levels at temperatures below approximately 11°C. We therefore viewed growth rate as a better indicator of starvation than food concentration.

### 2.3. Environmental Drivers

Seasonal cycles in food concentration, temperature and oceanic circulation drive the model. The only data with sufficient spatial and temporal coverage of food concentration are satellite estimates of sea surface color. SeaWIFS satellite estimates of chlorophyll were therefore used to derive food fields.

Insufficient observations are available for 1997. We therefore used a climatological 8 day mean of chlorophyll concentration from 1998 to 2000. There is a poor relationship between time series derived from SeaWIFS and field estimates of chlorophyll (Speirs et al., 2005; Clarke et al., 2006). We used the estimates of Clarke et al. (2006), who developed a statistical methodology, where thin plate regression splines modeled local estimates of chlorophyll concentration in relation to SeaWIFS estimates, bathymetry and time of year. Field estimates of chlorophyll concentration in the top 5 m were used, assuming they reflect chlorophyll concentration throughout the vertical distribution of Calanus. However, it is possible that this does not fully capture deep-water chlorophyll concentrations. Phytoplankton abundance was calculated assuming that 1 mg m−<sup>3</sup> of Chl a is equivalent to 40 mg Cm−<sup>3</sup> (the approximate median of the values reported by Parsons et al. (1984). Estimates of food extend to regions covered by sea ice, where we masked food levels to zero. This mask was derived from 1997 satellite percentage ice cover from the Defense Meteorological Satellite Program's (DMSP) spatial sensor microwave/imager (SSM/I) (Comiso, 1997). The approach taken to food was the same as in Speirs et al.

Temperature and velocity fields come from the Nucleus for European Modeling of the Ocean (NEMO) Ocean General Circulation Model (OCGM) (version 3.2) (Madec, 2012). The forcings and model implementation are described in Yool et al. (2011). NEMO is resolved at 64 vertical levels, and it resolves the primitive equations on a C-type Arawkawa grid. Ocean surface forcing comes from the DFS4.1 fields produced by the European DRAKKAR collaboration. This differs from Speirs et al., who used the OCCAM model to derive temperatures and flow fields. Computation of the NEMO model was performed using the free Java tool Ichthyop version 3.2 (Lett et al., 2008).

We assumed that surface developers experience the temperatures and velocities which occur at a depth of 20 m. Diapause depth varies in space. We therefore derived a map of diapause from the data reported by Heath et al. (2004). A loess smooth was used to estimate the median diapause depth in regions close to where Heath et al. (2004) reported data.

Where the smoothed estimate exceeded bathymetry, we used a depth 10 m shallower than the bathymetry at a location. In other regions we assumed that if bathymetry was greater than 800 m that diapause depth was 800 m. For locations where bathymetry was shallower than 800 m we used the predictions of a general additive model which related median diapause depth with bathymetry using the data of Heath et al. (2004). Transport updates occurred every 7 days. At the start of each time step, 100 seeds were placed at the center of each model cell. Particle trajectories over a 7-day period were then calculated, and transition matrices were calculated to show the proportion of particles which move to each nearby

cell. The approach outlined above was in agreement with Speirs et al.

### 2.4. Data Sources

### 2.4.1. The Continuous Plankton Recorder Survey

The Continuous Plankton Recorder Survey (CPR) is made up of data collected by devices attached to ships which traverse commercial shipping lanes. It is designed for towing depths of 10 m at the operating speeds of vessels (Batten et al., 2003). Water enters the CPR through a 1.27 cm<sup>2</sup> opening and is filtered by a 270 µm silk mesh. Abundance estimates are semiquantitative, with each observation being placed in one of 12 distinct abundance categories (Rae, 1952). CPR provides reliable temporal and spatial measures (Batten et al., 2003; Hélaouët et al., 2016) of abundance. We used CPR data from 1958 to 2002.

### 2.4.2. Time Series

The EU TASC project collected time series of C. finmarchicus copepodite abundance in 1997 at three locations (Planque and Batten, 2000). Data was collected at Ocean Weather Ship Mike (OWS M) (66°N, 2°E) from 24 February to 17 December 1997 (Heath et al., 2000; Hirche et al., 2001) using a 180 µm mesh opening and closing multinet. Concentrations of copepodite stages (m−<sup>3</sup> ) were converted to stage abundances (m−<sup>2</sup> ) at 0– 100 and 100–1600 m. During autumn and winter the population largely resided in the deep layer. We assume that deep animals were diapausing at that time. Per-capita egg production rates were also recorded at this station (Niehoff et al., 1999).

Data was collected at 2 locations near the Westmann Islands (63°27.25′N, 20°00.00′W, depth 100 m, and 63°22.20′N, 19°54.85′W, depth 200 m) (Gislason and Astthorsson, 2000). This site was visited 29 times, with C. finmarchicus being collected by vertically integrating hauls from 5 m above the seabed to the surface with a 200 µm mesh, 56 cm Bongo net. In addition, data was collected from Murchison (61°30.00′ N, 01°40.00′ E, depth 160 m) on 29 occasions, using a 200 µm mesh with a 30 cm Bongo net from a depth of 150 m to the surface.

We include data from Ocean Weather Ship India (OWS I) (59°N, 19°E), which was collected between 1971 and 1975 (Irigoien, 1999). This time series is used because we lack data for a truly oceanic location in 1997. Sampling occurred at approximately weekly intervals from 1971 to 1975 using oblique hauls of a Longhurst-Hardy plankton recorder (280 µm mesh). Stage-resolved copepod samples were then collected from a depth of 500 m to the surface, with a resolution of 10 m. We used data from the top 100 m.

The US GLOBEC program started in 1995 (Durbin et al., 2000), and includes extensive zooplankton sampling in the Gulf of Maine and Georges Bank. C. finmarchicus densities (m−<sup>3</sup> ) were estimated during the first half of the year at varying depths using a 1 m<sup>2</sup> MOCNESS fitted with 0.15 mm mesh nets. Estimates of density (m−<sup>2</sup> ) were calculated for the top 100 m and from 100 m to the sea floor by considering regions where bathymetry exceeded 200 m.

C. helgolandicus abundance data has been collected of Stonehaven, Scotland (56°57.8′ N, 2°6.2′W) since 1997. Sampling uses fine mesh nets, which collect an integrated sample of zooplankton throughout the water column (Bresnan et al., 2015). Integrated abundance data is provided for C5, female and male stages.

Station L4 in the English Channel (50°15′N, 4°13′W) is one of the longest standing zooplankton time series in European waters (Harris, 2010), with monitoring beginning in 1988. Seabed depth is 51 m, while observations typically range between 40 and 45 times each year (Harris, 2010). This time series contains information on the abundance of male, female and total copepodites, and egg production rate (Irigoien et al., 2000).

### 2.5. Parameter Derivation and Sensitivity Experiments

Our underlying goal was to reproduce the biogeography of both species displayed by the CPR. We therefore carried out an extensive set of simulations to assess how well different parameter sets could reproduce the geographic distributions of both species.

As discussed in Section 2.2, laboratory and field data were used to derive the following traits: development time, growth, fecundity, diapause duration, background mortality and body size. The remaining free, i.e., unknown, parameters related to the equations for diapause entry and starvation and biomass dependent mortality. We initially sought a single parameter set for mortality and diapause entry that would result in credible predictions of geographic distributions for both species. However, a large number of exploratory runs showed that this was not possible. We therefore sought parameter sets that reproduce the geographic distributions of both species while minimizing the differences between the model parameters of both species. A suite of runs showed that this was only achievable by assuming that mortality responded differently to temperature in both species.

Model parameters were derived by simultaneously altering the terms for mortality and diapause entry for both species and recording each parameterization's fit to CPR abundance data. First, CPR data was split into cells of dimension 2°E and 1°N, and we then removed cells without a CPR abundance record for each month of the year. Annual mean abundance was then calculated by averaging the mean abundance of the mean monthly abundance for C5 and adults in each cell.

This resulted in 333 cells for model comparisons. Each CPR abundance record represents approximately 3 m<sup>3</sup> of filtered seawater (Richardson et al., 2006). Therefore, CPR data must be divided by 3 to get estimates of abundance per m<sup>3</sup> . This must then be multiplied by a further conversion factor of 20 (Speirs et al., 2006) to provide estimates of abundance (m−<sup>2</sup> ) over the top 100 m of the water column.

Simulations began by seeding a large number of eggs over the entire North Atlantic and in the eastern North Atlantic for C. finmarchicus and C. helgolandicus, respectively. The model was then run to a quasi-stable state and we then calculated the correlation coefficient (r) between predicted annual surface abundance (m−<sup>2</sup> ) and CPR abundance (m−<sup>2</sup> ).

We report two sensitivity experiments. First, we show the geographic distributions of both species when there are no interspecific differences in free parameters, i.e., only differences in growth, development and fecundity are assumed. In this case we are using the diapause entry and starvation and temperature dependent mortality parameters for C. helgolandicus for both species.

Our initial model of diapause duration used a model of maximum potential diapause duration (Wilson et al., 2016), which possibly results in diapause durations which are unrealistically long. We therefore carried out a sensitivity analysis which relates the ability to reproduce the geographic distributions of both species to the assumptions for diapause duration and temperature dependent mortality. Temperature dependent mortality is proportional to (T/8)<sup>z</sup> for temperature T (°C). The parameterization assumed different values of z for each species.

### 3. RESULTS

### 3.1. Model Results

**Figures 2**, **3** compare the model predictions and CPR estimates of bimonthly abundance for C. finmarchicus and C. helgolandicus respectively. **Table 1** shows the correlation coefficients between monthly modeled and CPR abundance for both species. The large-scale geographic pattern of C. finmarchicus abundance was successfully reproduced in comparison with CPR. The correlation coefficient between simulated mean annual abundance and CPR abundance over the 2°E by 1°N cells is 0.75. Bimonthly comparisons between C. finmarchicus predictions and the CPR abundance are shown in **Figure 2**. Importantly, we reproduced the relatively high abundance of C. finmarchicus in the West Atlantic in autumn. In addition, the model predicts a year round surface population in coastal waters in the West Atlantic, in accordance with CPR. However, it perhaps over-predicted abundance in November and December.

A comparison of bimonthly predictions of C. helgolandicus abundance with the CPR abundance is shown in **Figure 3**. The correlation coefficient between predicted mean annual abundance and CPR abundance over the 2°E by 1°N cells was 0.76. Importantly, C. helgolandicus was restricted to the continental shelf. The autumn bloom of C. helgolandicus in the North Sea was also reproduced. However, predicted abundance

TABLE 1 | The correlation coefficient (r) between modeled monthly abundance and the mean CPR abundance in each cell.


in November and December in the region to the south west of the British Isles appears too high.

**Figure 4** shows simulated combined abundance for stage C5 and adult C. finmarchicus compared with those from the time series. Predicted peak abundances are within a factor of 2 of those recorded in the time series, with the exception of the Westmann Islands. OWS I is notable for getting the scale of the first generation very accurate, but we predicted a much larger second generation than is apparent in the time series. We failed to show the apparent sharp increase in C5 and adult at OWS M before day 100. Additionally, the second peak in C5 and adult abundance at OWS M appears to be time shifted by approximately 50 d.

We compare predictions for C. helgolandicus with field time series and time series derived from CPR in **Figure 5**. The timing of the autumn peak of C. helgolandicus abundance at Stonehaven was successfully reproduced. However, we failed to reproduce the small spring bloom. Predicted time and the magnitude of peak abundance was close to that in the L4 time series. However, abundance appeared to be over-predicted during winter.

Predicted EPR is compared with field time series at OWS M and L4 for C. finmarchicus and C. helgolandicus respectively in **Figure 6**. Predicted C. helgolandicus EPR is lower in the first half of the year of the time series, and is slightly time shifted compared with the time series. Predictions depart significantly from the times series in the second half of the year, with EPR being significantly higher than in the time series. The C. finmarchicus EPR time series at OWS M is of short duration. We can therefore only make a limited comparison. However, the predicted EPR is approximately the same as the median EPR in the time series.

### 3.2. Sensitivity Experiments

In the results shown in Section 3.1, the only differences between the species are the relationship between growth, development and fecundity and temperature, and a parameterized difference in the response of mortality to temperature. **Figure 7** shows the predicted geographic distribution of C. finmarchicus when the

temperature-dependent mortality parameter for C. helgolandicus was used. The geographic distribution in the west Atlantic is successfully reproduced. However, the geographic distribution in the east Atlantic is too southerly, with a large population predicted to exist in the Celtic Sea.

Exploratory simulations showed that the C. helgolandicus predictions were sensitive to diapause assumptions. First, the model performed well if C. helgolandicus was assumed to remain at the surface year round and to never diapause. In fact, this simplified model arguably performed better than the original. The key features of the distribution of C. helgolandicus were largely reproduced, with the correlation coefficient (0.78) of model performance compared with CPR actually improving in comparison with our original model.

Further exploratory simulations showed that the state of populations of C. helgolandicus is sensitive to diapause duration. A sensitivity analysis showed that small changes to diapause or mortality assumptions can result in C. helgolandicus becoming an oceanic species. **Figure 8** shows the correlation coefficient between predictions and CPR abundance of C. helgolandicus under varying assumptions for diapause duration and the scaling of mortality with temperature. A small reduction in how steeply mortality scales with temperature results in a reduction in model performance, with C. helgolandicus becoming an oceanic species. Likewise, an increase in diapause duration can result in C. helgolandicus becoming an oceanic species. Notably, the high sensitivity to changes in temperature dependent mortality was not evident diapause duration is reduced by 60%, which is potentially a more biologically realistic assumption for diapause duration.

### 4. DISCUSSION

This study can be framed by a single question. What differences between C. finmarchicus and C. helgolandicus explain the relative geographic distributions of these two species? Alternatively, we can ask how much we need to change C. finmarchicus's traits before it effectively becomes C. helgolandicus.

In this setting, the model equations can be viewed as describing a generic Calanus species, while the parameters determine where a species lies in trait space. We showed that the geographic distributions of both species can be reproduced by assuming only two interspecific differences. These were the temperature response of mortality and the temperature influence on ingestion rate, which in turn influences growth, development and fecundity. In other words, we can effectively turn C. finmarchicus into C. helgolandicus by modifying those two traits. This framework has the potential to be applied to a number of

Calanus species, and represents a complimentary approach to that taken by others (e.g., Record et al., 2010, 2013; Maps et al., 2012).

A key assumption underlying almost all population models of Calanus is that growth and egg production rate increase monotonically with temperature. This is the second study after Maar et al. (2013) to assume they do not. Instead, we use a dome-shaped relationship between growth and fecundity and temperature. Similar responses have now been established for a number of zooplankton species (White and Roman, 1992; Koski and Kuosa, 1999; Halsband-Lenk et al., 2002; Holste and Peck, 2006; Holste et al., 2009; Rhyne et al., 2009; Pasternak et al., 2013).

The relationships between fecundity and development time and temperature were derived from the experimental ingestion rate data of Møller et al. (2012). A review of the literature shows that we have little knowledge of the key traits of C. finmarchicus such as development, growth and fecundity above 12°C (**Table 2**). Further, we are not aware of published evidence of the influence of temperature on C. helgolandicus's fecundity. Clarifications of the relationship between growth and temperature are therefore a priority of Calanus research. Importantly, conventional models of development are problematic in the context of climate change, where they may falsely predict ever increasing growth rates as temperatures rise. This is highlighted in the Gulf of Maine, where despite summer surface temperatures now often exceeding 20°C (Mills et al., 2013) there have recently been record high levels of C. finmarchicus abundance (Runge et al., 2014).

Understanding the relative geographic distributions of both species can arguably be answered by asking why only C. helgolandicus exists in the region south west of the British Isles. On the basis of our models of growth and fecundity, this region is not noticeably favorable to C. helgolandicus. However, the population model's performance is instructive. Simulated abundance of C. helgolandicus is much higher in winter at L4 than in reality, and we significantly over-predicted EPR in the second half of the year compared with the long-term seasonal pattern (Maud et al., 2015). This is potentially related to food quality. Resolving the apparent contradictions in understanding of the influence of food quality on fecundity (Niehoff et al., 1999; Jønasdøttir et al., 2002; Maud et al., 2015) and development time (Diel and Klein Breteler, 1986) may therefore be the key to fully explaining the relative biogeographies of both species.

Measuring mortality in copepods is commonly viewed as an intractable problem (Ohman, 2012), and therefore models of mortality are inherently uncertain and difficult to validate. This problem is highlighted by our formulation of starvation

TABLE 2 | Temperature ranges for measurement of key C. finmarchicus traits.


\**indicates the reference with the highest reported temperature. References: 1. Ingvarsdøttir et al., 1999; 2. Rey et al., 1999; 3. Harris, 2000; 4. Campbell et al., 2001 5. Hygum et al., 2000b; 6. Saumweber and Durbin, 2006; 7. Runge and Plourde, 1996; 10. Hirche, 1983; 11. Meyer et al., 2002; 12. Hirche et al., 1997; 13. Hirche, 1987; 14. Møller et al., 2012; 15. Preziosi and Runge, 2014; 16. Kjellerup et al., 2012; 17. Rey-Rassat et al., 2002; 18. Cook et al., 2007; 19. Hygum et al., 2000a; 20. Ikeda et al., 2001; 21. Corkett et al., 1986; 22. Tande, 1988; 23. Diel and Klein Breteler, 1986.*

mortality, where it was related to growth rate. The formulation was similar to that used by other modelers (e.g., Tittensor et al., 2003), however it was ad-hoc and impossible to validate. Importantly, the modeled biogeography of C. helgolandicus was dependent on starvation mortality, where it plays a key role in reducing post-diapause populations in oceanic regions to a low enough level to eliminate long-term persistence. However, alternative formulations of mortality could potentially achieve this. Some zooplankton modelers have used U-shaped relationships between mortality and temperature (Rajakaruna et al., 2012), which could act as a limit on the north-western distribution of C. helgolandicus. Further, allee effects (Kiørboe, 2006) and the impact of starvation on long-term fecundity (Niehoff, 2004) could significantly deplete the populations of low-abundance post-diapause C. helgolandicus populations. Including these mortality effects in our model would result in a more complete representation of copepod ecology. However, there is little evidence to quantify the relative magnitude of these sources of mortality. Further advances in understanding copepod mortality (Gentleman et al., 2012; Ohman, 2012) are therefore likely necessary to justify increasingly complex mortality models. However, the influence of mortality should be considered if the model is to be applied, particularly in climate change contexts where changes might be dependent on the specific mortality formulation.

There is a spring bloom of C. helgolandicus in the North Sea (Bresnan et al., 2015), which we did not predict. However, the apparent phenology of C. helgolandicus in the North Sea is difficult to reconcile with the known influence of temperature on its development time (Cook et al., 2007; Bonnet et al., 2009). The first Stonehaven bloom typically occurs before day 130, and temperatures are below 9 °C before then. Evidence indicates that C. helgolandicus either cannot develop from egg to adult (Bonnet et al., 2009) or has a development time greater than 120 d at these temperatures (Møller et al., 2012). Research is therefore needed to reconcile development time studies of C. helgolandicus and phenology in the North Sea. Further, additional model runs (not shown) indicated that most of the modeled autumn bloom in the northern North Sea resulted from animals that are advected into the North Sea from the North. The importance of advection for North Sea C. finmarchicus populations has been previously been studied (Heath et al., 1999), however the role of advection in influencing year to year North Sea C. helgolandicus abundance has not. It may be possible that C. helgolandicus phenology in the North Sea can be explained by the existence of hybrids of C. helgolandicus and C. finmarchicus. This is a speculative hypothesis. However, at the fringes of its northern distribution, C. finmarchicus hybridizes with C. glacialis (Parent et al., 2011; Gabrielsen et al., 2012; Berchenko and Stupnikova, 2014), and we cannot rule out a similar phenomenon for C. finmarchicus and C. helgolandicus.

Finally, our model highlights the importance of lipid dynamics and deep-water temperatures as influences on the distribution of Calanus. Existing statistical models of Calanus biogeography (Helaouët and Beaugrand, 2007; Chust et al., 2013; Hinder et al., 2013) and projections of future distributions (Reygondeau and Beaugrand, 2011; Villarino et al., 2015) have only considered surface conditions. However, the distribution of C. helgolandicus appears to be strongly influenced by deep-water temperatures. Conditions in large parts of the North Atlantic are sufficient to support at least one generation of C. helgolandicus, but high overwintering temperatures result in the inability of a sufficiently large overwintering population to maintain a persistent population. Recent work showed that projected potential diapause duration of C. finmarchicus in the Norwegian Sea under a high emissions scenario was largely unchanged this century, whereas surface temperature increases significantly (Wilson et al., 2016). Development conditions will therefore improve significantly for C. helgolandicus in the Norwegian Sea, whereas diapause conditions would remain largely unchanged. There is therefore potential for C. helgolandicus to become an oceanic species as a result of deep-water warming lagging that at the surface. Similarly, these marginal changes in potential diapause duration may act as a brake on the northward retreat of C. finmarchicus. However, the expected temperature increases across the North Atlantic will reduce lipid levels of animals (Wilson et al., 2016) and the consequences are poorly understood. The future evolution of lipid dynamics may therefore be pivotal in determining the fate of Calanus communities and will have important consequences for the fish, seabirds and marine mammals that depend on the lipids provided by copepods (Beaugrand and Kirby, 2010; Frederiksen et al., 2013).

### AUTHOR CONTRIBUTIONS

RW, MH, and DS contributed to the design of the model. RW implemented and analyzed the model and led the writing of the paper. All authors contributed to the editing and refining of the paper.

### FUNDING

This work received funding from the MASTS pooling initiative (The Marine Alliance for Science and Technology for Scotland) and their support is gratefully acknowledged. MASTS is funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions.

### ACKNOWLEDGMENTS

We thank the Continuous Plankton Recorder Survey for providing access to data, and Neil Banas for fruitful discussions that helped shape the diapause model in the paper. Andrew Yool provided output from the NEMO model. Nicholas Record

### REFERENCES


and a second reviewer provided helpful critical comments which improved the manuscript. Finally, we thank Ian Thurlbeck for invaluable IT support.

### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fmars. 2016.00157

C. hyperboreus Krøyer with comment on the equiproportional rule. Syllogeus 58, 539–546.


Atlantic oceanic copepods in the face of climate change. Global Change Biol. 20, 140–146. doi: 10.1111/gcb.12387


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Wilson, Heath and Speirs. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Resource Competition Affects Plankton Community Structure; Evidence from Trait-Based Modeling

Marc Sourisseau<sup>1</sup> \*, Valerie Le Guennec2, 3, Guillaume Le Gland<sup>4</sup> , Martin Plus <sup>1</sup> and Annie Chapelle<sup>1</sup>

<sup>1</sup> Unité Dynamiques des Écosystèmes Côtiers, Laboratoire D'écologie Pélagique, Département Océanographie et Dynamique des Ecosystèmes, Institut Français de Recherche pour l'Exploitation de la Mer, Plouzané, France, <sup>2</sup> National Oceanography Center, Liverpool, UK, <sup>3</sup> Department of Earth, Ocean and Ecological Sciences, School of Environmental Sciences, University of Liverpool, Liverpool, UK, <sup>4</sup> Laboratoire des Sciences de l'environnement Marin (UMR6539), Institut Universitaire Européen de la Mer, Université de Bretagne Occidentale, Plouzané, France

Understanding the phenology of phytoplankton species is a challenge and despite a lot of theoretical work on competition for resources, this process is under-represented in deterministic models. To study the main driver of the species selection, we used a trait-based model that keeps phenotypic variability through physiological trait parameterization. Next, we validated the results by using the toxic dinoflagellate Alexandrium minutum which is a toxic species. Due to their monitoring, we show that harmful algae are ideal models for studying ecological niches and for contributing to this more global challenge. As a first step, a dimensionless model of an estuary (France) was built with water temperature and water exchanges deduced from a hydro-dynamic model. The biological parametrization takes into account the size (from pico- to microphytoplankton) and the type of assimilation. The results show that temperature, competition for nutrients and dilution are important factors regulating the community structure and Alexandrium minutum dynamics (more especially the bloom initiation and magnitude). These drivers contribute to the determination of the ecological niche of A. minutum, influence the shape of its blooms and provide potential explanations of its interannual variability. This approach makes the community structure more flexible in order to study how environmental forcings could drive its evolution.

Keywords: Droop, competition, inter-specific, estuary, Bay of Brest, *Alexandrium minutum*, phenology, niches

### 1. INTRODUCTION

Over the past few decades, the frequency and intensity of observed events termed Harmful Algal Blooms (HABs), and commonly called red tides, have rapidly increased in global coastal waters (Hallegraeff, 1993, 2010). These phenomena are characterized by the fast growth or accumulation of one phytoplankton species (which can grow up to several million cells.L−<sup>1</sup> ) which can color the surface water. Being photosynthetic, their occurrence is mainly dependent on light, nutrient availability and temperature. However, although phytoplankton enhances biological productivity and plays an outstanding role in the regulation of atmospheric carbon by scavenging it into deep water (Falkowski and Oliver, 2007), these algal blooms can be harmful by causing hypoxia or anoxia

#### *Edited by:*

Kevin John Flynn, Swansea University, UK

#### *Reviewed by:*

Akkur Vasudevan Raman, Andhra University, India David Suggett, University of Technology Sydney, Australia

> *\*Correspondence:* Marc Sourisseau marc.sourisseau@ifremer.fr

#### *Specialty section:*

This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Marine Science

*Received:* 26 May 2016 *Accepted:* 14 February 2017 *Published:* 04 April 2017

#### *Citation:*

Sourisseau M, Le Guennec V, Le Gland G, Plus M and Chapelle A (2017) Resource Competition Affects Plankton Community Structure; Evidence from Trait-Based Modeling. Front. Mar. Sci. 4:52. doi: 10.3389/fmars.2017.00052 during bloom degradation or by spreading toxicity through the food chain for species producing toxin. They have a dramatic impact on aquaculture, fisheries, tourism and public health and often lead to severe economic losses. Among the dinoflagellates which are only a part of the marine phytoplankton, it is estimated that at least 60 species produce endogenous toxins (Burkholder, 1998) that can accumulate in shellfish (clams, mussels, oysters, scallops), fish, and even in birds and mammals to levels that can be lethal for humans.

Monitoring programs dedicated to these algae have provided a large (twice a month to weekly measurements on several years) data sets at the species level to test assumptions on ecological process such as the ecological niche definition. The description of species niches (specially for toxic species) and their evolution through abiotic and sometimes biotic factors is an important and useful goal to forecast the evolution of communities (Wiens et al., 2009; Elith et al., 2010; Kearney et al., 2010) but it requires a detailed understanding of the mechanisms driving their fitness. Our capacity of realistic predictions of species niches with mechanistic model remains however weak and mainly because mechanistic models still include a great deal of empirical fitting that decreases their generic aspect. Although our understanding of HABs events has increased, it remains complex and difficult to assess all the pathways that generate a succession of monospecific blooms (resources, predation, life cycle, etc...). Among all ecological processes and despite its use in conceptual models (Margalef, 1978; Reynolds, 2003), competition has been only poorly or partially used by mechanistic models for understanding and/or predicting future outcomes. However, during a bloom; when the resources required for phytoplankton growth become limited, strong interspecific competition should occur in most cases. The familiar assumption in aquatic microbiology (Bass Becking, 1934) that all the species are in the environment (Everything Is Everywhere) but environmental selection leads to species succession, also identifies interspecific competition as one of the key processes in coastal environment management. However, HABs species are mainly simulated in the environment alone (MacIntyre et al., 2004; Fauchot et al., 2008; He et al., 2008; Jeong et al., 2015 for three of the four groups proposed) or with a physiological description that differs between the other phytoplankton functional types (Lacroix et al., 2007). The relevance of the competition for resources is thus difficult to estimate because a great part of the community adaptation is removed by this reduction. A trait-based approach (Litchman et al., 2012) associated with the EIE assumption provides an interesting methodology that allows us to go further in understanding bloom events.

Thus, we present the first trait-based model that simulates the competition for resources between several phytoplankton species (including the toxic species A. minutum) with a consistent physiological resolution and in realistic conditions. Obtained from trade-offs, this consistency enables species fitness to be analyzed in a more reliable way. With this general model framework, the challenge was to reproduce phytoplankton phenology and A. minutum bloom dynamics. The approach was based on trait-based models that already exist on a global scale (Dutkiewicz et al., 2009; Barton et al., 2010) and one of the difficulties initially considered was the selection of traits and their parametrization for coastal waters. The parametrization of traits was achieved with a random process using a range of realistic values. In doing so, defining the trade-offs (evolutionary compromise for the resource allocation between different functional traits) was also an important step. By using this general approach, we also propose a way of studying phytoplanktonic bloom by understanding which relevant factors may favor A. minutum blooms and how the diversity of trait values can control species invasion and succession. The study was applied in the Bay of Brest due to the fact that since summer 2012, the bay has been affected by one of the most problematic organisms, i.e., the dinoflagellate Alexandrium minutum (Erard-Le Denn, 1997), which gives rise to toxic events. The selection of this species was driven by the large set of physiological parameters provided by the literature and previous studies with local strains (Labry et al., 2008). We focused on the simulated timing of A. minutum and its maximal intensity values for comparison with in-situ observations. This capacity to predict A. minutum blooms could be a good step toward improving coastal management measures.

### 2. MATERIALS AND METHODS

### 2.1. Study Site

The Mignonne estuary, located within the Bay of Brest (**Figure 1**), was chosen as a good example of a so-called "invasion" by a toxic pelagic species. The Alexandrium minutum blooms started in 2012 despite a few earlier observations of low densities in the water (close to the detection threshold of the methodology used by the monitoring program: 10,000 cells.L−<sup>1</sup> ). This site is a typical shallow estuary of Brittany with a mean depth of 3.75 m subjected to tidal effects. The Mignonne is a small coastal river with a mean discharge of 1.47 m<sup>3</sup> .s−<sup>1</sup> . The Mignonne river inputs exhibit very high concentrations of nutrients such as nitrate, silicate and phosphate with concentrations reaching 2,000 µmol.L−<sup>1</sup> , 2,000 µmol.L−<sup>1</sup> and 20 µmol.L−<sup>1</sup> respectively.

### 2.2. Area Definition and Forcings

To simulate inter-specific competition in a simple way, we chose to remove the spatial dimension by using a model similar to a chemostat with a Droop model (Droop, 1968, 1974) which is more reliable to physiological traits (Flynn, 2005) and accurate in many comparative studies (Grover, 1991, 1992). With this simplification, only the temporal variability of the niches in this small environment was analyzed and the spatial definition of this environment was fixed according to the recurrent observed distribution of Alexandrium minutum blooms during the 3 years considered: the Mignonne estuary (**Figure 1**). This approximation was possible because the strong tidal mixing and shallow depths in this area prevent front and stratification formation.

The considered area which sometimes provides favorable conditions for A. minutum growth; undergoes water exchanges associated with tide and river inputs. All these physical values (water residence time, water depth, nutrient exchanges and water temperature) were estimated using the hydrodynamic model MARS3D (Lazure and Dumas, 2008) configured for

the Bay of Brest and forced by realistic weather conditions (wind, air temperature, relative humidity and atmospheric pressure from Météo-France AROME model, Seity et al., 2011) as well as by the measured daily Mignonne flow (HYDRO database, Governmental Environmental Agency, monitoring station Irvillac, see **Figure 1** for river location). These forcing fields constitute the best set available for this area and the water residence time remains rather insensitive to the weather conditions. The model bathymetry was provided by the SHOM (French Naval Hydrographic and Oceanographic Service). Three years of interest (2012, 2013, and 2014) were simulated. The dilution rates (D) were computed by a classic methodology of tracer dilution over a time period close to 25 h (the period between two high tides): a passive tracer was initialized in the whole area at high tide and the decreasing concentration due to dilution was simulated by the threedimensional (3D) model during 25 h until the next high tide. The dilution rate was computed as the difference between the two concentrations divided by the exact time lag between the two high tides, and the tracer was re-initialized for the next 25 h. Concomitantly, the simulated water temperature was recorded to calculate the mean temperature. Then, both dilution rates and temperatures were interpolated to provide values for a 24 h period. The mean water volume of the Mignonne estuary (V) was estimated at mean sea level height using the model bathymetry.

Commonly used to simulate phytoplankton dynamics in experiments or coastal waters (Flynn, 2005), the selected resources for phytoplankton competition were light and three macronutrients: nitrogen (as ammonium and nitrate), phosphorus (as phosphate) and silicium (as silicate). Light intensity was estimated from Sea Surface Irradiance (SSI) of daily satellite data (provided by METEOSAT Second generation satellites, full description available on the OSI-SAF web server www.osi-saf.org/index.php, validation by Le Borgne et al., 2006). The SSI is the mean daily solar irradiance reaching the earth's surface in the 0.3–4 m band expressed in W.m−<sup>2</sup> . It was multiplied by 0.95 to remove sea surface albedo and then by 0.425 (fraction of the total spectra wavelengths that is used by photosynthetic pigments) in order to estimate the mean daily Photosynthetically Active Radiation (PAR, I0). Then, instantaneous PAR was calculated as a sinusoidal function of the mean daily PAR and the Julian day length was calculated following the method described in Forsythe et al. (1995). The light extinction coefficient due to the water column (Kpar) was calculated following Gohin et al. (2005) using OSI-SAF satellite data for suspended matter (SM in mg.L−<sup>1</sup> ) and chlorophyll a (in mg.L−<sup>1</sup> ).

Nutrient concentrations in Mignonne waters were calculated by taking into account (i) the nutrients brought by the Mignonne River (interpolated from monthly data measured by Brest Metropole Oceane) and (ii) the nutrient concentrations prevailing in the rest of the Bay of Brest (interpolated from weekly data provided by the SOMLIT "Service d'Observation en Milieu Littoral," INSU-CNRS, at the Porzic station).

### 2.3. Traits Description of Phytoplankton Model

A large diversity of traits and trade-offs associated can structure phytoplankton communities (Litchman et al., 2007; Litchman and Klausmeier, 2008). From these, we pragmatically selected only the traits (cell size, optimal temperature and silicate dependence, see **Figure 2**) relevant for the considered area and well defined for phytoplankton groups and species.

### 2.3.1. Cell Size and Cell Quotas

Cell size is a key trait that impacts growth, metabolism and access to resources (Litchman and Klausmeier, 2008). Major parameters of nutrient uptake and growth scale with cell size and the size is here considered as a fixed trait for each phenotype. The size range covers the whole size spectrum usually used to characterize the phytoplankton community from 1 to 120 µm (**Figure 2**). Size corresponds to the equivalent spherical diameter (Equivalent Spherical Diameter - ESD) and allows calculating cell volume which is next used to simulate trade-offs with nutrient uptake and growth. The Capacity of the phytoplankton cells to modify their size (Smith and Zhao, 2001; Arino et al., 2002; Flynn, 2005) was not considered here as we decided to simulate nutrients storage capacity (quota). In fact, the quota-based approach was used (Droop, 1968, 1974) because it is more reliable for physiological traits (Flynn, 2005) and simulations. All previous comparative studies concluded that growth is better described as a function of internal rather than environmental nutrient concentration (Grover, 1991, 1992). This approach and its application to species competition has been widely investigated in the literature (Pascual, 1994; Legovic and Cruzado, 1997; Smith, 1997; Smith and Zhao, 2001; Sunda et al., 2009) and the theoretical results are also fully applicable in our study. As the conditions are not stationary and perturbations occur at several frequencies from the seasonal cycle to tidal oscillations, the exclusive competition in our simulations was better reproduced by a Droop model. In this way, our approach is close to Sommer (1991) work and novative compared to Darwin model (Follows and Dutkiewicz, 2011). Intracellular cell quotas of phosphate and nitrogen were also considered.

### 2.3.2. Optimal Temperature

Temperature is a major environmental parameter that governs physiological functions like photosynthesis, respiration, growth, resource acquisition, motility and sinking (Eppley, 1972; Litchman and Klausmeier, 2008). This dependence may be characterized by the optimal temperature. It has been used here to model phytoplankton maximal growth rate with all other factors (nutrient, light) being optimal.

### 2.3.3. Silicate Dependence

Diatoms are one of the major microphytoplankton group observed in the Bay of Brest. All species in this taxonomic group are silicified species and this major trait induces a silicate assimilation. Without considering any relation between this trait and physiological rate (uptake, growth...) in our simulation, we wanted to determine how the relevance of the potential specific limitation of this large cell size could occur to permit a higher growth of non-silicate large size species (including Alexandrium minutum).

Other traits proposed by Litchman and Klausmeier (2008) such as toxin production, light adaptation and swimming capacities were considered but rejected. Chemical cues are relevant processes for species interactions (Ianora et al., 2011). Several metabolites have allelopathic effects and toxins of toxic algae are obviously widely studied in this way (Hulot and Huisman, 2004; Graneli et al., 2008). A. minutum thus produce allelopathic substances that would shift the grazing pressure to non-toxic species (Guisande et al., 2002) or decrease the growth rate of other phytoplankton species (Arzul et al., 1999). However, the "toxin" property is linked to a negative effects on humans (from a food safety aspect) and/or macro-organisms (fish or shellfish). This characteristic is not linked to the competition for resources or interactions with specific grazers. Even the toxic blooms can be grazed extensively (Jeong et al., 2015). We can thus assume that many other cellular metabolites can have allelopathic effects without affecting animal physiology and conversely, are not measured. The action of toxins in the environment is still being debated in the scientific community (Hulot and Huisman, 2004; Jonsson et al., 2009), we therefore chose to neglect this trait despite its potential implication in the results of competition (Roy and Chattopadhyay, 2007; Grover and Wang, 2014). The optimal irradiance for a cell is also a key parameter and is modulated by the quantity and quality of its pigment content. Although, the tidal mixing in the considered area removed the possibility of a vertical discretization of the phenotypes (Hickman et al., 2010), the bloom timing of each one could be modified according to their optimal irradiance. MacIntyre et al. (2004) used a remarkable adaptation to low light levels of one phytoplankton species to simulated its bloom initiation. However, despite the interest of such trait integration, we first used a constant optimal irradiance for all phenotypes by considering that, at the first order, the relevance should remain low because the light resource is rarely limiting during the blooming period of Alexandrium minitum (mid-May to August). One of the last critical traits considered is the organism's behavior and mobility. Dinoflagellates have especially significant swimming capacities (Kamykowski, 1995) that can lead: to heterogeneous vertical distributions (Kamykowski et al., 1992) and accumulation processes (Anderson and Stolznbach, 1985; Janowitz and Kamykowski, 2006) and to higher nutrients uptakes in oligotrophic conditions due to the depletion around the cell (Falkowski and Oliver, 2007). However, according to the hydrodynamic of the considered estuary (Raine, 2014), stratification (haline or thermal) never occurs over the year in the estuary because the mixing intensity is mainly driven by the interaction of the tide and the bathymetry. We therefore assume that this physical-biological interaction remains stable over the year and is included in the parametrization of the uptake rates.

### 2.3.4. Modeling the Phytoplankton Diversity

The large variability was implemented by using 50 species (or phenotypes for the selected traits) (Ns) with random trait values. Each species is defined by its cell size, its capacity or not to

assimilate silicate and its optimal temperature. As it isnt linked to precise species, it can also be considered as phenotype. Only one species was fixed and defined for A. minutum. 51 phenotypes were thus in competition for a limited number of resources in each simulation. To analyze the outputs of the simulated phytoplanktonic community, 2 or 4 cell groups were created according to their size (or volume, see **Figure 2**). The small cells include the picoplankton (0.5–5 µm<sup>3</sup> ) and a fraction of the small nanoplankton (ESD < 5 µm) while the large cells include the largest cells of the nanoplankton (ESD < 5 µm) and the microplankton (4,000–10<sup>6</sup> µm<sup>3</sup> ). This size range covers the whole size spectrum (pico-, nano-, and micro-phytoplankton) usually used to characterize the phytoplankton community. The size division in nanoplankton is related to the identification limit by optic microscopy (ESD > 5 µm). Alexandrium minutum belongs to the microplankton group with a volume close to the value of 5,832 µm<sup>3</sup> (18 µm of ESD, Maranon et al., 2013).

### 2.4. Mathematical Model Description

The differential equations governing the dynamics of the system are usual. The abundance of each species (Ni), nutrient concentrations ([PO4], [NH4], [NO3], and [Si]) and intracellular cell quotas of phosphate and nitrogen (QP,<sup>i</sup> and QN,i) are state variables whose evolution over time can be expressed as follows (for symbols and parameter values, see **Tables 1**, **2**, respectively):

$$\begin{aligned} \frac{dN\_i}{dt} &= \mu\_i N\_i - DN\_i \\ \frac{d[PO\_4]}{dt} &= -\sum\_{i=1}^{N\_0} Vp\_{i,i}N\_i - D[PO\_4] \\ &+ [PO\_4]\_{ir\bar{V}} \frac{F}{V} + [PO\_4]\_{\text{day}}(D - \frac{F}{V}) \\ \frac{d[NO\_4]}{dt} &= -k\_{NH\_4i}[NH\_4] - \sum\_{i=1}^{N\_0} V\_{NH\_4i}N\_i - D[NH\_4] \\ &+ [NH\_4]\_{\text{riv}} \frac{F}{V} + [NH\_4]\_{\text{boy}}(D - \frac{F}{V}) \\ \frac{d[NO\_3]}{dt} &= k\_{NH\_4i}[NH\_4] - \sum\_{i=1}^{N\_0} V\_{NO\_3i}N\_i - D[NO\_3] \\ &+ [NO\_3]\_{\text{riv}} \frac{F}{V} + [NO\_3]\_{\text{boy}}(D - \frac{F}{V}) \\ \frac{d[Si]}{dt} &= -\sum\_{i=1}^{N\_0} Q\_{Si}\mu\_i N\_i - D[Si] \\ &+ [Si]\_{\text{riv}} \frac{F}{V} + [Si]\_{\text{boy}}(D - \frac{F}{V}) \\ \frac{dQ\_{P,i}}{dt} &= V\_{P,i} - \mu\_i Q\_{P,i} \\ \frac{dQ\_{N,i}}{dt} &= V\_{N,i} - \mu\_i Q\_{N,i} \end{aligned} \tag{2}$$

#### TABLE 1 | Table of symbols.


The net growth rate (µ net i ) of change in the abundance (Ni) is the gain from the growth rate (µi) minus the dilution (D). There is no specific term for a mortality process because it was overlooked compared to the dilution values. To prevent the extinction of a species due to dilution and to simulate a possible migration after unfavorable conditions, a minimal concentration (Nmin,i) is considered for each species. Due to the exponential distribution of the cell abundance according to their sizes, it is calculated in such a way that the total cell volume of each species is equal to 106µm<sup>3</sup> L −1 . This approach gives lower abundances for big cells (at least 1 cells.L−<sup>1</sup> ) compared to small cells (at least 10<sup>6</sup> cells.L−<sup>1</sup> ). Concerning A.minutum, the threshold is thus 171 cells.L−<sup>1</sup> and similar to the detection threshold by using the protocol of the monitoring program (100 cells.L−<sup>1</sup> ).

### 2.5. Parameter Values

The growth rate of each species is modulated by their maximal growth rate µmax,<sup>i</sup> (d −1 ), the temperature fT,<sup>i</sup> , and four limitation factors fL,<sup>i</sup> , fN,<sup>i</sup> , fP,<sup>i</sup> , fSi,<sup>i</sup> (dimensionless ranging from 0 to 1) TABLE 2 | Global parameters and allometric coefficients.


where only the most constraining is retained (Liebig's minimum law):

$$
\mu\_i = \mu\_{\text{max},i} f\_{\text{T},i} \min(f\_{\text{L},i}, f\_{\text{N},i} f\_{\text{P},i}, f\_{\text{Si},i}) \tag{3}
$$

Temperature limitation (fT,i) is simulated in the same way for all species with a function developed for A. minutum in the Bay of Cork (Nì Rathaille, 2007):

$$fr\_{i} = \begin{cases} 0 \text{ if } T < T\_{opt,i} - 10 \\ 0.1(T - T\_{opt,i} - 10) \text{ if } T\_{opt,i} - 10 < T < T\_{opt,i} \\ 1 \text{ if } T > T\_{opt,i} \end{cases} \\ \text{(4)}$$

where Topt,<sup>i</sup> is the optimal temperature of growth for each species and T is the simulated temperature. The light limitation (fL,i) on phytoplankton growth rate is expressed by a hyperbolic tangent (Jassby and Platt, 1976):

$$f\_{L,i} = \tanh(\frac{I}{I\_{opt}}) \tag{5}$$

where I corresponds to the Photosynthetically Available Radiation (PAR) and Iopt to the optimal light intensity. This value is assumed to be constant for all the phenotypes. Variations of the water depth associated with the tide are taken into account by calculating I for each given depth (z) with the Beer-Lambert law:

$$I = I\_0 e^{(-K\_{par} \cdot Z)} \tag{6}$$

where Kpar is the light attenuation coefficient. The growth rate is calculated for each depth and the mean of these growth rates was used in the model.

Nitrogen (fN,i) and phosphorus (fP,i) limitations follow a normalized Droop function (Droop, 1974), which is a hyperbole depending on the minimum (Q min j,i ) and maximum (Q max j,i ) cell quotas for the element j:

$$f\_{j,i} = \frac{Q\_{j,i}^{max}}{Q\_{j,i}^{max} - Q\_{j,i}^{min}} (1 - \frac{Q\_{j,i}^{min}}{Q\_{j,i}}) \tag{7}$$

According to Flynn (2008), silicate is not stored by siliceous cells and is only used for the fabrication of the frustule which occurs during cell division. The limitation in silicate is therefore expressed through a simple Michaelis-Menten formulation :

$$f\_{\rm Si,i} = \frac{[\rm Si]}{K\_{\rm si,i} + [\rm Si]} \tag{8}$$

where KSi is the half-saturation constant for siliceous species.

The nutrient uptake rates (V max NO3,i , V max NH4,i , and V max P,i ) follow Michaelis-Menten kinetics and decrease linearly when cell quotas increase:

$$\begin{split} V\_{NH\_4,i} &= V\_{NH\_4,i}^{\max} \ast \frac{[NH\_4]}{k\_{N,i} + [NH\_4]} \frac{(Q\_{N,i}^{\max} - Q\_{N,i}) \cdot N\_i}{Q\_{N,i}^{\max} - Q\_{N,i}^{\min}} \\ V\_{NO3,i} &= V\_{NO3,i}^{\max} \ast \frac{[NO\_3]}{k\_{N,i} + [NO\_3]} \left(1 - \frac{[NH\_4]}{k\_{N,i} + [NH\_4]}\right) \\ &\frac{(Q\_{N,i}^{\max} - Q\_{N,i}) \cdot N\_i}{Q\_{N,i}^{\max} - Q\_{N,i}^{\min}} \\ V\_{P,i} &= V\_{P,i}^{\max} \ast \frac{[PO\_4]}{k\_{P,i} + [PO\_4]} \frac{(Q\_{P,i}^{\max} - Q\_{P,i}) \cdot P\_i}{Q\_{P,i}^{\max} - Q\_{P,i}^{\min}} \end{split} \tag{9}$$

The absorption of nitrogen as nitrate is inhibited by ammonium absorption (Parker, 1993) because the necessary reduction of nitrate ions to ammonium ions requires a great deal of energy.

### 2.6. Key Physiological Trade-Offs

Some trade-offs are used in order to define competition between all the species within the model ecosystem. Functional traits used to simulate phytoplanktonic diversity thus follow different types of distribution (see **Table 3**). Although, a large proportion of the traits is related to the cell volume, phytoplankton maximal growth rate is simulated by the temperature according to a global exponential law (Eppley, 1972). There is a relationship with Topt but not with cell size:

$$
\mu\_{\text{max},i} = \mu\_{\text{max},ref} \cdot e^{(k\_T \cdot T\_{\text{opt},i})} \tag{10}
$$

k<sup>T</sup> is the temperature coefficient for the growth rate and µmax,ref is the growth rate at 0◦ without other limitations. The following traits Q min N,i , Q max N,i , V max NH4,i , V max NO3,i , Q min P,i , Q max P,i , V max P,i , QSi,<sup>i</sup> , KN,<sup>i</sup> , KP,<sup>i</sup> and KSi,<sup>i</sup> are dependent on the cell volume through an allometric relationship in the form of a power function β ·V α (see **Table 3** for the allometric coefficient values). Hence, some sizerelated differences are introduced in the storage capacity and TABLE 3 | Distribution of the functional trait.


The optimum irradiance is fixed for all the species (20 Wm<sup>2</sup> ).

maximal nutrients uptake rate. Indeed, large cells possess a bigger storage capacity than small ones. The maximal uptake rate of small cells is lower than that of large cells but the reverse is true for nutrient affinity (1/KN,<sup>i</sup> , 1/KP,i). Consequently, small cells will outcompete large ones in oligotrophic conditions.

Alexandrium minutum traits were obtained from the literature (see **Table 4** for references). Its maximal growth rate is identical to species with the same volume but its distinction lies in its maximum phosphate uptake rate and its maximum cell quota which are both higher than in other cells (Chapelle et al., 2010).

### 2.7. Phenological Characterization of *A. minutum* Bloom

Phenology refers to changes in the timing of seasonally reoccurring biological events due to environmental changes. Due to the random selection, 200 simulations were carried out with different random draws and their mean values were analyzed. To compare the simulated dynamics of A. minutum with the in situ observations, the method developed by Rolinski et al. (2007) was used instead of a simple correlation with the data. Some particular points of A. minutum phenology such as the maximum abundance, the date of this maximum, the beginning, end and duration of the bloom were thus obtained. To determine these shape parameters, a Weibull function is proposed by Rolinski et al. (2007):

$$\mathcal{W}(\mathbf{x}) = \left(d + e^{\left(-\left(\mathbf{x}/e\right)'\right)}\right) \cdot \left(1 - a \cdot \exp(-(\frac{\mathcal{X}}{b})^c)\right) \tag{11}$$

After a log-transformation of the data, the values of the parameters (a, b, c, d, e, and f) that provide the best fit are chosen. The maximum abundance and its date are directly provided by the Weibull function. From these values, the area under the curve is calculated. The start date of the bloom corresponds therefore to the 2% quantile of the area under the curve before the date of the maximum. By contrast, the 98% quantile of the area under the curve after the date of the maximum, corresponds to the date of the end of the bloom. The duration of the bloom is the difference between the beginning and end of the bloom. This part aims to

TABLE 4 | Specific parameters used for *A. minutum*.


#### TABLE 5 | Parameters obtained with the Weibull function fitted on *A. minutum* blooms for the three years.


Date of maximum was estimated for different number of phenotypes, and bloom initiation, termination and maximal values (cells L−<sup>1</sup> ) were estimated with only 50 phenotypes (N<sup>s</sup> = 50).

and the latest in 2012 (25TH May). Concerning the termination, the bloom in 2014 ended earlier (end of August) whereas the one in 2012 ended the latest (end of September). The small oscillations during the bloom dynamics (notably in 2012) are associated with the spring/neap tidal cycle which affects the dilution rate.

discover if the modeled phenology reveals strong variations over the years as observed in the field.

Several ensembles of simulations were then carried out through a selected range of phenotype numbers (Ns = 20, Ns = 100, Ns = 150, and Ns = 200). Next, the cardinal dates (beginning, maximum, and termination), timing and maximum abundances of the A. minutum bloom were recalculated with the same process (**Table 5**).

### 3. RESULTS

### 3.1. *A. minutum* Appearance and Bloom Characteristics

Whatever the year and the simulation, the presence of A. minutum is simulated from the beginning of May until the beginning of September (**Figure 3**). Despite a simulated interannual variability for the A. minutum bloom, the duration of the bloom is quite constant (≈ four and a half months). The random number of species is also sufficient to limit the variability of each ensemble with some reduced differences between the 25TH and 75TH percentiles. This observation enables some comparisons to be made between each year.

The model simulates the highest abundances of A. minutum in 2012 with a mean value of 1 million cells.L−<sup>1</sup> on 5TH July. In 2014, the maximum abundance remains large (around 3.10<sup>5</sup> cells.L−<sup>1</sup> ) but three times lower than in 2012. The lowest values are observed in 2013 with 85,000 cells.L−<sup>1</sup> . Besides these maximal values and close bloom duration, some differences in the timing of the maximal abundances are also simulated in a significant way. In 2014, the maximum is reached on 5TH July which is a little bit sooner than in 2013 (8TH July) and 2012 (14TH July). Again, the percentiles indicate a low variability in these values related to the random process. They are driven by the phenotype succession and the environmental forcing. Regarding 2013, the lowest maximum abundance is simulated but with a long duration around this value (≈ one month). The earliest bloom initiation is simulated in 2014 (4TH May)

### 3.2. Factors Controlling *A. minutum* Blooms

The difference between sink and source terms (the net growth) controls the simulated bloom timing and intensity, and thus the potential A. minutum appearance period during 2012 is four months from mid-May to the end of September (**Figure 4**). The growth rate depends on the following factors: temperature, nutrients (nitrogen and phosphate) and light. At the end of the winter of 2012, despite nitrogen and phosphate cell quota values close to their maximums, A. minutum growth is limited at low water temperatures (below 10◦C). During the spring, the main limitation remains the temperature until the beginning of May after which the growth period occurs (**Figure 5**). Until mid-June, the nitrogen limitation is the most important, followed by a phosphate limitation that limits A. minutum growth in summer (after mid-June) until October 2012. In autumn, despite some new nutrient inputs from the river, the second growth period remains limited to 1 month and the simulated abundances remain very low due to light and temperature limitations.

The same patterns are observed for subsequent years. There is therefore a marked temperature control for bloom initiation (**Tables 5**, **6**). The shift of the onset toward an earlier period in 2014 is explained by a warmer temperature in mid April (12.8◦C) compared to 2012 and 2013 (11.8 and 11.9◦C, respectively). The simulated variability of the A. minutum bloom intensity is next explained by nutrient concentrations. Phosphate limitation is less important in 2012 due to higher flow rates from the Mignonne river (respectively 1.5, 0.47, 0.66, 0.55·105m<sup>3</sup> s <sup>−</sup><sup>1</sup> mean flow from May to August in 2012, 2013, 2014, and 2015) which allow higher maximum abundances. The relationship between river flow and nutrient concentrations is illustrated by the mean in situ PO4 concentrations that have been weekly measured in 2013, 2014, and 2015 with respective values of 0.12, 0.26, and 0.17 µmol.l−<sup>1</sup> . These measurements follow A. minutum maximum abundances, 2012 being higher than 2013.

ensemble and 25th and 75th percentiles are plotted only for 2013 (dashed lines). Positions of the three estimated Weibull parameters are added (date of initiation, maximum and termination of the bloom).

### 3.3. Phenology of *A. minutum* and Phytoplankton Successions

The outputs show a variation in the community structure that is repeated for each year. In fact, large cells (ESD > 5 µm) are the first to grow (**Figure 6**) and can be considered opportunist phenotypes (higher growth rates when nutrients are high). They are then replaced by smaller cells as the phosphate concentration decreases with a low evolution from opportunists to gleaners (more competitive cells when nutrients are low) from mid-May to September. Small cell abundances increase at the beginning of June and due to their higher affinity for phosphate than large cells, they generate a sharp decrease in phosphate concentration after 15th June (with a minimum of 0.01 µmol.L−<sup>1</sup> ). Until October, phosphate concentration is the most limiting factor, which only rises in October because nutrient inputs from the river increase. The model thus simulates a second peak of A.

minutum and large cell abundances well marked in October 2014 (with 2,000 cells.L−<sup>1</sup> ). This is due to a lower dilution rate (0.2 d −1 in 2013 and 2012 against 0.1 d−<sup>1</sup> in 2014). However, the growth period remains too short to create a significant peak. At the end of November in the 3 years simulated, A. minutum and large cell abundances return to their initial and minimal values. It is through an exclusive competition via phosphate limitation, that the termination of the A. minutum bloom is simulated.

To sum up, simulated A. minutum bloom initiation is controlled by temperature while the bloom duration and termination are controlled by interspecific competition for the nutrient resources (nitrogen and phosphate). The simulated difference in the A. minutum bloom intensity for the three years is due to the nutrient concentrations inside the area and the simulated limitation in phosphate is less in 2012 thus leading to higher values of maximum abundances.

### 3.4. Sensitivity Analysis and Comparison with the Data Set

Due to the small variability within the ensemble (see the percentiles in **Figure 3**), we assume the ensemble size sufficient to permit comparison between average results. The sensitivity tests were thus conducted on the number of selected phenotypes (Ns). Four quantities of phenotypes in competition with A. minutum inside the ecosystem were used (Ns = [20; 50; 100; 150]). By doubling the number of species, (Ns = 50–100} and Ns = 100– 200}), the maximum abundance is divided by 2 for the 3 years (**Figure 7**). The total cells per size class remain however constant and show the redundancy between phenotypes. Except for the lowest number (Ns = 20), the timing of the highest concentration remains independent of the number of selected species (**Table 5**). The small differences (±3 days) in 2013 are created by the fitting of the Weibull function and the relatively large bloom duration around the highest concentration.

Although the more realistic maximum values are obtained with Ns = 20 for all 3 years, the beginning and end of the associated bloom do not fit with these observations. By comparison with the in situ observations, the simulation with

TABLE 6 | Observed interannual variability of *A. minutum* blooms.


50 phenotypes is more realistic and this was the main reason for choosing this value for the model validation.

For the 3 years and as explained above, the simulated intensity of the A. minutum bloom is slightly underestimated and reaches the values of 10<sup>6</sup> , 4·10<sup>5</sup> , and 7.8·10<sup>5</sup> cells.L−<sup>1</sup> against 4.2·10<sup>6</sup> , 8.4·10<sup>5</sup> , and 1.5·10<sup>6</sup> respectively (**Figure 8**). Otherwise, for the years 2012 and 2013, the model reproduces very well the seasonal dynamics of A. minutum with a growth starting at the end of May, a maximum at the end of June and a rapid decrease in July. Concerning the year 2014, the growth of A. minutum occurs earlier and is well reproduced by the model. However, it does not fit with the decrease phase which is simulated on 29TH August instead of the 16TH September.

The total microphytoplankton flora was compared to the simulated dynamics of the large cells (large nanoflagellates + microphytoplankton, A.minutum included). Their spring bloom initiation is clearly not well simulated by the model (**Figure 8**). In fact, this delay in the bloom timing is related to an underestimation of the net growth rate and/or immigration. In 2012, the model simulates a maximum of 5.7·10<sup>6</sup> against 7.4·10<sup>6</sup> for the observations on approximately the same date. In 2013, the maximum abundance simulated reached 2.8·10<sup>6</sup> against 5.5·10<sup>5</sup> for the observations.

Conversely, for all 3 years, the dynamics after the bloom maximum fit well with the observations although small differences do appear in 2014. These simulated values are higher than the observations that were made that year (4.5·10<sup>6</sup> against 2.4·10<sup>6</sup> ). The decrease is also simulated earlier than observed (one month of delay) and overestimated by the model. A second

increase in the abundance is simulated during October with values again higher than the observations.

### 4. DISCUSSION

### 4.1. Dynamic of the Community Structure

Despite all the assumptions inherent to a model conception, the simulations are in good agreement with the observations. The community starts from opportunist phenotypes and during 2 months, progress to gleaners due to an increase of the resources competition. The strong initial assumption that the predation was negligible compared to dilution and constant over the years appears consistent for the selected area and period. However, for an application of the model in another area or over an extended period, this assumption could be challenged. An integration of a predation more or less specific could be required with a large set of formulation available in the literature going from a generalist grazer by keeping the same differences between phenotypes fitness (its capacity to invade the environment considered) only driven by their growth rates to the use of a "Kill The Winner" (KTW) strategy (Prowe et al., 2012; Vallina et al., 2014) which modifies the inter-specific competition by bringing the fitness of phenotypes very close.

The main error of the model is the delay of the bloom timing for diatoms and large flagellates. We link this bias to the lack of spatial dimension and the migration processes through open boundaries. The bloom timing of large cells is dependent on the available light and temperature but is mainly driven by the dilution rate. By considering another area or by increasing the considered area, the dilution rate will be strongly modified. All the connected areas, such as the up- and down-stream parts of the estuary, are associated with different dilution rates and later or earlier blooms can be expected with phenotypes having different optimal temperatures. The results of the simulation can thus be analyzed by assuming that an earlier bloom should take place in the bay of Brest from March to April before an advection

in the estuary but that these phenotypes are not adapted to the Mignonne estuary conditions.

## 4.2. Dynamic of *A. minutum*

The initial objective, to simulate one species of interest with similar organisms inside a common framework based on trait, was successful. Without any particular fitting of the physiological parameters (all the parameters used are based on the literature at the community and species levels) and the same resolution of the biological processes for all the organisms, the model shows very interesting capacities to simulate the right timing and variability of the bloom intensity over the 3 years. Only one condition was required for A. minutum parameter set: for at least one trait, this species must have an equivalent or a better fitness than other theoretical species with the same size and optimal temperature. Without respecting this condition, A. minutum would not be able to invade.

The model also shows that the local growth is sufficient to support the observed densities and that the timing and intensities were driven only by local conditions and resources competition. This simulated growth and presence period must however be analyzed as the potential ecological niche defined by abiotic factors and inter-specific competition for resources with all external forcings being constant over time. Similar to the community structure, a modification of the phenotype fitness due to a variation of the selective grazing pressure will introduce a bias between the simulated and the observed inter-annual variability. Such variations over time in the grazers community were already observed in similar estuaries in recent studies. The grazer community observed was dinoflagellate parasites (Erard-Le Denn et al., 2000; Guillou et al., 2008) that can be both highly specific of their prey (Coats and Park, 2002; Chambouvet et al., 2008) or not (Figueroa et al., 2008) and can change over time.

The main difference between our work and previous theoretical studies focused at the community level (Grover, 1991, 1992; Pascual, 1994; Legovic and Cruzado, 1997; Smith, 1997; Smith and Zhao, 2001; Sunda et al., 2009) is the introduction of temperature preferences. This additional trait is independent of all the others with an optimal temperature that was randomly selected in the temperature range measured in the area [10–20]◦C. The use of these two independent traits (size and optimal temperature) explains the minimum number of phenotypes required to obtain a good estimation of the bloom duration. Fifty is the minimal value required to sample correctly the traits-space. It must also be notice that the maximal densities of A. minutum bloom are always strongly correlated with this number of phenotypes (**Figure 7**). With a random process to select size and temperature instead of a regular distribution along the trait ranges, we accept the possibility of a full redundancy between a few phenotypes if the total number is large enough to sample correctly all the traits-space. The biomasses of these redundant phenotypes are obviously close but the temporal niche remains stable and particularly the bloom initiation timing. The relevance of the forcing on the timing is thus highlighted by the model: temperature and dilution appear as the main drivers of the bloom timing for A. minutum in the Mignonne estuary; the nutrient inflows mainly drive the maximal abundance values reached by the bloom while the interspecific competition can also drive the bloom magnitude and termination.

The high capacity of the model to simulate correctly the right timing of the bloom initiation with only one average phenotype for one species raises the question of the phenotypic variability. The parameters used here are provided by only a few strains whereas intra-specific variability studies have highlighted a high heterogeneity of physiological parameters (Aguilera-Belmonte et al., 2011; Kremp et al., 2012; Hadjadji et al., 2012). The "surprising" good fit between the observations and simulations using this average phenotype could result from an average of many local dynamics mixed by the tide and the average of the ensemble simulation. Nevertheless, the effect of this intraspecific variability on the species dynamics remains another process to understand and a great challenge to the ecology of communities.

### 5. CONCLUSION AND PERSPECTIVES

The main interest of the model was to understand, due to the mechanistic aspect, the processes driving the seasonal and inter-annual variability of the niche successions in the community. In this respect, this work was successful and was validated by considering one particular species in this area. Temperature and dilution appear to be the main factors enabling bloom events but competition process is also an important factor despite the high nutrient inputs. The trait based approach that integrates some variability in the organisms fitness instead of an empiric selection and limitation of the ecosystem complexity keeps more flexibilities for the adaptation of the community to environment pressure. We expect that by using and developing (increase of the traits complexity) this approach for ecosystem management, there will be larger spectrum of potential replies by the phytoplankton community to environment modifications. Despite that the forecasting potential of the model was not the initial objective, the model thus shows some very good capacities to simulate the ecological niche of A. minutum as well as the potential link with warning period. Finally, in the context of global change, these models could be used to study the relevance of abiotic factors on the species niches as well as their interaction through the competition

### REFERENCES


process which could lead to more efficient management efforts.

### AUTHOR CONTRIBUTIONS

MS, MP, and AC had substantial contributions to the conception and design of the work. VL and GL contributed mainly to the acquisition but all the authors participated to analysis of data for the work. MS and VL participated mainly to the draft the work but all the authors revised it critically. All the authors approved the submitted version and agreed to be accountable for all aspects.

### FUNDING

The project was supported by the Agence de l'Eau Loire Bretagne and the Region Bretagne (Daoulex project).

### ACKNOWLEDGMENTS

We thank Meteo-France, the REPHY monitoring program and the VELYGER program for providing the data set (Pouvreau et al., 2016). Data were successively collected in the framework of the Daoulex project. We thank S. Petton for the setting of the hydrodynamic configuration.


Elith, J., Kearney, M., and Phillips, S. (2010). The art of modelling range-shifting species. Methods Ecol. Evol. 1, 330–342. doi: 10.1111/j.2041-210X.2010.00036.x


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Sourisseau, Le Guennec, Le Gland, Plus and Chapelle. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Modeling What We Sample and Sampling What We Model: Challenges for Zooplankton Model Assessment

Jason D. Everett 1, 2 \*, Mark E. Baird<sup>3</sup> , Pearse Buchanan<sup>4</sup> , Cathy Bulman<sup>3</sup> , Claire Davies <sup>3</sup> , Ryan Downie<sup>3</sup> , Chris Griffiths 4, 5, Ryan Heneghan<sup>6</sup> , Rudy J. Kloser <sup>3</sup> , Leonardo Laiolo3, 7 , Ana Lara-Lopez <sup>8</sup> , Hector Lozano-Montes <sup>9</sup> , Richard J. Matear <sup>3</sup> , Felicity McEnnulty <sup>3</sup> , Barbara Robson<sup>10</sup>, Wayne Rochester <sup>11</sup>, Jenny Skerratt <sup>3</sup> , James A. Smith1, 2 , Joanna Strzelecki <sup>9</sup> , Iain M. Suthers 1, 2, Kerrie M. Swadling4, 12, Paul van Ruth<sup>13</sup> and Anthony J. Richardson6, 11

#### Edited by:

Dag Lorents Aksnes, University of Bergen, Norway

#### Reviewed by:

Frederic Maps, Université Laval, Canada Webjørn Melle, Institute of Marine Research, Norway

\*Correspondence:

Jason D. Everett Jason.Everett@unsw.edu.au

#### Specialty section:

This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Marine Science

Received: 03 August 2016 Accepted: 07 March 2017 Published: 22 March 2017

#### Citation:

Everett JD, Baird ME, Buchanan P, Bulman C, Davies C, Downie R, Griffiths C, Heneghan R, Kloser RJ, Laiolo L, Lara-Lopez A, Lozano-Montes H, Matear RJ, McEnnulty F, Robson B, Rochester W, Skerratt J, Smith JA, Strzelecki J, Suthers IM, Swadling KM, van Ruth P and Richardson AJ (2017) Modeling What We Sample and Sampling What We Model: Challenges for Zooplankton Model Assessment. Front. Mar. Sci. 4:77. doi: 10.3389/fmars.2017.00077 <sup>1</sup> Evolution and Ecology Research Centre, University of New South Wales, Sydney, NSW, Australia, <sup>2</sup> Sydney Institute of Marine Science, Sidney, NSW, Australia, <sup>3</sup> CSIRO Oceans and Atmosphere, Hobart, TAS, Australia, <sup>4</sup> Institute for Marine and Antarctic Studies, University of Tasmania, Hobart, TAS, Australia, <sup>5</sup> School of Mathematics and Statistics, University of Sheffield, Sheffield, UK, <sup>6</sup> Centre for Applications in Natural Resource Mathematics, School of Mathematics and Physics, University of Queensland, St. Lucia, QLD, Australia, <sup>7</sup> Plant Functional Biology and Climate Change Cluster, Faculty of Science, University of Technology Sydney, NSW, Australia, <sup>8</sup> Integrated Marine Observing System, University of Tasmania, Hobart, TAS, Australia, <sup>9</sup> CSIRO Oceans and Atmosphere, Floreat, WA, Australia, <sup>10</sup> CSIRO Land and Water, Canberra, ACT, Australia, <sup>11</sup> CSIRO Oceans and Atmosphere, Dutton Park, QLD, Australia, <sup>12</sup> Antarctic Climate & Ecosystems CRC, Hobart, TAS, Australia, <sup>13</sup> South Australian Research and Development Institute - Aquatic Sciences, West Beach, SA, Australia

Zooplankton are the intermediate trophic level between phytoplankton and fish, and are an important component of carbon and nutrient cycles, accounting for a large proportion of the energy transfer to pelagic fishes and the deep ocean. Given zooplankton's importance, models need to adequately represent zooplankton dynamics. A major obstacle, though, is the lack of model assessment. Here we try and stimulate the assessment of zooplankton in models by filling three gaps. The first is that many zooplankton observationalists are unfamiliar with the biogeochemical, ecosystem, size-based and individual-based models that have zooplankton functional groups, so we describe their primary uses and how each typically represents zooplankton. The second gap is that many modelers are unaware of the zooplankton data that are available, and are unaccustomed to the different zooplankton sampling systems, so we describe the main sampling platforms and discuss their strengths and weaknesses for model assessment. Filling these gaps in our understanding of models and observations provides the necessary context to address the last gap—a blueprint for model assessment of zooplankton. We detail two ways that zooplankton biomass/abundance observations can be used to assess models: data wrangling that transforms observations to be more similar to model output; and observation models that transform model outputs to be more like observations. We hope that this review will encourage greater assessment of zooplankton in models and ultimately improve the representation of their dynamics.

Keywords: plankton net, bioacoustics, optical plankton counter, Continuous Plankton Recorder, size-spectra, ecosystem model, observation model, model assessment

### THE IMPORTANCE OF ZOOPLANKTON

All marine phyla are part of the zooplankton—either permanently as holoplankton (e.g., copepods or arrow worms) or temporarily as meroplankton (e.g., crab or fish larvae). In this review we define zooplankton as all organisms drifting in the water whose locomotive abilities are insufficient to progress against ocean currents (Lenz, 2000). Their sizes range from flagellates (about 20 µm) to siphonophores up to 30 m long. Zooplankton are the intermediate trophic level between phytoplankton and fish and are an important component of carbon and nutrient cycles in the ocean. They account for a large proportion of the energy transfer to fish on continental shelves (Marquis et al., 2011), temperate reefs (Kingsford and MacDiarmid, 1988; Champion et al., 2015), seagrass meadows (Edgar and Shaw, 1995), and coral reefs (Hamner et al., 1988; Frisch et al., 2014). Zooplankton are also key in the transfer of energy between benthic and pelagic domains (Lassalle et al., 2013). Zooplankton are responsible for transferring energy to deep water through the sinking of fecal pellets and moribund carcases (Stemmann et al., 2000; Henschke et al., 2013, 2016) or through diel vertical migration (Ariza et al., 2015) and can play an important role in deoxygenating the upper ocean (Bianchi et al., 2013). In a review of 41 Ecopath models, (Libralato et al., 2006) found that zooplankton (including Euphausiids) had high "keystoneness" (i.e., the largest structuring role in food webs relative to its biomass) in 68% of the ecosystems studied (from tropical to polar regions, and reefs to gyres), including 100% of the eight upwelling systems. Accounting for variations in the dynamics of zooplankton is thus essential to understanding energy flow in marine systems (Mitra et al., 2014), particularly to fisheries (Friedland et al., 2012).

Given the critical role zooplankton plays in the marine environment, models need to capture adequately the dynamics of zooplankton. Models are extremely sensitive to zooplankton parameterization (Edwards and Yool, 2000; Mitra, 2009) and undoubtedly poor parameterization has hindered model performance (Carlotti and Poggiale, 2010). However, significant progress in modeling zooplankton has been made in recent research and reviews focused on improving zooplankton parameterization (Tian, 2006; Mitra et al., 2014) and in better representing zooplankton functional groups (Le Quere et al., 2015). What remains a major obstacle is the lack of model assessment. Based on an examination of 153 published biogeochemical models, Arhonditsis and Brett (2004) found that 95% of them compared output with phytoplankton data, but <20% compared model output with zooplankton data. And in the relatively rare instances where zooplankton were assessed in biogeochemical models, they were more poorly simulated than almost any other state variable (Arhonditsis and Brett, 2004).

In this manuscript, we focus on how we can best use observations of zooplankton biomass and abundance for assessment of zooplankton in models. We define model assessment as the process whereby model output is compared with observed data in time and space to evaluate model performance. We identify and fill three key gaps we perceive as hampering assessment of zooplankton in models. First, many zooplankton observationalists are unfamiliar with the models that typically have zooplankton functional groups, so we describe the primary research questions addressed by biogeochemical, ecosystem, size-based and individual-based models, and how each typically represents zooplankton (**Table 1**). Second, many modelers are unaware of the available data on zooplankton biomass and abundance (**Table 2**) and are unaccustomed to the different types of zooplankton sampling systems and observations they produce (**Table 3**). We thus describe the traditional sampling platforms [e.g., nets (Wiebe and Benfield, 2003) and Continuous Plankton Recorders (CPRs; Richardson et al., 2006)] used for assessing zooplankton in models and more modern techniques [e.g., Laser Optical Plankton Counters (Herman, 2004) and bioacoustics (Greene and Wiebe, 1990)] that present new opportunities for incorporating high-resolution observations into models. Filling these gaps in our understanding of models and observations provides the necessary context to address the last gap—a blueprint for model assessment of zooplankton. Our last section thus provides a detailed discussion and case studies of the two most common ways that zooplankton observations can be used for model assessment: data wrangling that transforms observations to be more similar to model output (Kandel et al., 2011); and observation models that transform model outputs to be more like observations (Dee et al., 2011; Handegard et al., 2012; Baird et al., 2016).

Our focus in this review is on assessment of zooplankton state variables (i.e., abundance and biomass pools) and we do not address better model parameterization (Mitra et al., 2014) or better representation of zooplankton functional groups (Le Quere et al., 2005) which have previously been well-reviewed. Additionally, we do not consider model initialization, although the approaches we suggest for model assessment are equally applicable. We also do not consider data assimilation, although we would highlight that the more modern observation approaches (e.g., laser optical plankton counters and bioacoustics) have considerable potential in this regard. This review will be useful for both zooplankton observationalists who want to produce useful data products for modelers, and modelers interested in new and robust ways of assessment of zooplankton biomass and abundance in their models.

### CURRENT ZOOPLANKTON REPRESENTATION IN MODELS

### Biogeochemical Models

The classic structure of a marine biogeochemical model includes Nutrients, Phytoplankton, Zooplankton, Detritus (NPZD; **Figure 1A**). In the simplest NPZD structure, a single zooplankton compartment represents a broad spectrum of zooplankton and denotes the highest trophic level, which grazes on the single phytoplankton class (Wroblewski et al., 1988; Oke et al., 2013; Robson, 2014). In many biogeochemical models, if zooplankton are included, it is often as the top closure term (Steele and Henderson, 1992; Edwards and Yool, 2000), meaning that the mortality rate in the zooplankton compartment is treated as both a natural and predatory mortality rate. This releases

#### TABLE 1 | A list of common biogeochemical, ecosystem and size-based models and how they represent zooplankton groups.


The key references for each model is provided. The list is not intended to be an exhaustive list, but rather provide a starting point for those researchers interested in a particular modeling approach. For a more detailed list of models we point the reader to Bopp et al. (2013) and Arora et al. (2013).

nutrients held within the zooplankton back into the environment over time. Given this simple structure, it is arguable whether "zooplankton" included in some biogeochemical (lower trophic level) models can be considered to equate even conceptually with zooplankton in real systems. The "zooplankton" pool in these models must account for storage of all carbon and nutrients that has been taken up from phytoplankton and detritus by grazing but not yet returned to the pool of detritus and available nutrients through respiration and mortality, i.e., the biomass of all animals in the system.

In addition, many of the global biogeochemical models do not include a zooplankton compartment. Instead, the role of

#### TABLE 2 | A list of some zooplankton data repositories whose data can be used for model assessment.


Please note there will be overlap in the data contained within some of these repositories.

#### TABLE 3 | An overview of the resolution, data type and strengths and weaknesses of the four main observation platforms described in this manuscript.


\*Typical scales over which observations are made and analyzed. Not the resolution of the instrument.

zooplankton is represented as an all-encompassing mortality rate for phytoplankton (Christian et al., 2010; Dunne et al., 2013; Holzer and Primeau, 2013; Matear and Lenton, 2014). Instead of explicitly modeling the interaction between primary and secondary consumers, these models include a parameter that captures the consumption of phytoplankton. These kinds of scaling parameters are rarely determined experimentally but rather they are tuned during model development and assessment to produce realistic model outputs for the region and parameter set (e.g., Holzer and Primeau, 2013).

Biological complexity can be increased within this simple NPZD structure to represent the lower trophic levels of marine ecosystems with various elemental cycles or to include multizooplankton compartments separated into different functional and/or size groups (Fennel and Neumann, 2004). The use of multiple phytoplankton functional groups based on physiology (Follows et al., 2007), taxonomy (Chan et al., 2002), or morphology (Kruk et al., 2010) is common, but the use of zooplankton functional groups is relatively less common. There are however some examples that distinguish zooplankton functional groups on the basis of grazing strategies and basal metabolism (Zhao et al., 2008) or feeding strategies, size and palatability to higher trophic levels (Sun et al., 2010). If we are to increase the complexity of zooplankton in a biogeochemical model, we not only need improved parameterization (Mitra, 2009), but also quantitative observations with which to help assess an expanded model that includes multiple zooplankton functional groups.

### Ecosystem Models

Ecosystem models attempt to describe the whole ecological system, from primary producers to higher trophic levels, often including human components (**Figure 1B**). Generally, these models have complex predator-prey interactions, including dozens to hundreds of species. Zooplankton however, are generally only represented by a few classes (e.g., Yool et al., 2011; Piroddi et al., 2015; **Table 2**), defined by diet (Pinnegar et al., 2005), functional type (Le Quere et al., 2005), or size (Griffiths et al., 2010; Ward et al., 2012; Savina et al., 2013; Watson et al., 2013; Pedersen et al., 2016), or a combination of these. Of course, some ecosystem models have many more zooplankton classes (e.g., Pavés et al., 2013). Despite these exceptions, research using common ecosystem modeling approaches— ECOPATH with ECOSIM (Christensen and Walters, 2004), ATLANTIS (Fulton et al., 2005), ERSEM (Baretta et al., 1995), and SEAPODYM (Lehodey et al., 2008)—tend to focus on fish and fisheries (Griffiths et al., 2010) and are hindered by uncertainties in the prey and predator relationships of zooplankton (Mitra and Flynn, 2006). Of course, models (of any kind) do not need to represent every detail of the environment to be useful or address a specific question (Fulton et al., 2003), however we do know that zooplankton is essential to understanding the transfer of energy to fish and fisheries (Friedland et al., 2012; Lassalle et al., 2013), and therefore care needs to be taken in the representation of this link between the lower and upper tropic levels (Rose et al., 2010; Shin et al., 2010).

The simplification of zooplankton groups in ecosystem models, while not always ideal, enables operationalization of the model, however understanding the effects of climate variability and change on the target species or fisheries (for example), can only be understood if the trophic pathways leading to them are well-defined. A common problem with how zooplankton are represented in both ecosystem and biogeochemical models is the false assumption that the same zooplankton assemblage is present throughout the whole domain, both horizontally and vertically, and the structure of this assembly does not change over time (Ward et al., 2014). These models lump multiple zooplankton functional groups together and use an "average" set of parameter estimates. Zooplankton assemblages change markedly in character from eutrophic systems, dominated by the classic short food chains and larger species, to oligotrophic systems, dominated by longer food chains and smaller species. They differ vertically, with predatory and larger species below the euphotic zone and are further complicated due to the complexity of zooplankton behavior and life-cycle strategies such as molting and diapause. These changes, which fundamentally affect nutrient cycles and fisheries production, are often poorly represented in models.

### Size-Based Models

The size-based approach to marine ecosystem modeling (**Figure 1C**) has developed as an alternative to more traditional taxonomy-based frameworks by simplifying the community structure through classifying individuals based on size as opposed to species identity (**Figure 1C**; Sheldon and Parsons, 1967; Sheldon et al., 1972; Andersen and Beyer, 2015; Andersen et al., 2016). Developed over the past 50 years, this approach is based on empirical observations that individual and community processes such as growth, respiration, and predator-prey relationships and trophic position all scale with body size (Peters, 1983; Jennings et al., 2001; Brown et al., 2004; Andersen et al., 2016). Sizebased modeling has two main approaches: (1) static size spectra models (Trebilco et al., 2013) and (2) dynamic size spectra models (Blanchard et al., 2017). Similar to the trophic food web structuring of Lindeman (1942), discrete size spectrum models (or macroecological models) aggregate individual organisms into discrete trophic levels based on size (Jennings and Mackinson, 2003; Jennings et al., 2008a). In comparison, dynamic size spectrum models add the element of time, and scale individual size-based growth and mortality rates to the population and community level (Benoit and Rochet, 2004; Blanchard et al., 2009; Hartvig et al., 2011; Jacobsen et al., 2013; Maury and Poggiale, 2013; Dueri et al., 2014; Guiet et al., 2016).

How zooplankton are treated in size-based models depends on the primary focus. Most of these models focus on higher trophic levels and simply lump microzooplankton together with phytoplankton into a background food source for fish and macrozooplankton as "small fish"—i.e., using equations and parameters for metabolism and feeding for fish that are the size of zooplankton (Heneghan et al., 2016). This simplification eases computational costs, but has recently been called into question because lower trophic levels are critical to improving predictions

of biomass and production at higher tropic levels in these models (Jennings and Collingridge, 2015).

Those models that have focused on zooplankton dynamics and food web structure explicitly resolve size-based zooplankton dynamics (Zhou and Huntley, 1997; Zhou, 2006; Baird and Suthers, 2007, 2010; Zhou et al., 2010), but do not explicitly include fish. To date, there have been few attempts to link these size-based zooplankton models to dynamic size spectrum models that have focused on higher trophic levels (but see OSMOSE; Shin and Cury, 2004). With increasing emphasis on understanding ecosystem impacts of climate variability and change, comes the need to better model bottom-up processes and thus the representation of zooplankton.

### Individual Based Models

Individual based models (IBM) simulate individual animals, or groups of individuals as "superorganisms" that are treated as individuals. This allows a sophisticated representation of the behavior and/or physiology of each animal. For instance, IBMs can be structured so that they simulate the movements of animals in response to local light conditions (Batchelder et al., 2002), predator/prey encounters (Gerritsen and Strickler, 1977), or other environmental cues (Batchelder et al., 2002). In the planktonic environment, the main advantage of using an IBM is to account for rare individuals, circumstances or behaviors that contribute strongly to determining the overall population structure or variability; these are difficult to include in a statevariable approach (Werner et al., 2001). Rice et al. (1993), for example, show how variability in larval growth and survival rates can mean that the characteristics of a population of zooplankton can be quite different from the mean characteristics of the individuals within that population.

By simulating individual organisms, IBMs replicate the stochastic variability in the nutritional status, life-cycle stage, or behavior that exists within a population and that may have emergent implications for the overall properties of that population. These include modeling the variability in the survival of larval fish (Letcher et al., 1996), investigating implications of nutrition and reproductive status for food web dynamics of Daphnia (Perhar et al., 2016), the role of individual variability in physiological traits in sustaining zooplankton populations (Bi and Liu, 2017), and examining the effect of early/late diapause termination, food availability and initial stock size of the copepod Calanus finmarchicus in the Norwegian Sea (Hjøllo et al., 2012). This may come at a cost of increased model complexity and computational costs. In addition, IBMs require significantly more information on the modeled species if the model is to be rigorously parameterised and evaluated. As a result, IBMs are often applied to well-studied species such as the krill Euphausia pacifica (Dorman et al., 2015a,b) and the copepod C. finmarchicus (Skaret et al., 2014; Opdal and Vikebø, 2016). IBMs are also coupled to hydrodynamic, ecosystem or biogeochemical models (Skaret et al., 2014; Dorman et al., 2015a; Opdal and Vikebø, 2016; Parada et al., 2016), thus allowing twoway nesting within larger-scale modeling environments. Werner et al. (2001) reviewed the use of IBMs in marine modeling, while

Breckling et al. (2006) provide a more general discussion of the use of IBMs in ecological theory.

### ZOOPLANKTON SAMPLING SYSTEMS FOR MODEL ASSESSMENT

Before we discuss approaches to integrate zooplankton observations and models, we will briefly describe the major zooplankton sampling systems used for collecting zooplankton observations (**Table 3**), the different types of data each produces, and the characteristic temporal and spatial sampling scale, which includes the sampling extent, interval, and grain size (resolution).

There is no single best way to sample zooplankton. In the treatise by Wiebe and Benfield (2003), essential reading for observationalists and modelers, they describe 164 different zooplankton sampling systems, ranging from nets to optical sensors. This staggering variety of systems, each with distinct sampling characteristics, has evolved to answer specific zooplankton research questions, not for ease of uptake into models. Here we discuss four major types of zooplankton sampling systems that have been used in model assessment: nets; the CPR; size-based systems (e.g., OPC/LOPC and ZooScan); and bioacoustics (see **Table 3**).

### Net Sampling

The use of nets is the oldest and most common method of sampling zooplankton. The recent history of zooplankton net sampling dates back to Thompson in 1828 (Wiebe and Benfield, 2003), but there are recorded observations prior to this (e.g., Sir Joseph Banks on the Endeavor in 1770; Baird et al., 2011). There are many different net configurations in use, but the key attributes that influence model assessment are the monitoring design, sampling characteristics, and the information derived from samples.

### Sampling Characteristics

The large spatial and temporal extents of net sampling programs make their data well-suited for model assessment. Nets are used to collect zooplankton over a broad range of temporal extents—from hours to decades—and horizontal and vertical sampling grain sizes—from 10s of meters to 100s of kilometers (**Table 3**). The scale of a particular data set is usually dependent upon the aim of the survey. Process cruises tend to be oneoff and are usually less useful for model assessment, unless the research cruise was specifically designed to answer a question that the model is addressing. Typically, data collected from longterm monitoring programs are more useful. Most monitoring programs involve point sampling, sampling weekly or monthly over many years. There are also many larger-scale surveys, often linked with fisheries assessments, that are collected seasonally or annually (e.g., CalCOFI: Edwards et al., 2010; or SARDI: Ward and Staunton-Smith, 2002).

There are four main characteristics to consider when using zooplankton data for model evaluation: type of tow, depth (and vertical resolution) of sampling, time of day, and mesh size. In terms of type of tow, nets can be dragged vertically, obliquely or more or less horizontally at specific depths (depth-stratified by an opening-closing net). All three types of net tows are good for sampling mesozooplankton (0.2–20 mm), although oblique and depth-stratified tows are better for capturing macrozooplankton (2–20 cm), as the net often has a larger mouth area and is towed faster, providing less opportunity for zooplankton to escape. Conversely, faster tow-speeds can result in increased extrusion of smaller individuals. Net avoidance of macrozooplankton such as Antarctic Krill can be minimized with the use of strobelights (Wiebe et al., 2004) which are thought to either "dazzle" the plankton, or attract them. Nets are typically towed in the mixed layer (top 50–100 m) or from near the seafloor to the surface. Nets that sample in the mixed layer during the day typically underestimate zooplankton abundance and biomass because larger zooplankton often vertically migrate out of the mixed layer during the day; thus, higher biomass is typically found during the night.

Mesh size is probably the most important net characteristic and varies depending on the size of the target group of zooplankton and the ecosystem of interest. Macrozooplankton are usually sampled with a larger mesh size—500 µm, for example, is commonly used for fish larvae. Historically, many researchers have used 330 µm mesh for mesozooplankton (Moriarty and O'Brien, 2013), but a finer mesh of 200 µm is now almost universally used in temperate and polar systems to better sample smaller zooplankton (Sameoto et al., 2000). However, fine mesh nets (100 µm) more quantitatively capture the smaller part of the mesozooplankton and some of the larger microzooplankton (e.g., juvenile stages of small copepods). Fine mesh nets are most commonly used in tropical areas where the zooplankton are generally smaller. Although coarse mesh nets extrude smaller zooplankton and thus underestimate abundance and biomass (**Box 1**), they still capture large organisms reasonably well (Sameoto et al., 2000).

### Information Derived from Net Samples

For model assessment, probably the simplest and most useful information derived from net samples is zooplankton biomass. Biomass is measured in several different ways: settled volume, displacement volume, wet weight, dry weight, or occasionally carbon (Postel et al., 2000). Each is measured on different scales, and can be converted from one to another using standard conversions (**Box 1**). Occasionally, samples are poured through meshes of several different sizes and then weighed, providing biomass in different size categories (Huo et al., 2012; Banaru et al., 2014). Other information available from net samples is typically some idea of the zooplankton community present. This can vary from a coarse identification of the community (e.g., copepods, chaetognaths, jellyfish) to species-level identification. Taxonomic identification allows for use in IBM, or the subsequent aggregation of data into functional groups that might be represented in ecosystem models (e.g., mesozooplankton, herbivores, calcifiers).

### The Continuous Plankton Recorder

The CPR has been used for the past 85 years to sample over large regions of the North Atlantic Ocean, and has spawned surveys in the North Pacific Ocean, Southern Ocean, around Australia,

#### BOX 1 | DATA WRANGLING: CONVERTING ZOOPLANKTON BIOMASS BETWEEN DIFFERENT UNITS.

Model assessment using zooplankton biomass is not as straightforward as it might seem because observationalists use a range of different measures, from volumetric to elemental measures, of zooplankton biomass. Table B1 briefly outlines the different units used to measure zooplankton biomass; for detailed information on the various methods see Postel et al. (2000). These different measures of zooplankton biomass all have their different strengths and weaknesses. We have ordered the rows of Table B1 by the robustness of the different methods and the ease in which they can be used in modeling, ranging from the most imprecise (Settled Volume) to the most robust (Carbon Mass).

Most models usually use a currency of Nitrogen (or sometimes Carbon) biomass, which is rarely measured. Table B2 provides a series of equations to convert different biomass to Carbon Mass. Once estimates are in Carbon Mass, they can be converted to Nitrogen Mass by using the C:N ratio of zooplankton, which typically varies from 4:1 to 6:1, but is commonly 5:1 (Postel et al., 2000).

#### TABLE B1 | Glossary of zooplankton biomass terms, and their strengths/weaknesses.



and in southern Africa. Unlike nets, there is only one main CPR design that has remained relatively unchanged over the years (Reid et al., 2003). Key attributes of the CPR that influence model assessment are monitoring design, its sampling characteristics, and the information derived from the samples (Richardson et al., 2006).

#### Sampling Characteristics

The large spatial and temporal extents characteristic of CPR surveys make the data well-suited for model assessment. The CPR collects zooplankton over greater time and space scales than net sampling—from days to decades and from 10s of kilometers to 1,000s of kilometers (**Table 3**). The temporal grain size (duration of a transect segment) is 15–30 min and the sampling interval between transects is typically a month or longer. The horizontal resolution (length of a transect segment) is 10–20 km. The CPR is not used for short-term process studies, but is deployed routinely by commercial vessels plying common shipping routes, making it ideal for studying trends over time (Richardson et al., 2006).

The CPR is towed near-surface (∼7 m), but the draft of the large towing vessels probably mixes water down to 15 m. The aperture of the CPR is small (1.27 × 1.27 cm) and prevents large macrozooplankton such as jellyfish (scyphomedusae) from entering, although small and juvenile euphausiids are sampled (Hunt and Hosie, 2003). Fragile organisms, such as gelatinous plankton, are poorly sampled by the CPR because they are damaged when they come in contact with the silk mesh. For more detailed information about CPR sampling characteristics, see Richardson et al. (2006).

It is well-known that the CPR provides semi-quantitative rather than truly quantitative estimates of zooplankton abundance (Clark et al., 2001; John et al., 2001; Batten et al., 2003; Richardson et al., 2004, 2006), underestimating absolute numbers of zooplankton, but relative changes through time and over space are robust (see Section Simple Observation Models: Simulated Sampling from a Model). Small zooplankton are likely to be under-sampled because of extrusion through the relatively large mesh size of silk used in the CPR (270µm) compared with standard nets (Sameoto et al., 2000). Large zooplankton are likely to be under-sampled by the CPR because of active avoidance (Clark et al., 2001; Hunt and Hosie, 2003; Richardson et al., 2004).

Notwithstanding the semi-quantitative nature of CPR sampling, it captures a roughly consistent fraction of the in situ abundance of each taxon and thus reflects the major patterns observed in the plankton (Batten et al., 2003). Seasonal cycles estimated from CPR data for relatively abundant taxa are repeatable each year (Edwards and Richardson, 2004) and show good agreement with other samplers such as WP-2 nets (Clark et al., 2001; John et al., 2001) and the Longhurst Hardy Plankton Recorder (Richardson et al., 2004). Inter-annual changes in plankton abundance are also captured relatively well by the CPR (Clark et al., 2001; John et al., 2001; Melle et al., 2014) because the time-series has remained internally consistent, with few changes in the design of the CPR or in counting procedures.

### Information Derived from CPR Samples

Data from the CPR are zooplankton abundance, with no direct estimate of biomass. Data are normally expressed in numbers per sample. Although each sample represents ∼3 m<sup>3</sup> of filtered seawater, abundance estimates are seldom converted to per m<sup>3</sup> estimates in practice because of their semi-quantitative nature.

As with net samples, a strength of CPR data is that taxonomic information is available. Typically, the copepods are wellresolved to species and the other groups to higher taxonomic levels (see Table 5 in (Richardson et al., 2006) for the taxa counted). This means that the data may be aggregated into functional groups that equate to those in models (e.g., Lewis et al., 2006). The CPR also retains phytoplankton (although not quantitatively) because of the leno silk weave of the mesh (see Richardson et al., 2006 for details). Phytoplankton are counted to the lowest possible level using light microscopy and these data can be aggregated into phytoplankton functional groups that equate to those in models, such as diatoms and dinoflagellates, and used for model assessment alongside zooplankton data (e.g., Lewis et al., 2006).

### Optical Plankton Counters

The most common instruments for measuring in-situ size spectra are the Optical Plankton Counter (Herman, 1988) and Laser Optical Plankton Counter (Herman, 2004). These instruments use either light emitting diodes-LEDs (LED-OPC) or lasers (LOPC) to measure the optical density and cross-sectional area of each particle as it passes through the sampling tunnel, and thereby estimate surface area (Sprules and Munawar, 1986; Suthers et al., 2006; Basedow et al., 2010). Hereafter we generalize, and refer collectively to both instruments as an OPC.

### Sampling Characteristics

The large temporal and/or spatial extents and high temporal and spatial resolutions characteristic of OPC deployments make the data well-suited for model assessment. The OPC collects information of the size-spectra of zooplankton over a broad range of temporal and spatial extents—from minutes to years and from 10s of meters to 100s of kilometers (**Table 3**). Due to the continuous electronic data collection of OPCs, there is no typical grain size (length of sample segment), and it depends largely on the purpose of the study and deployment method. OPCs can be deployed vertically (Vandromme et al., 2014; Marcolin et al., 2015; Wallis et al., 2016), mounted on a towed undulating vehicle to obtain high-resolution estimates of size spectra through space and time (Zhou et al., 2009; Everett et al., 2011; Basedow et al., 2014), mounted on a net frame (Herman and Harvey, 2006; Checkley et al., 2008; Marcolin et al., 2013), integrated with autonomous floats (Checkley et al., 2008), or mounted in the laboratory for the processing of net-samples (Moore and Suthers, 2006). OPCs are capable of sampling through the water column (up to 660 m deep) and if mounted on a towed body, over regional scales (100s km). OPCs are only deployable on research vessels for a range of reasons including: they need a trained technician to monitor them, require power via the tow-cable (or regular changing of data-logger batteries) and cannot be towed at the full speed of most commercial vessels. Therefore, unlike the CPR, they are not suited to ships of opportunity.

Taxonomic information is not directly available from OPCs, but they are often partnered with net samples, either by mounting within the net mouth (Herman, 2004) or as part of a broader sampling program whereby net and OPC samples are taken in close proximity to provide species-specific information, particularly for mono-cultures (e.g., overwintering C. finmarchicus; Gaardsted et al., 2011 or swarms of Thalia democratica; Everett et al., 2011). As for all sampling techniques, gear avoidance and sampling volume can be a problem when zooplankton abundance is low (Basedow et al., 2013), due to the small aperture of the OPC (20–49 cm<sup>2</sup> ) however these can be partially resolved by towing at a higher speed or for longer periods. Size-based data are also available from other instruments such as the in-situ Video Plankton Recorder (Davis et al., 2004) or the lab-based ZooScan (Vandromme et al., 2014 requires net samples). Inter-comparisons of size spectra between LOPC and ZooScan (Schultes and Lopes, 2009; Vandromme et al., 2014; Marcolin et al., 2015) or LOPC and VPR (Basedow et al., 2013) have shown mixed results. The biggest differences between ZooScan and the LOPC are thought to be due to the sampling of sediment in the small size-classes by the LOPC in coastal areas (Schultes and Lopes, 2009), although techniques have been developed to account for this (Jackson and Checkley, 2011) and can result in improved correlations between LOPC and ZooScan (Marcolin et al., 2015).

### Information Derived from OPC

The key strength of OPCs is their ability to quantify abundance, size and biovolume of plankton simultaneously over a large size range (0.1–35 mm for LOPC; Herman, 2004). In particular, OPCs are ideal for comparison with size-based models as they share the common currency of size and abundance. One common way to represent the size-distribution of plankton in the ocean is the normalized biomass size spectrum (NBSS; Silvert and Platt, 1978). The NBSS is a histogram-style size-distribution, in which the biovolume (or biomass) in a size class is normalized by the width of the size-class, such that the normalized distribution is independent of the width of size-classes (Platt and Denman, 1977). Using size-spectra theory, it is possible to extract trophic level and growth and mortality rates from in-situ OPC data (Edvardsen et al., 2002; Zhou, 2006; Basedow et al., 2014).

### Other Optical Instruments

While OPCs are the most common in-situ optical instruments, the field is developing rapidly and there are a range of other systems which deserve to be mentioned. In particular, camera and imaging systems such as ZooScan (Laboratory only; Grosjean et al., 2004), FlowCam (Laboratory only; Sieracki et al., 1998), Zooplankton Visualization system (ZOOVIS; Trevorrow et al., 2005), Video Plankton Recorder (VPR; Davis et al., 2005), Lightframe On-sight Keyspecies Investigation (LOKI; Schmid et al., 2016), and the In Situ Ichthyoplankton Imaging System (ISIIS; Cowen and Guigand, 2008) have become more widespread. Additionally, increased effort has been invested in the identification of zooplankton from images (Zooniverse, www.planktonportal.org). The highly depth-resolved individual images from these systems provide detailed information on both taxonomy and individual features (e.g., proportion of females carrying egg sacs) which will be beneficial to model assessment of IBM's. Moreover, developing artificial intelligence techniques (Layered neural networks, random forest algorithm and evolutionary algorithms) have permitted impressive advances in the automated detection of such features (Bi et al., 2015) and will add significant value to these optical systems.

### Bioacoustics

### Sampling Characteristics

Bioacoustic data can provide estimates of zooplankton and fish distribution, behavior and abundance using soundwaves and knowledge of the target strength of individual taxa (Foote and Stanton, 2000; Simmonds and MacLennan, 2005). Bioacoustic systems operate over fine to large scales, and are able to measure horizontal and vertical scales simultaneously (**Table 3**). Bioacoustic data for zooplankton can be obtained from single, multiple and broad band frequencies using ship-based systems or fixed platforms such as moorings (Godø et al., 2014). For mesozooplankton (∼0.2–20 mm) high frequencies are used from 100 KHz to 10 MHz in moored or profiling devices to resolve the size classes and types of organisms (Holliday et al., 2009). Acoustical backscatter from zooplankton are collected by the acoustic receiver and analyzed to estimate biomass or relative change in biomass of dominant scattering groups (Holliday and Pieper, 1995; Lavery et al., 2007; Kloser et al., 2009; Godø et al., 2014; Irigoien et al., 2014; Lehodey et al., 2014). The spatial resolution can be increased by moving the acoustic sensor, by using multiple spatially distributed sensors, or by tracking organisms within the acoustic beam (Godø et al., 2014). The temporal resolution of the backscatter can be improved by increasing the ping rates to resolve an individual's distribution and behavior patterns (Holliday et al., 2009; Godø et al., 2014).

Bioacoustic techniques offer a number of advantages over traditional net or CPR sampling because they provide highresolution data at both spatial (horizontal and vertical) and temporal scales depending on the deployment platform. Highfrequency, broadband systems enhance the sampling resolution to millimeter scale so that smaller targets, such as copepods, can be quantified (Holliday et al., 2009; Godø et al., 2014). Where patches of plankton and fish are small (Benoit-Bird et al., 2013), plankton nets and the CPR do not provide an accurate picture of the spatial distribution of the organisms that they capture as the sampling volumes are far larger than the patches (Godø et al., 2014). In addition, bioacoustics can provide better biomass estimates when combined with other methods such as nets (Kaartvedt et al., 2012) as there are minimal gear avoidance problems.

### Information Derived from Bioacoustics

Raw data from bioacoustics platforms is backscatter intensity over a single multiple or broad band of frequencies. A skilled analyst, using in isolation or a combination of scattering models, nets or optical sampling, is able to convert backscatter intensity to estimates of either biomass, abundance or (with more difficulty) broad taxa or potentially size groups (Holliday et al., 2009) depending on the region being considered. The high spatial and temporal resolution of these data are ideal for integration with modeling techniques. In the case of zooplankton, a major complicating factor in the use of multi-frequency bio-acoustic techniques is the diversity of this community, where a wide range of organisms of different sizes, shapes, orientations, and material properties occur together in the water column (Holliday and Pieper, 1995; Lavery et al., 2007). All these characteristics, along with their behavior, influence the way in which they scatter sound. To estimate their individual acoustic reflectance or target strength (TS), a series of zooplankton sound scattering models have been developed (Table 1 from Lavery et al., 2007) to account for that diversity.

### ZOOPLANKTON DATA IN MODEL ASSESSMENT

The performance of the zooplankton component of numerical models is rarely assessed against field observations because, unlike other parameters such as temperature or chlorophyll a biomass, observations of zooplankton do not generally resemble the resolution of the modeled zooplankton variables (temporally or spatially), are in a very different format (species abundance rather than mass of nitrogen), or are inaccessible (e.g., hidden in gray literature/personal collections). Because zooplankton observations are collected using a range of platforms that measure different parameters such as abundance (e.g., CPR, nets, bioacoustics), size (e.g., LOPC) or biomass (e.g., nets), model assessment requires uncertain and generally speciesand location-dependent conversion factors (Arhonditsis and Brett, 2004) to approximate the zooplankton biomass in models (Postel et al., 2000). This makes it difficult to compare modeled zooplankton information with observed data. To address this challenge, we turn our focus to a discussion of the two primary ways to link zooplankton in models with zooplankton observations: (1) data wrangling that transforms observational data to be directly comparable with model outputs; and (2) observation models that transform model output to be more comparable with observational data.

### Data Wrangling: Transforming Observational Data to Be More Like Model Outputs

Data wrangling is the process of iterative data exploration and transformation from one format to another to make them more useful (Kandel et al., 2011). We use the term here to describe the series of steps that transforms observational data into a form that is more comparable with model output. Data wrangling transforms observed data into model-ready datasets. Data wrangling takes many forms, but two of the most important are conversion of observed biomass into appropriate values to compare with model estimates (see **Box 1** for details), and collating biomass estimates collected using nets with different mesh sizes or different sampling devices (see **Box 2** for details).

One example of data wrangling is finding the optimal way to interpolate scattered observations onto a regular model grid at a fixed point in time (Buitenhuis et al., 2013; Moriarty and O'Brien, 2013). A more complex example is the conversion of observed zooplankton abundance (or biovolume) to nitrogen (or carbon) biomass, which is how many models represent zooplankton biomass (**Box 1**). This approach requires assumptions about the size distribution and stoichiometry of zooplankton in the sample. Given these assumptions, modelers are able to use these data, but need to understand the basis of the assumptions that are made, and the magnitude of the error inherent in the conversion.

Often gridded data products—think of the global chlorophyll a products—are the most readily used for model assessment of phytoplankton. Similarly, the wrangling of 153,163 zooplankton biomass values, from a variety of locations, formats and collection methods, into a freely-available gridded global database of consistent biomass units was an amazing effort (COPEPOD; http://www.st.nmfs.noaa.gov/copepod/; Moriarty and O'Brien, 2013). Unlike chlorophyll a however whose global satellite maps are updated daily, the time-consuming nature of zooplankton collection means there isn't a truly global database (see gaps in **Figure 2**) which is updated on time-scales relevant to many modeling studies. These data are extremely useful however, to constrain model estimates by providing biomass limits against which to assess our models. There are many statistical tools available to assist with the practical side of data-wrangling (e.g., "tidyr" or "dplyr" in R), but the most important aspect is dialogue between modelers and observationalists.

### Observation Models: Transforming Model Output So It Is More Like Observational Data

Where zooplankton observations are incorporated into models, there is often a mismatch between the observations (often infrequent point measurements) and the high spatial and temporal resolution of models. Observation models are one technique that can help address these mismatches, allowing model assessment at a range of scales. We define an observation model as a model that takes the output of a simulation and transforms it to a form that closely resembles the observations with which it is being compared. This approach of generating observations from models is used in numerical weather prediction (Dee et al., 2011), acoustic observations of mid-trophic levels (Handegard et al., 2012), and remotely-sensed ocean color observations (Baird et al., 2016).

The observation model needs to be based on sufficient process understanding, so that it applies well over a broad range of environments and the error in the output of the observation model is due primarily to the simulation model estimate (i.e., zooplankton biomass) and not the accuracy of the parameters or equations within the observation model itself. Essentially, the rationale of an observation model is to allow comparison of observed and modeled data, by removing inconsistencies in the structure or scale of these data. Here we review some of the steps and challenges to developing zooplankton observation models, for improved interpretation of the observations and assessment of numerical models. Below we discuss the range of observation models, from simple to more complex.

### Simple Observation Models: Simulated Sampling from a Model

The simplest approach to developing an observation model is to undertake simulated sampling within a model, and compare these sampled data to zooplankton observations. For example, zooplankton biomass estimates can be extracted from a simulation corresponding to the time, location, and depth of the samples collected by nets, CPR, OPC, or bioacoustics. While not directly comparing their model to observations, Wiebe and Holland (1968) were likely the first to simulate net tows within a computer simulation when they determined the effect of net size and patchiness on sampling error.

An example using the CPR highlights the approach of simulated sampling from a model. Lewis et al. (2006) compared the abundance of zooplankton as measured by the CPR with plankton output from an ecosystem model of the Northeast Atlantic Ocean. Simulated "tows" were performed by extracting biomass data of omnivorous mesozooplankton from the model at the time (day and nearest hour), location (longitude and latitude), and depth (7 m) of corresponding samples collected by the CPR (**Figure 3**). Because the CPR provides semi-quantitative abundance estimates, and not biomass (Richardson et al., 2006), both the samples and corresponding model output were standardized to a mean of zero and a unit standard deviation to produce a dimensionless z-score (Cheadle et al., 2003). This allowed a direct semi-quantitative evaluation of spatio-temporal model performance of omnivorous mesozooplankton. This evaluation highlighted that the model had the ability to reproduce the main seasonal features such as the spring and autumn blooms, and plankton succession observed in the CPR data and showed good correlation between magnitudes of these features with respect to standard deviations from a long-term mean. The model assessment also highlighted differences in the timing of

#### BOX 2 | DATA WRANGLING: CONVERTING ZOOPLANKTON BIOMASS BETWEEN DIFFERENT MESH SIZES AND USING PROXY ESTIMATES

Different mesh sizes: Different mesh sizes of nets provide very different biomass values, with higher zooplankton biomass estimates from finer mesh nets. To convert biomass data collected with different mesh sizes to an equivalent mesh size, common conversions can be applied (Table B3; Moriarty and O'Brien, 2013), although it must be acknowledged that the best conversion is dependent upon the zooplankton assemblage present. Fortunately, different net systems produce similar estimates of zooplankton when operated with similar mesh sizes (Skjoldal et al., 2013).


Proxy estimates—Abundance: Sometimes zooplankton abundance and not biomass is measured. It is difficult to convert abundance to biomass because you do not know the size of individuals and thus their mass. In this situation, we recommend using abundance data for relative patterns—for example seasonal cycles, spatial variation, or inter-annual variation. Lewis et al. (2006) assessed their ecosystem model by normalizing both the model biomass and the observed abundance data and comparing the normalized patterns spatially and temporally.

Proxy estimates—Biovolume: Size-based methods of measuring zooplankton (LOPC/OPC/VPR/ZooScan) can provide estimates of zooplankton biomass. These instruments measure organism size (2-D area) and this can be converted to organism volume. Biovolume can then be converted to biomass by summing organism volume across all individuals and assuming zooplankton has the same density of seawater. Zooplankton biomass from the VPR and ZooScan has the advantage that detritus and sediment can be removed. An advantage of these size-based methods are that they can be used to estimate biomass in size classes. They could also be used to partition observed zooplankton total biomass into size classes (i.e., using the size spectra to estimate the % of biomass in different size classes and applying this to measured biomass).

) for mesozooplankton (0–200 m depth) is shown illustrating the distribution of records from the most comprehensive database available. The data shown here are freely available from "COPEPOD: The Global Plankton Database" (http://www.st.nmfs.noaa.gov/copepod/).

patterns in phytoplankton seasonality (e.g., spring diatom bloom in the model is too early), allowing the reparametrizing of the model (Lewis et al., 2006).

### More Complex Observation Models: Add-On Models That Convert Output to Observations

With improving technologies and computing power comes the opportunity to embrace increasingly complex observation models. Here we borrow many examples from state-of-the-art applications in other fields of model assessment that have not yet been fully applied to zooplankton. These are ideally suited for the assessment of zooplankton models due to the inherent disconnect between the spatial and temporal resolution and model currency of observations and models.

Historically, in phytoplankton model assessment, satellitederived chlorophyll a is compared with modeled phytoplankton (Oschlies and Schartau, 2005; Lacroix et al., 2007; Gregg, 2008; Brewin et al., 2010; Kidston et al., 2011, 2013), but inaccuracies in both the satellite observation (e.g., measurement error due to CDOM in the water) and conversion of model units (e.g., conversion of nitrogen biomass to chlorophyll a) introduce errors into the model assessment. To limit these inaccuracies, Baird et al. (2016) used an optical observation model, nested within a biogeochemical model, to assess water-leaving irradiance from

FIGURE 3 | Sampling the model—(A) Simulated "tows" within the model were performed by extracting biomass data of omnivorous mesozooplankton from the exact time (day and nearest hour), location (longitude and latitude), and depth (7 m) of corresponding samples collected by the CPR. (B) The data are then standardized due to the different units, and the difference between normalized z -scores for both simulation and observation between January 1988 and December 1989 with a 3-day running mean (solid line) is shown. Black is model data, red is CPR data; dots are individual model tow points, crosses are individual CPR tow points (redrawn from Lewis et al., 2006).

the model, against satellite-derived water-leaving irradiance. The water-leaving irradiances, from the observation model and the satellite, can be directly compared against each other to assess the model. Alternatively, the water-leaving irradiance measures from both the observation model and the satellite, can be converted to chlorophyll a using one of the satellite algorithms in order to allow a comparison which may be more informative for those used to thinking about chlorophyll a. In either case, both the units of assessment, and the method used to derive them, are the same. Thus, the mismatch between simulated and observed remote-sensing reflectance provides an excellent metric for model assessment of the coupled biogeochemical model (Baird et al., 2016; Jones et al., 2016).

This approach—of building an observation model that enables the model to produce information more comparable to observations—has not yet been applied to zooplankton but would be a valuable way forward. For zooplankton model assessment, building observation models for size-spectra models would be fairly straightforward given that observational techniques (OPC, ZooScan and VPR) measure the size and abundance of the zooplankton community—metrics easily extracted from sizespectra models. It is also made easier because size spectra are typically represented as Normalized Biomass Size Spectra (NBSS; Section Optical Plankton Counters), where size classes are normalized by the width of the size-class, making the shape of the spectrum independent of the size-classes chosen (Platt and Denman, 1977). The NBSS can thus be generated from both the observations and models, even if they each have different sizeresolutions. In addition to comparing state-variables, the sizebased approach developed by Zhou (2006), Zhou et al. (2010) provides an intuitive framework for estimating time-averaged rates (e.g., growth, mortality) for zooplankton from observed NBSS, which could then be tested within dynamic size spectrum models that include zooplankton (Heneghan et al., 2016) or compared to observed rates in the field (Zhou et al., 2010).

Another potential area for development of an observation model is in bioacoustics. Traditional outputs from zooplankton bioacoustic observations are the distribution, behavior, biomass and abundance of trophic levels, size categories, or species of interest derived from scattering models (Lavery et al., 2007; Holliday et al., 2009; Kloser et al., 2009; Godø et al., 2014). These scattering model measures can then be used to assess ecosystem models (Luo and Brandt, 1993; Holliday et al., 2009; Kloser et al., 2009). This requires the aggregation of focal taxa from the ecosystem model output and conversion to a common currency. This need to transform both observation

and model outputs to a common format introduces error and inconsistencies into each. An alternative approach is to create a bioacoustic observation model which uses scattering models to estimate the backscatter intensity of zooplankton within the ecosystem model and compare this to bioacoustic observations in the ocean (**Figure 4**; Handegard et al., 2012). The main challenge for the observation model is to simulate the observed backscatter at a particular frequency and depth within the model. In this case, we are not directly modeling sound within the ecosystem model, so this observation model does not provide feedback (external forcings or changes in state variables) to the ecosystem model. It is simply about avoiding inconsistencies in the comparison of modeled and observed data, and enabling the comparison of "like with like." Building such an acoustic observation model would simulate acoustic observations, producing an echogram (**Figure 4**). Thus, for all model points in time and space, the observation model could produce an echogram based on the zooplankton functional groups predicted by the ecosystem model. As with all model-observation comparisons, care must be taken to consider the temporal and spatial resolution measured or modeled. In the case of bioacoustics, the measurements will often be at a higher spatial resolution (meters; **Table 3**), but lower temporal resolution (minutes; **Table 3**) than the model. Highresolution bioacoustic measurements of abundance and biomass can be downscaled to match the resolution of ecosystem models. Clean acoustic observations will need to be readily available for comparison with the simulated outputs of the observation model, which could be achieved with the use of a multi-frequency acoustic mooring, which delivers acoustic data resolved vertically and temporally at a single site (Urmy et al., 2012).

### CONCLUDING REMARKS

In this review, we summarize many of the fundamentals of zooplankton modeling for observationalists and zooplankton observations for modelers. As highlighted by Flynn (2005), we believe that there needs to be greater discussion and collaboration between modelers and observationalists. Only through dialogue will we be able to perform the data wrangling and develop

### REFERENCES


the observation models that are needed so our observations and model outputs align. In particular, observation models have not been applied in the assessment of zooplankton in models and are likely to be a powerful approach, as they have been in other disciplines. These observation models range from the simple (sampling the model) to the more complex (bioacoustics) and can even result in the underlying model being changed to output data that is directly comparable to the observations (e.g., water leaving irradiance and chlorophyll a). The development and use of complex observing models can be time consuming, but many of the techniques described above are already being implemented (Handegard et al., 2012; Baird et al., 2016). The adoption of these ideas for use in zooplankton research would be a major step forward, allowing zooplankton observations to be more readily used in model assessment as real-time data becomes a possibility with optical and acoustic systems. Here we have provided a few ideas. We hope that this review will increase the dialogue between modelers and observationalists, and provide the impetus for greater model assessment of zooplankton output through data wrangling and state-of-the-art observation models.

### AUTHOR CONTRIBUTIONS

JE, AR, and MB conceived the original idea for this workshop and manuscript. All authors contributed to the writing of the manuscript. JE and AR wrote the final draft.

### ACKNOWLEDGMENTS

This manuscript was written as part of the Integrated Marine Observing System (IMOS) "Zooplankton Ocean Observing and Modelling" workshop held in Hobart 15–16 February 2016. The workshop was funded by IMOS. JE was funded by an Australian Research Council Discovery Grant (DP150102656). The CPR and fauna images in Figures 1, 4, and 5 were provided by the Integration and Application Network, University of Maryland Center for Environmental Science (ian.umces.edu/imagelibrary/).


size-spectrum including life history diversity. J. Theor. Biol. 324, 52–71. doi: 10.1016/j.jtbi.2013.01.018


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Everett, Baird, Buchanan, Bulman, Davies, Downie, Griffiths, Heneghan, Kloser, Laiolo, Lara-Lopez, Lozano-Montes, Matear, McEnnulty, Robson, Rochester, Skerratt, Smith, Strzelecki, Suthers, Swadling, van Ruth and Richardson. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Zooplankton Are Not Fish: Improving Zooplankton Realism in Size-Spectrum Models Mediates Energy Transfer in Food Webs

Ryan F. Heneghan<sup>1</sup> \*, Jason D. Everett 2, 3, Julia L. Blanchard<sup>4</sup> and Anthony J. Richardson1, 5

<sup>1</sup> Centre for Applications in Natural Resource Mathematics, School of Mathematics and Physics, University of Queensland, Brisbane, QLD, Australia, <sup>2</sup> School of Biological, Earth and Environmental Sciences, University of New South Wales, Sydney, NSW, Australia, <sup>3</sup> Sydney Institute of Marine Science, Sydney, NSW, Australia, <sup>4</sup> Institute of Marine and Antarctic Studies, University of Tasmania, Hobart, TAS, Australia, <sup>5</sup> Ecosciences Precinct, CSIRO Ocean and Atmosphere, Brisbane, QLD, Australia

#### Edited by:

Christian Lindemann, University of Bergen, Norway

#### Reviewed by:

Jan Marcin Weslawski, Institute of Oceanology (PAN), Poland Francis Poulin, University of Waterloo, Canada

\*Correspondence:

Ryan F. Heneghan ryan.heneghan@uqconnect.edu.au

#### Specialty section:

This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Marine Science

Received: 03 August 2016 Accepted: 29 September 2016 Published: 19 October 2016

#### Citation:

Heneghan RF, Everett JD, Blanchard JL and Richardson AJ (2016) Zooplankton Are Not Fish: Improving Zooplankton Realism in Size-Spectrum Models Mediates Energy Transfer in Food Webs. Front. Mar. Sci. 3:201. doi: 10.3389/fmars.2016.00201 The evidence for an equal distribution of biomass from bacteria to whales has led to development of size-spectrum models that represent the dynamics of the marine ecosystem using size rather than species identity. Recent advances have improved the realism of the fish component of the size-spectrum, but these often assume that small fish feed on an aggregated plankton size-spectrum, without any explicit representation of zooplankton dynamics. In these models, small zooplankton are grouped with phytoplankton as a resource for larval fish, and large zooplankton are parameterized as small fish. Here, we investigate the impact of resolving zooplankton and their feeding traits in a dynamic size-spectrum model. First, we compare a base model, where zooplankton are parameterized as smaller fish, to a model that includes zooplankton-specific feeding parameters. Second, we evaluate how the parameterization of zooplankton feeding characteristics, specifically the predator–prey mass ratio (PPMR), assimilation efficiency and feeding kernel width, affects the productivity and stability of the fish community. Finally, we compare how feeding characteristics of different zooplankton functional groups mediate increases in primary production and fishing pressure. Incorporating zooplankton-specific feeding parameters increased productivity of the fish community, but also changed the dynamics of the entire system from a stable to an oscillating steady-state. The inclusion of zooplankton feeding characteristics mediated a trade-off between the productivity and resilience of the fish community, and its stability. Fish communities with increased productivity and lower stability were supported by zooplankton with a larger PPMR and a narrower feeding kernel–specialized herbivores. In contrast, fish communities that were stable had lower productivity, and were supported by zooplankton with a lower PPMR and a wider feeding kernel—generalist carnivores. Herbivorous zooplankton communities were more efficient at mediating increases in primary production, and supported fish communities more resilient to fishing. Our results illustrate that zooplankton are not just a static food source for larger organisms, nor can they be resolved as very small fish. The unique feeding characteristics of zooplankton have enormous implications for the dynamics of marine ecosystems, and their representation is of critical importance in size-spectrum models, and end-to-end ecosystem models more broadly.

Keywords: zooplankton dynamics, marine size-spectrum, end-to-end modeling, fish productivity, ecosystem stability

### INTRODUCTION

In the 50 years since Sheldon et al. (1967) first hypothesized an equal concentration of biomass from bacteria to whales, a range of size-spectrum models have been developed to explain this remarkable consistency (Andersen et al., 2015; Guiet et al., 2016b). Size-spectrum models represent the entire marine community as a size distribution, and traditionally do not resolve species identity. Their simplicity and parsimonious parameterization makes it possible for them to be used to investigate human impacts at the community level, including fishing (e.g., Andersen and Pedersen, 2010; Jacobsen et al., 2014; Law et al., 2016), climate change (e.g., Blanchard et al., 2012; Woodworth-Jefcoats et al., 2013; Barange et al., 2014; Dueri et al., 2014), and habitat loss (Rogers et al., 2014).

The focus of these models has been on higher trophic levels—primarily fish and fishing—and in recent years there has been considerable effort in improving their parameterization (Andersen et al., 2015; Guiet et al., 2016b). For example, recent theoretical developments now allow size-spectrum models to resolve different functional groups and even species by their traits, and this has been implemented for various fish (e.g., Blanchard et al., 2014; Dueri et al., 2014; Zhang et al., 2015). The focus on fish has meant that the dynamics of the plankton-dominated lower trophic levels has been neglected in model formulations. Zooplankton, as the main consumers of phytoplankton and prey of small fish are the chief intermediaries between primary production and higher trophic levels, and thus play a critical role in marine food web dynamics (Carlotti and Poggiale, 2010; Mitra and Davis, 2010).

In current dynamic size-spectrum models, the minimum size of the dynamic consumer spectrum extends to mesozooplankton. For smaller zooplankton, there are three common representations. First, phytoplankton and small zooplankton are represented as a fixed resource spectrum (with a varying intercept and a slope held at −1), and are considered only as a food source for the smallest fish size classes (Maury et al., 2007; Blanchard et al., 2009, 2011, 2012; Law et al., 2009; Datta et al., 2010; Guiet et al., 2016a). Second, the phytoplankton and small zooplankton spectrum is determined by an external nutrient–phytoplankton–zooplankton (NPZ) model, with no predation feedback from the larger dynamic size classes (Woodworth-Jefcoats et al., 2013; Lefort et al., 2015; Le Mézo et al., 2016). Third, phytoplankton and small zooplankton are modeled as a semi-chemostat system, with a fixed carrying capacity and predation feedback from higher trophic levels (Hartvig et al., 2011; Blanchard et al., 2014; Scott et al., 2014; Zhang et al., 2015, 2016). The latter approach is the only one in which the size-spectrum of fish dynamically interacts with phytoplankton and small zooplankton. These current representations essentially group smaller zooplankton and phytoplankton together as food for the smallest dynamic size classes, and resolve larger zooplankton as small fish.

Assuming zooplankton have the same dynamics as phytoplankton or small fish is not only incorrect, but could have considerable effects on energy transfer in food webs. Zooplankton have feeding characteristics distinctly different from fish. For instance, the average predator–prey mass ratio (PPMR; in grams of wet weight) for fish is typically around 100 (Jennings et al., 2001) but for zooplankton it is >1000 (Kiørboe, 2008; Wirtz, 2012). Additionally, zooplankton exhibit vast phylogenetic biodiversity, with at least eight phyla commonly present (crustaceans, chordates, chaetognaths, molluscs, cnidarians, echinoderms, ctenophores, and annelids), each with considerable differences in their feeding ecology, from passive suspension grazing of the water column to active ambushing and carnivory (Kiørboe, 2011). Further complicating their feeding, various species of jellyfish, copepods, and microzooplankton can switch between suspension and ambush feeding modes, and this is reflected in different optimal prey sizes realized by the same species (Landry, 1981; Goldman and Dennett, 1990; Saiz and Kiørboe, 1995).

Size-based predation is the key driver of dynamics in sizebased ecosystems (Jennings et al., 2001; Woodward et al., 2005; Andersen et al., 2016) and is broadly defined by five key parameters: (1) PPMR; (2) search rate coefficient; (3) body-size exponent, which determines how the search rate scales with body-size; (4) assimilation efficiency; and (5) the width of the feeding kernel (the diet breadth around the preferred PPMR), and modeling studies of the size-spectra of fish have shown that these parameters have a large effect on food web dynamics (Law et al., 2009; Datta et al., 2011; Zhang et al., 2013). For instance, a wider feeding kernel and lower PPMR dampens traveling waves through the fish community size-spectrum (Blanchard, 2008; Law et al., 2009; Zhang et al., 2013). Further, there is evidence that higher assimilation efficiency has a similar effect on the steady state of the size-spectrum (Datta et al., 2011). The sensitivity of ecosystem dynamics to parameterization of fish feeding characteristics strongly suggests that zooplankton feeding characteristics could be important to energy transfer through the food web. Therefore, the first step toward including zooplankton in end-to-end size-spectrum models is to include an accurate representation of their feeding characteristics.

The extensive experimental work elucidating zooplankton feeding characteristics has formed the basis of several recent syntheses of size-based feeding (Fuchs and Franks, 2010; Kiørboe, 2011; Wirtz, 2012, 2014) and provides an opportunity for improving zooplankton parameterization in size-spectrum models. Wirtz (2012) used the data collected by Hansen et al. (1994) and Fuchs and Franks (2010) to develop a mechanistic model that links zooplankton PPMR with their feeding characteristics. In another paper, Wirtz (2014) derived an ideal feeding kernel width for zooplankton from simple biomechanical laws, which agrees well with empirical data. Fuchs and Franks (2010) synthesized data from previous studies to investigate the relationship between zooplankton PPMR and the width of the feeding kernel. They found that the feeding kernel width decreased with decreasing PPMR, suggesting increasing selectivity amongst individuals who prey on individuals closer to their own size. Kiørboe (2011) found that the size-specific zooplankton search rate is independent of body size across seven different functional groups.

Here, we evaluate how the size-dependent feeding characteristics of zooplankton affect the dynamics of higher trophic levels in size-structured pelagic ecosystems. We extract feeding characteristics from a range of syntheses of size-based feeding (Fuchs and Franks, 2010; Kiørboe, 2011, 2013; Wirtz, 2012, 2014) and implement them in a dynamic size-spectrum model framework (Datta et al., 2010; Andersen et al., 2015; Guiet et al., 2016b). To our knowledge this is the first dynamic size-spectra model to resolve predation-based growth and mortality of zooplankton. The model has three components—a static phytoplankton resource spectrum and two dynamic spectra representing a general zooplankton and fish community, respectively. In our model, biomass flows from smaller to larger size classes as a consequence of larger organisms consuming smaller organisms, and growth at one size is balanced by mortality in smaller size classes. We separate our findings in three parts. In Zooplankton Are Not Fish, we provide a size-spectrum model using the best parameter estimates from the literature, and establish the individual effect each of the five key zooplankton feeding parameters has on the community size-spectrum, by comparing against a base model where zooplankton are parameterized as just another fish community. In Sensitivity Analysis, we assess how varying the feeding characteristics of the zooplankton community impact the stability and productivity of the fish community size-spectrum. Finally in Mediating Primary Production and Fishing, we evaluate how the feeding characteristics of different zooplankton functional groups—salps, chaetognaths, herbivorous copepods, flagellates, and carnivorous copepods—mediate changes in phytoplankton abundance and increased fishing mortality on the fish community size spectrum. The purpose of this study is not to give a quantitative evaluation of zooplankton or fish abundance, rather we wish to illustrate how incorporating zooplankton-specific feeding characteristics could affect the dynamics of sizestructured ecosystems. Our ultimate aim is to investigate how zooplankton feeding characteristics influence energy transfer from phytoplankton and fish, and thus move toward a more realistic and consistent parameterization for the zooplankton component of size-spectrum models.

### METHODS

### The Model

We developed a size-spectrum model that consists of a sizespectrum comprised of three communities: phytoplankton, zooplankton, and fish (**Figure 1**; **Tables 1**,**2**). The phytoplankton component covers the smallest size classes [wp,wz] and is held constant as a background resource spectrum for zooplankton. Size-dependent processes of growth and mortality drive the zooplankton and fish components. These two components are delineated by different size ranges and feeding characteristics. The zooplankton community covers the size range between phytoplankton and fish [wz, Wz], and the fish community covers the largest size classes [w<sup>f</sup> , W<sup>f</sup> ], although some of the smallest fish size classes extend into the zooplankton range (from w<sup>f</sup> = 0.1 g to W<sup>z</sup> = 1 g). Fish community size classes that extend into the zooplankton range represent larvae and very small fish that are smaller than the largest zooplankton. Predation is sizedependent, with big things eating smaller ones, so depending on their size, zooplankton can feed on phytoplankton, smaller zooplankton, and the smallest fish size classes. Similarly, fish feed on zooplankton and smaller fish. The temporal dynamics of the zooplankton and fish communities are governed by separate McKendrick–von Foerster equations with second-order diffusion terms (Datta et al., 2010),

$$\begin{split} \frac{\delta}{\delta t} N\_i(\boldsymbol{\omega}, t) &= -\frac{\delta}{\delta \boldsymbol{w}} \left( \mathcal{g}\_i(\boldsymbol{\omega}, t) N\_i(\boldsymbol{\omega}, t) \right) - \mu\_i(\boldsymbol{\omega}, t) N\_i(\boldsymbol{\omega}, t) \\ &\quad + \frac{1}{2} \frac{\partial^2}{\partial \boldsymbol{w}^2} \left( f\_i(\boldsymbol{\omega}, t) N\_i(\boldsymbol{\omega}, t) \right). \end{split} \tag{1}$$

The density of individuals in community i (where i is either zooplankton or fish) per unit mass per unit volume (g−1m−<sup>3</sup> ) is denoted by Ni(w, t). Growth, mortality, and diffusion rates of individuals of group i at size w and time t, are denoted by g<sup>i</sup> (w, t), µ<sup>i</sup> (w, t), and f<sup>i</sup> (w, t), respectively. In this context, the diffusion

governed by Equation (1) and the Equations in Table 2.



Sources: 1. Zhou et al. (2010), 2. Blanchard et al. (2009), 3. Benoît and Rochet (2004), 4. Blanchard et al. (2011), 5. Andersen et al. (2015), 6. Wirtz (2012), 7. Wirtz (2014), 8. Kiørboe (2011), 9. Peters (1983), 10. Hall et al. (2006), 11. Brown et al. (2004), 12. Barnes et al. (2011), 13. Rousseaux and Gregg (2015).

term allows the model to incorporate demographic variation in the growth rates of each community. That is, within each community two individuals of the same weight eating the same food will not grow by the same amount (Datta et al., 2010). This not only increases model realism, but the stability of the system steady state, over the traditional first-order McKendrick–von Foerster equation (Datta et al., 2011).

Phytoplankton dynamics in the background resource spectrum are not explicitly modeled, with the density of individuals held constant through time:

$$N\_{\mathcal{P}}\left(\omega,t\right) = a\omega^{-b},\tag{E11}$$

Equations are also found in **Table 2**. We use an exponent of −1 for the background spectrum, implying equal biomass over logarithmically equal body–mass intervals in keeping with past dynamic size-spectrum models Benoît and Rochet, 2004; Law et al., 2009, 2016; Blanchard et al., 2012). The coefficient a for the background spectrum (Equation 11) was calculated using the empirical equation from Barnes et al. (2011) and annual median chlorophyll-a concentrations for different ocean basins between 2005 and 2010 (Rousseaux and Gregg, 2015). Unless specified otherwise, we use the global median chlorophyll-a value (0.16 mg m−<sup>3</sup> ) to give a value of 0.017 for a.

From the predator's perspective, total consumption depends on the total biomass of suitable prey. For an individual of size w at time t from community i, this is determined by the predator's search rate:

$$V\_i(\omega) = \gamma\_i \mathcal{W}^{\alpha\_i},\tag{E5}$$

and the density of suitable prey:

$$D\_i\left(\boldsymbol{w},t\right) = \int\_{\boldsymbol{w}\_P}^{\boldsymbol{w}} \phi\_i\left(\boldsymbol{w},\boldsymbol{w}'\right) \sum\_j N\_j\left(\boldsymbol{w}',t\right) \boldsymbol{w}' d\boldsymbol{w}'.\tag{E6}$$

The growth rate of an individual of size w at time t is fuelled by consumption of prey from smaller size classes:

$$\mathcal{g}\_i(\boldsymbol{w}\_i, t) = K\_i V\_i \left( \boldsymbol{\omega} \right) D\_i \left( \boldsymbol{\omega}, t \right), \tag{E7}$$

where K<sup>i</sup> is the assimilation efficiency of community i.

#### TABLE 2 | Model equations with their units.


An equation number is given that is used in the main text.

Kiørboe (2011) found that the search rate (Equation 5) for zooplankton, across a wide range of taxa is largely independent of organism size (α<sup>Z</sup> = 1.01). This stands in contrast to the scaling for fish (α<sup>F</sup> = 0.8; Peters, 1983) that implies the specific search-rate per unit mass declines with increasing body size. Further, the search rate coefficient is higher for zooplankton γ<sup>Z</sup> = 875g−αZm−<sup>3</sup> year−<sup>1</sup> (Kiørboe, 2011), compared to fish γ<sup>F</sup> = 640g−αFm−<sup>3</sup> year−<sup>1</sup> (Peters, 1983). The probability that a predator of size w will consume an individual of size w ′ is given by the log-normal function (Equation 4), where β<sup>i</sup> and σ<sup>i</sup> are community i 's PPMR and feeding kernel width.

In previous size-spectrum models the PPMR is held constant across the entire size range of the community (Andersen et al., 2015). For zooplankton, the wide variation in observed PPMR across phyla suggests a constant value across all zooplankton size classes is inappropriate (Wirtz, 2012). We have thus used the mechanistic formulation from Wirtz (2012) who argues that for zooplankton, PPMR will increase non-linearly as predator size increases, due to the nonisometric scaling of feeding-related apparatus with body size (**Figure 2**):

$$\beta\_{\rm Z}(w) = \left( \exp \left( 0.02 \ln \left( D\_{\rm w} / D\_{0} \right)^{2} - m + 1.832 \right) \right)^{3}, \qquad \text{(E2)}$$

where D<sup>w</sup> is the predator equivalent spherical diameter (ESD) in µm:

$$D\_{\le} = 2\sqrt[3]{3\pi \times 10^{12}/4\pi}. \tag{E1}$$

The mechanistic model from Wirtz (2012) also allows the range of feeding modes across different zooplankton functional groups to be quantitatively incorporated. The feeding mode of the zooplankton community is denoted by m, and ranges from −3 to 2. A larger, positive m-value (say m = 2) suggests a more raptorial, carnivorous feeding strategy with a lower PPMR (**Figure 1**). Alternatively, a negative m-value (say m = −3) implies a more passive, herbivorous feeding strategy. For the fish community, we set β<sup>F</sup> = 100 (Andersen et al., 2015).

A wider feeding kernel means an individual feeds over a wider range of size classes, implying a more generalist feeding strategy. Wirtz (2014) obtained a general feeding kernel width for zooplankton of 0.75 log<sup>10</sup> grams body-size from simple biomechanical laws, and found this value agreed well with measured values from different species. Fuchs and Franks derived an empirical equation that links zooplankton PPMR β<sup>Z</sup> with the feeding kernel width:

$$
\sigma\_{\overline{Z}} = \mathfrak{Z} \left( 0.05 \log\_{10} \left( \beta\_{\overline{Z}} \right) + 0.11 \right). \tag{E3}
$$

This equation suggests a positive relationship between the width of the feeding kernel and the PPMR. In other words, more active, carnivorous groups (m > 0), have a narrower, more selective prey size range compared to passive, filter feeding groups (m < 0) that have a wider, more generalist prey size range. For the fish community, we set σ<sup>F</sup> = 1 (Andersen et al., 2015).

For individuals in community i, a fraction K<sup>i</sup> of consumed biomass, the assimilation efficiency, is assimilated into new biomass. Observational and experimental work across different zooplankton functional groups show that assimilation efficiency of ingested food into new biomass ranges from 0.3 to 0.9 (Landry et al., 1984; Kiørboe, 2008; Montagnes and Fenton, 2012; Abe et al., 2013). Assimilation efficiency of copepods (Landry et al., 1984), dinoflagellates and larval fish (Kiørboe, 2008) depends on whether they were acclimated to low or high food environments; those from low food environments have a higher assimilation efficiency compared to those from high food environments. Similarly, the density and type or prey available had a significant effect on zooplankton assimilation efficiency—higher density and higher carbon content of prey gave lower assimilation efficiencies (Montagnes and Fenton, 2012; Abe et al., 2013). In previous models, assimilation efficiency for zooplankton is usually held constant at 0.70 (e.g., Zhou, 2006; Fuchs and Franks, 2010; Ward et al., 2012, 2014). Unless specified otherwise, we keep K<sup>Z</sup> = 0.7 to follow previous size-based planktonfocused models (Baird and Suthers, 2006; Zhou, 2006; Stock et al., 2008; Fuchs and Franks, 2010; Banas, 2011). For the fish community, we set K<sup>F</sup> = 0.6, as this is a common values given in previous dynamic size-spectrum models (Andersen et al., 2015).

From the prey's perspective, the total predation pressure from all larger size classes gives the predation mortality rate:

$$\mu\_{\mathcal{P}}\left(\boldsymbol{w},t\right) = \sum\_{j} \mathbb{I}\_{\{\boldsymbol{w} < \overline{W\_{j}}\}} \int\_{\boldsymbol{w}}^{\overline{W\_{j}}} \phi\_{\boldsymbol{j}}\left(\boldsymbol{w}',\boldsymbol{w}\right) V\_{\boldsymbol{j}}(\boldsymbol{w}) \mathbf{N}\_{\boldsymbol{j}}\left(\boldsymbol{w}',t\right) d\boldsymbol{w}'.\tag{E8}$$

To account for other sources of mortality (e.g., disease), we include a U-shaped intrinsic mortality term:

$$
\mu\_{0\_l}(\boldsymbol{\omega}, t) = B\_0 \boldsymbol{\omega}^\varepsilon + \mathbf{S}\_{0\_l} \boldsymbol{\omega}^s \tag{E9}
$$

that covers non-predation sources of mortality such as disease and senescence (Brown et al., 2004; Hall et al., 2006; Blanchard et al., 2009, 2011). Since individuals grow through time, the background mortality term describes rapidly decreasing background mortality in the early stages of life, a constant mortality for middle-age individuals, and an increasing mortality with senescence. The increase in senescence mortality with body size acts as a closure term for the largest size classes, by preventing a buildup of very large individuals (Andersen et al., 2015).

#### Community Characteristics

To evaluate effects of feeding characteristics of the zooplankton community on the fish community, we calculated several community-level measures. The total biomass of community i was obtained by integrating the abundance in all size classes:

$$B\_i\left(t\right) = \int\_{\overline{W}\_i}^{\overline{W\_i}} \nu \, N\_i\left(\nu, t\right) \, d\nu. \tag{E15}$$

Similar to Blanchard et al. (2011), we defined the total throughput of community i as the total consumption rate:

$$T\_i\left(t\right) = \int\_{\mathcal{W}\_i}^{\overline{W\_i}} \nu \, V\_i\left(\nu\right) D\_i\left(\nu, t\right) N\_i\left(\nu, t\right) d\nu. \tag{E16}$$

The production to biomass ratio of a community i —where production was defined as the total flux out of the community from all sources of mortality (Brown et al., 2004)—was used to evaluate the total energy flux through a community:

$$PB\_i\left(t\right) = \left(\int\_{\mathcal{W}\_i}^{\overline{W\_i}} \nu \,\mu\_i\left(\nu, t\right) N\_i(\nu, t) d\nu\right) / \left(\int\_{\mathcal{W}\_i}^{\overline{W\_i}} \nu \, N\_i(\nu, t) d\nu\right). \tag{E17}$$

Total throughput is a measure of how energy moves internally through the system from predation processes, whereas the production to biomass ratio is an indicator of how much new biomass is produced to replace biomass lost to mortality, per unit of existing biomass. To evaluate the transfer efficiency from zooplankton to the fish community, we calculate the ratio of total fish biomass to total zooplankton biomass:

$$FZ\left(t\right) = B\_F\left(t\right) / B\_Z\left(t\right). \tag{\text{E.18}}$$

This is similar to the approach taken in previous studies evaluating the transfer efficiency of phytoplankton to zooplankton (Friedland et al., 2012; Havens and Beaver, 2013).

Heneghan et al. Zooplankton Are Not Fish

We use two measures to evaluate the stability and total variability of the system. First, the nature of the system steady state was determined using the Newton–Raphson multidimensional root-finding method (Press et al., 2007). For each configuration of zooplankton feeding characteristics in this study, the abundance of the zooplankton and fish communities was taken after 20 years. The stability of this abundance was determined by the maximum real part (λmax) of the eigenvalues of the Jacobian matrix calculated with the Newton–Raphson method. If λmax < 0, the entire system will settle into a stable equilibrium over time where the abundance in each size-class does not fluctuate. The more negative λmax is, the faster the system will recover from local perturbations to the steady state. Alternatively, if λmax > 0, over time the system will settle into a repeating, periodic traveling wave of abundance from smaller to larger size-classes. In this case, the more positive λmax is, the faster the traveling wave moves through the size classes. Second, we measured the total variability of the system by calculating the coefficient of variation (CV) of the time-series of biomass over the last 10 years of the simulation. The Newton–Raphson stability analysis and the CV work together; the first will identify if the steady state is stable or oscillating, and the CV gives a measure of the magnitude of these oscillations through time.

#### Numerical Implementation

Dynamics of the zooplankton and fish communities are modeled with Equation (1), which we solve numerically using a secondorder semi-implicit upwind finite difference scheme (Press et al., 2007). We present the results in log<sup>10</sup> space for ease of interpretation, mathematical convenience and comparison with previous work. For the numerical implementation we discretize the dynamic size range [10−<sup>5</sup> , 10<sup>6</sup> ] into equal 0.1 log<sup>10</sup> size intervals (on a log<sup>10</sup> gram scale), and use a daily-time step for the time interval. We chose these values to discretize the time and weight ranges to ensure convergence in our numerical implementation without requiring unnecessary computational effort, in keeping with past studies (Press et al., 2007; Plank and Law, 2012; Zhang et al., 2013; Law et al., 2016). For simplicity we are not explicitly modeling reproduction, thus the abundances of the smallest size classes in the zooplankton and fish communities are held constant. This implies that we are assuming constant recruitment for zooplankton and fish (Law et al., 2009; Blanchard et al., 2012). The assumption of constant recruitment permits a clearer evaluation of how the feeding characteristics of the zooplankton affect the dynamics of a fish community, in keeping with previous community size-spectrum models (e.g., Benoît and Rochet, 2004; Maury et al., 2007; Law et al., 2009; Zhang et al., 2013). For the zooplankton community, the density of individuals in the smallest size class is determined from the continuation of the phytoplankton size-spectrum:

$$\text{Nz } (\boldsymbol{w}\_{\boldsymbol{z}}) = a \boldsymbol{w}\_{\boldsymbol{z}}^{-b}, \tag{E12}$$

and the density of the smallest size class in the fish community is held equal to the equivalent zooplankton size class:

$$N\_{\rm F} \left( \boldsymbol{w}\_{\rm f}, t \right) = N\_{\rm Z} (\boldsymbol{w}\_{\rm f}, t). \tag{E13}$$

We ran each simulation for a 20-year period. In each simulation, our initial condition starts the zooplankton and fish community spectra as a continuation of the resource spectrum (Equation 11). If the solution was stable (λmax < 0), there would initially be some oscillations around the steady state that would diminish over time. For a stable solution, the closer λmax was to zero the greater the initial variance and the longer it took for the system to stabilize. When the solution was a traveling wave (λmax > 0), the variance of the system and magnitude of the oscillations would increase over time until the steady state was achieved. In this situation, the closer λmax was to zero, the longer the system took to find the unstable steady state. In all simulations the system achieved steady state within the first 5 years, therefore we discarded the first 10 years as a burn-in period.

### Zooplankton Are Not Fish

To establish the individual effect each of the five zooplankton feeding parameters has on the fish community, we begin with a base model where zooplankton are parameterized as another general fish community. From the base model, we build up to a model where the zooplankton community feeding characteristics are parameterized to represent a general, mixed zooplankton community. To do this, we use m = 0 to represent the average PPMR of a zooplankton community characterized equally by herbivorous and carnivorous feeding behavior, and set σ<sup>Z</sup> = 0.75, K<sup>Z</sup> = 0.7, γ<sup>Z</sup> = 875g−αZm−<sup>3</sup> year−<sup>1</sup> , and α<sup>Z</sup> = 1.01 to reflect the average feeding characteristics of zooplankton across multiple functional groups.

We change each zooplankton feeding parameter one at a time, then all together, and evaluate their individual relative impact on fish community measures against the base model, by calculating the change in the measure against the base model. For example, the relative fish biomass (rFB) for a new parameterization of the zooplankton community is obtained by dividing the fish biomass from the new model by the fish biomass from the base model.

### Sensitivity Analysis

In this section, we assess how variation in the feeding characteristics of the zooplankton community affects the productivity and stability of the fish community. We focus on zooplankton feeding mode (m), feeding kernel width (σZ), and assimilation efficiency (Kz), since these parameters vary across different zooplankton functional groups and environmental conditions. We vary m between −3 and 2, σ<sup>Z</sup> between 0.4 and 2.2, and K<sup>Z</sup> between 0.3 and 0.9.

### Mediating Primary Production and Fishing

In our final section, we assess how the feeding characteristics of different zooplankton functional groups affect the productivity and stability of the fish community, and mediate increased primary production and fishing pressure, by evaluating the effect of these changes on the average total biomass of the fish community. We use the m-values from Wirtz (2012) for five different zooplankton functional groups (salps, chaetognaths, herbivorous copepods, flagellates, and carnivorous copepods) and a general zooplankton community (**Table 1**). The width of the feeding kernel for each of the six groups was determined with Fuchs and Franks' (2010) empirical Equation (Equation 3), which links the average zooplankton community PPMR with the feeding kernel width. For all groups, we hold the search rate and assimilation efficiency constant (see **Table 1**).

We used chlorophyll-a concentrations from two ocean basins—the North Central Pacific (0.06 mg m−<sup>3</sup> ) and the North Atlantic (high concentration, 0.28 mg m−<sup>3</sup> )—to give a range of coefficient values (intercept of the spectrum; a) between 0.010 and 0.024, which corresponds to a total phytoplankton abundance in the background resource spectrum of between 0.23 and 0.55 g−1m−<sup>3</sup> . To include fishing pressure, we incorporate an additive fishing mortality term with a value between 0 and 2 year−<sup>1</sup> , for all individuals in the fish community > 200 g.

### RESULTS

### Zooplankton Are Not Fish

The base model (denoted as the dashed line in each of the sub-plots in **Figure 3**) was a stable spectrum (λmax of −0.58), with the dynamic zooplankton and fish communities essentially a continuation of the static background spectrum in the base model.

Individually changing the zooplankton assimilation efficiency K<sup>Z</sup> from 0.6 and 0.7 (**Figure 3A**) increased the total throughput and production to biomass ratio of the fish community, in comparison to the base model (**Table 3**), and increased resilience of the entire system to local perturbations, with λmax = −0.71. Increasing the zooplankton community search rate coefficient (γZ) from 640 to 875 (g−αZm−<sup>3</sup> yr−<sup>1</sup> ) (**Figure 3B**), had a negligible effect on the total biomass or productivity of the fish community, compared to the based model (**Table 3**), however it did increase the stability of the system, with λmax = −0.76. Changing the search rate exponent for the zooplankton community (αZ; **Figure 3C**) from 0.82 to 1.01 reduced the total fish biomass by almost 70%, and reduced the relative production to biomass ratio (45% decrease) and relative total throughput (87% decrease), against the base model. Updating γ<sup>Z</sup> decreased the resilience of the system, with λmax = −0.04, however the steady state remained a stable spectrum.

Individually reducing the zooplankton feeding kernel (σZ; **Figure 3D**) from 1 to 0.75, and changing the PPMR (**Figure 3E**) of the zooplankton component increased the total biomass, throughput and production to biomass ratio of the fish community, in comparison to the base model (**Table 3**). Changing the PPMR of the zooplankton gave the most significant increase in relative production to biomass (75% increase) and relative total throughput (335% increase) of the fish community. Only changing the zooplankton PPMR affected the relative fish to zooplankton biomass significantly, with a 22% increase against the base model. Changing the feeding kernel width and the PPMR for the zooplankton community changed the steady state from a stable spectrum to an oscillating system. Between the two parameters, changing PPMR gave the fastest oscillations, with

FIGURE 3 | The zooplankton and fish community size-spectra when various parameters are updated (A–E) one at a time and (F) all together. The dashed lines in each plot represent the zooplankton and fish communities in the base model parameterization, and the solid lines denotes the average abundance of the fish and zooplankton communities over 10 years in the modified model. The shaded areas show the regions of the traveling wave solutions over 10 years if the steady state is unstable.

TABLE 3 | Fish community biomass (FB), fish to zooplankton biomass ratio (F:Z), fish community production to biomass ratio (P:B), and throughput (TP) relative to the base model (r), the variation in fish community biomass (coefficient of variation; CV) and the maxmium real part of the Jacobian (λmax) when the zooplankton community feeding parameters are updated one at a time, and all-together.


The system has a stable steady state when λmax < 0, and an unstable, oscillating steady state when λmax > 0.

λmax = 0.65 compared to λmax = 0.24 for σZ. Further, the magnitude of the oscillations was larger when the zooplankton community PPMR was updated (CV = 0.28), compared to σ<sup>Z</sup> (CV = 0.07, **Table 3**, **Figures 3D,E**).

When all parameters were changed for the zooplankton community (**Figure 3F**) there were significant increases against the base model in total fish biomass (69%), the fish to zooplankton biomass ratio (44%), and the fish community production to biomass ratio and total throughput (44 and 140%, respectively). Except for the relative fish to zooplankton biomass ratio, the increase in the total fish biomass and productivity measures were lower when all the parameters were updated, compared to just updating the zooplankton PPMR. (**Table 3**) The overall system was not stable (λmax = 0.47), and the magnitude of the oscillations through the system were higher than any seen in a system with a single parameter updated, with CV = 0.62. However, oscillations were slower compared to the system where only zooplankton PPMR was updated.

### Sensitivity Analysis

The total biomass of the fish community increases exponentially as m decreases (**Figure 4A**). From m = 2 to −3 (corresponding to an average zooplankton community PPMR range of 1—7.5), total fish biomass increases over 3 orders of magnitude (0.3 g m−<sup>3</sup> for m = 2 to 620 g m−<sup>3</sup> for m = −3). The exponential increase in fish biomass and productivity measures with respect to zooplankton PPMR starts at around m = −0.5, which corresponds to an average zooplankton community PPMR of 4.5. Similarly, a smaller feeding kernel width (σZ)—indicating a predator that feeds on a narrower size range of prey—results in an almost exponential increase in total fish community biomass (**Figure 4B**). From σ<sup>Z</sup> = 0.4 to 1.1, total fish biomass increases from 0.25 g m−<sup>3</sup> to 2.9 g m−<sup>3</sup> . There is a roughly linear, positive relationship between total fish biomass and the assimilation efficiency K<sup>Z</sup> of the zooplankton community (**Figure 4C**). As K<sup>Z</sup> increases from 0.3 to 0.9, total fish biomass increases from 0.20 to 0.65 g m−<sup>3</sup> . Similar patterns can be seen in the relationship between zooplankton PPMR, feeding kernel width and assimilation efficiency and the fish community productivity measures (Supplementary Figure 1).

The fish to zooplankton biomass ratio peaks at around m = 0 (3.60), and stays around 2.9 for m < −1, and decreases for m > 0.5 to settle around 2.1 (**Figure 4D**). For σZ, the fish to zooplankton biomass ratio peaks at σ<sup>Z</sup> = 0.5 around 4.8, before uniformly declining as σ<sup>Z</sup> increases (**Figure 4E**). There is minimal change in fish to zooplankton biomass ratio with increasing KZ, which suggests zooplankton biomass and fish biomass increase at the same rate (**Figure 4F**). Except for m > 0.5, the fish to zooplankton biomass ratio was higher than the base model (dashed line in **Figures 4 D–F**) across the ranges of m, σ<sup>Z</sup> and KZ.

With σ<sup>Z</sup> = 0.75, the CV is zero for m-values above 1 (**Figure 5A**) which corresponds to a stable steady state region (**Figure 5D**). The CV increases as m decreases from 0.5 to −0.5, which implies increasing variability in total fish biomass as the zooplankton community shifts from carnivorous to herbivorous feeding behavior. The CV stabilizes between 1 and 1.5 for m < 0. This suggests that even though the total fish community biomass is still exponentially increasing as m becomes more negative, the relative variation in fish biomass through time does not increase. There is a negative relationship between increasing σ<sup>Z</sup> and CV, indicating increasing stability with a wider feeding kernel (**Figure 5B**). A similar pattern is observed in **Figure 5D**; the range of m-values that enable a stable system is larger, as σ<sup>Z</sup> increases. The CV of the fish community varies across the range of KZ-values but within a much smaller range than the other two parameters (**Figure 5C**). Increasing K<sup>Z</sup> slightly increases the minimum σZ, and decreases the minimum m required for a stable steady state (**Figures 5E,F**).

### Mediating Primary Production and Fishing

Our results suggest a trade-off between the stability of the overall system and the total average fish productivity and biomass for most zooplankton groups (**Figure 6** and **Table 4**). The herbivorous salp community (m = −2.68, PPMR ≈ 7) is an exception (**Figure 6A**). It supports the most abundant and productive fish community, yet it is a more stable system overall than the one dominated by herbivorous copepods and chaetognaths (**Figures 6B,C**; **Table 4**). The salp community has the widest feeding kernel (σ<sup>Z</sup> = 0.70), which suggests a wider feeding kernel gives a more stable system without sacrificing the productivity of the fish community.

A lower, increasingly negative m-value results in a zooplankton community with a flatter abundance spectrum. In other words, increasing herbivory results in a higher abundance in the larger zooplankton size classes. For the fish community, a shallower zooplankton spectrum leads to a higher abundance in the smallest fish size classes. The overall average slope of the fish community spectrum is similar across the 6 plots (**Figure 6**). This suggests the average slope of the fish community spectrum depends more on the feeding characteristics of the fish, over the dynamics of the zooplankton community. The total average fish biomass increases with increasing phytoplankton

FIGURE 4 | (A–C) The total fish community biomass (g m−<sup>3</sup> ) and (D–F) the fish to zooplankton biomass ratio (F:Z) for different values of zooplankton feeding mode (m) , feeding kernel width (σz) and assimilation efficiency (Kz). In each plot, the other feeding parameters not specified are held constant at m = 0, σz = 0.75 and Kz = 0.7. The dashed line in (D–F) indicates the F:Z in the base model, where the zooplankton community are parameterized as fish.

abundance, across all six systems (**Figure 7A**). The magnitude of the increase in fish biomass correlated with the F:Z and CV of the system (**Table 4**). More fish were associated with a higher F:Z, and lower CV. The general zooplankton community system had the highest fish to zooplankton biomass ratio (4.43) and had the largest increase in total fish abundance: an 800% increase in fish. In contrast, the herbivorous copepod and chaetognath systems had similar fish to zooplankton biomass ratios to the general community (4.40 and 3.78), but higher CV's (1.26 and 1.27). These systems' fish biomass

TABLE 4 | Fish community biomass (FB), fish to zooplankton biomass ratio (F:Z), fish community production to biomass ratio (P:B) and throughput (TP), the variation in fish community biomass (coefficient of variation; CV) and the maxmium real part of the Jacobian (λmax) when the zooplankton community is defined by the feeding characteristics of different functional groups.


The system has a stable steady state when λmax < 0, and an unstable, oscillating steady state when λmax > 0.

increased by 340 and 410%, respectively. The flagellate system had the lowest fish to zooplankton biomass ratio (1.73), the second lowest CV (0.11) and the lowest increase in total fish biomass (170%).

Fish communities supported by herbivorous zooplankton communities were more resilient to fishing pressure, compared to fish supported by more carnivorous zooplankton (**Figure 7B**). The salp system had a negligible decline in average fish biomass, and chaetognath, herbivorous copepod and general community systems declined by up to 1, 2, 5%, respectively, with increasing fishing pressure. The two systems with carnivorous zooplankton communities (flagellates and carnivorous copepods) had an almost identical relationship between total rFB and fishing pressure, with both losing up to 15% of their average unfished biomass.

### DISCUSSION

This study is the first qualitative assessment of how zooplankton feeding characteristics mediate the transfer of energy from phytoplankton to higher trophic levels with a dynamic sizespectrum model. Improving the realism of the zooplankton community with zooplankton-specific feeding parameters increased the transfer efficiency of the system and the total mean biomass of the fish community, but changed the steady state of the system from a stable linear spectrum, to a series of traveling waves of abundance from smaller to larger size classes (**Table 3**; **Figure 3**). The change in steady state came from updating the zooplankton community PPMR and feeding kernel width (σZ). The general zooplankton community had a m-value of 0, which corresponds to a log<sup>10</sup> PPMR of between 3 and 5 across the size range of the zooplankton community, and σ<sup>Z</sup> of 0.75. This is in contrast to the fish community log<sup>10</sup> PPMR of 2, and feeding

kernel width of 1. This observed change in the steady state agrees with the observed effects of increasing PPMR and decreasing σ<sup>Z</sup> for fish communities (Blanchard, 2008; Law et al., 2009; Datta et al., 2011; Zhang et al., 2013).

Our results suggest a trade-off mediated by the zooplankton community, between the stability of the overall system and the total biomass and productivity of the fish community. A zooplankton community with a more generalist, carnivorous feeding strategy—defined by a lower PPMR (larger, positive m) and a wider feeding kernel—stabilized the steady state of the system (**Figure 5**), but the fish community was less abundant and productive (**Figure 4**). In contrast, a zooplankton community characterized by specialized, herbivorous behavior—defined by a higher PPMR (larger, negative m) and a narrower feeding kernel—increased the total average biomass and productivity of the fish community (**Figure 4**), but destabilized the system steady state (**Figure 5**). Herbivorous and mixed communities (m ≤ 0) with a narrower σ<sup>Z</sup> had a higher ratio of fish to zooplankton biomass (**Figures 4D,E**), indicating a more efficient transfer of biomass from zooplankton to fish. This positive relationship between the zooplankton community PPMR and transfer efficiency corroborates with previous theoretical (Andersen et al., 2009) and empirical work (Jennings et al., 2002; Barnes et al., 2010); a higher PPMR yields a higher transfer efficiency between trophic levels, and fewer trophic levels separating phytoplankton from fish.

Zooplankton communities with a higher PPMR and narrower σ<sup>Z</sup> had more variance in their abundance (**Figure 5**). These results suggest the abundance of zooplankton communities characterized by specialized herbivorous feeding behavior could exhibit more variation in their abundance than carnivorous communities. A similar relationship for fish species was found by Blanchard (2008), who established a link between the variation in fisheries catch of certain species of fish with their PPMR and σ; species with a higher PPMR and narrower feeding kernel had greater variability in their fishing catch through time. Further, Jennings and Warr (2003) identified a link between environmental stability and a smaller ecosystem average PPMR, which in this context means increasing herbivory amongst zooplankton in unstable environments. Such a relationship has been observed in marine ecosystems; herbivorous zooplankton dominate in unstable coastal and upwelling regions, whereas more carnivorous zooplankton are abundant in the open ocean (Raymont, 1980).

The resilience of the fish community to fishing pressure increased, and ecosystems became more efficient in mediating energy from phytoplankton to fish, when zooplankton communities had a larger σ<sup>Z</sup> and higher PPMR characteristic of more herbivorous functional groups (**Figure 7**). The relationship between zooplankton community feeding characteristics, and the resilience of the fish community and ecosystem transfer efficiency, has potential implications for the marine environment under climate change. The world ocean's oligotrophic regions are expected to expand as a result of climate change (Doney et al., 2012; Sarmiento et al., 2004; Polovina et al., 2008). Food chains in warmer, oligotrophic oceans are traditionally believed to be longer than other regions, as a result of the dominance of smaller phytoplankton (Sprules and Munawar, 1986; Irwin et al., 2006; Morán et al., 2010), which would result in lower rates of energy transfer from primary producers to higher trophic levels. Further, recent studies suggest possible climate-driven shifts in the dominance of certain zooplankton functional groups, such as salps or jellyfish (Atkinson et al., 2004; Richardson et al., 2009; Schofield et al., 2010). Our results indicate that, everything else being equal, an increase in the dominance of carnivorous zooplankton groups could further decrease the transfer efficiency of expanding oligotrophic regions. Conversely, an increase in the abundance of herbivorous groups with a large PPMR, such as salps or herbivorous copepods, could decrease the number of trophic levels between phytoplankton and fish and thereby increase the transfer efficiency of these future oligotrophic regions.

Overall, increasing the zooplankton community PPMR had the greatest effect on increasing the total abundance, productivity and resilience of the fish community (**Figures 4**, **7**), and increasing σ<sup>Z</sup> had the greatest stabilizing effect on the steady state of the system (**Figure 5**). Zooplankton have a higher average PPMR and smaller σ<sup>Z</sup> in comparison to average observed values for fish and this difference has enormous implications for ecosystem transfer efficiency and stability (Barnes et al., 2010). This means that zooplankton feeding characteristics in particular PPMR and feeding kernel width—are a critical component to consider moving forward in how the transfer of energy from primary production to higher trophic levels is resolved in marine ecosystem models. This agrees with Jennings and Collingridge (2015), who suggest that a poor understanding of energy transfer in lower trophic levels is a potential cause for the order of magnitude discrepancy between model predictions and observed mesopelagic fish biomass over large spatial scales (Davison et al., 2013; Irigoien et al., 2014).

The large changes in fish biomass and productivity as a result of changes in the zooplankton community lead us to assess the implications of assuming a constant phytoplankton abundance spectrum within the model. In this study, we assume no feedbacks on the phytoplankton community from zooplankton (i.e., predation), however we know from empirical studies that the slope of the phytoplankton spectrum does change. The phytoplankton spectrum is shallower in eutrophic, upwelling systems—indicating a higher abundance of larger individuals such as diatoms—and steeper in oligotrophic systems where small-celled phytoplankton dominate (Sprules and Munawar, 1986; Irwin et al., 2006). The effects of eutrophy or oligotrophy on higher trophic levels could be investigated by varying not only the intercept, but also the slope of the phytoplankton community and incorporating feedback from zooplankton predation.

Our model did not investigate how changes in the body composition of different zooplankton functional groups affects energy transfer from phytoplankton to fish. Gelatinous zooplankton have around one-tenth of the carbon content per unit of live mass compared to non-gelatinous plankton (Kiørboe, 2013) and carbon content as a proportion of weight scales isometrically with increasing body size for carnivorous zooplankton (e.g., ctenophores and cnidarians), but decreases for filter feeders such as salps (Molina-Ramírez et al., 2015). This would have implications for the nutritional value of different zooplankton groups for the fish community, and the fish community's resultant growth rates. Future work could investigate the effect zooplankton body composition might have on energy transfer, by varying the assimilation efficiency of the fish community for different zooplankton functional groups.

Looking forward, theoretical studies have shown that including more traits than just individual body size increases the stability of the size-spectrum (Datta et al., 2011; Zhang et al., 2013) and improves the realism of modeled predator-prey dynamics (Boukal, 2014). Recent developments in dynamic sizespectrum theory now allow multiple functional groups and even species to be resolved within the community spectrum (Maury, 2010; Hartvig et al., 2011; Scott et al., 2014) and have been used to represent actual fish communities with increasing realism (e.g., Blanchard et al., 2014; Dueri et al., 2014; Spence et al., 2016; Zhang et al., 2016). The instabilities in our single-spectrum zooplankton community indicate that more complexity is needed if we are to represent realistic zooplankton communities within a dynamic size-spectrum framework. We envision the next steps toward this goal would involve a functional group approach, where the unique size-based characteristics of multiple sizebased zooplankton communities are represented, and the model is calibrated and compared with real-world data. The growing literature on the size-based behavior of zooplankton functional groups—coupled with the recent theoretical developments in dynamic size-spectrum modeling—means size-spectrum models that realistically resolve both zooplankton and fish may now be within reach.

### CONCLUDING REMARKS

In present size-spectrum model formulations focused on fish, small zooplankton are lumped together with phytoplankton in a background resource spectrum, and large zooplankton are represented as fish. The results of this study clearly demonstrate what we already know to be true: zooplankton are not fish, and nor are they phytoplankton. Current formulations that do not resolve the unique feeding characteristics of zooplankton are neglecting a significant factor in how energy is transferred from phytoplankton to fish. The results of this study motivate further work toward increasing the realism of zooplankton processes in size-spectrum models, and end-to-end marine ecosystem models more broadly.

### AUTHOR CONTRIBUTIONS

All authors were involved in conceiving the original idea for this study. JB provided code from past size-spectrum modeling studies. RH undertook the literature review to obtain zooplankton-specific feeding parameters, constructed the model, conducted the analysis, and wrote the manuscript, with input from AR, JB, and JE.

### ACKNOWLEDGMENTS

We thank Kai Wirtz for being available to answer questions about his mechanistic zooplankton feeding equations. We also thank Iain Suthers for helpful comments about the assumptions underlying our model, from a biological perspective. This study was supported by an Australian Research Council Discovery Grant (DP150102656).

### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fmars. 2016.00201

### REFERENCES


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Heneghan, Everett, Blanchard and Richardson. This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Impacts of Intraguild Predation on Arctic Copepod Communities

#### Karolane Dufour <sup>1</sup> \*, Frédéric Maps <sup>1</sup> , Stéphane Plourde<sup>2</sup> , Pierre Joly <sup>2</sup> and Frédéric Cyr <sup>3</sup>

<sup>1</sup> Takuvik Joint International Laboratory, Université Laval (Canada) – Centre National de la Recherche Scientifique (France), Québec-Océan and Département de Biologie at Université Laval, Québec, QC, Canada, <sup>2</sup> Institut Maurice-Lamontagne, Department of Fisheries and Oceans Canada, Mont-Joli, QC, Canada, <sup>3</sup> Aix-Marseille Université, Université de Toulon, Centre National de la Recherche Scientifique/INSU, IRD, Mediterranean Institute of Oceanography, UM 110, Marseille, France

Communities of large copepods form an essential hub of matter and energy fluxes in Arctic marine food webs. Intraguild predation on eggs and early larval stages occurs among the different species of those communities and it has been hypothesized to impact its structure and function. In order to better understand the interactions between dominant copepod species in the Arctic, we conducted laboratory experiments that quantified intraguild predation between the conspicuous and omnivorous Metridia longa and the dominant Calanus hyperboreus. We recorded individual egg ingestion rates for several conditions of temperature, egg concentration, and alternative food presence. In each of these experiments, at least some females ingested eggs but individual ingestion rates were highly variable. The global mean ingestion rate of M. longa on C. hyperboreus eggs was 5.8 eggs ind−<sup>1</sup> d −1 , or an estimated 37% of M. longa daily metabolic need. Among the different factors tested and the various individual traits considered (prosome length, condition index), only the egg concentration had a significant and positive effect on ingestion rates. We further explored the potential ecological impacts of intraguild predation in a simple 1D numerical model of C. hyperboreus eggs vertical distribution in the Amundsen Gulf. Our modeling results showed an asymmetric relationship in that M. longa has little potential impact on the recruitment of C. hyperboreus (<3% egg standing stock removed by IGP at most) whereas the eggs intercepted by the former can account for a significant portion of its metabolic requirement during winter (up to a third).

#### *Edited by:*

Susanne Menden-Deuer, University of Rhode Island, USA

#### *Reviewed by:*

Jose M. Riascos, Universidad del Valle, Colombia Øyvind Fiksen, University of Bergen, Norway

> *\*Correspondence:* Karolane Dufour karolane.dufour@gmail.com

#### *Specialty section:*

This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Marine Science

*Received:* 29 July 2016 *Accepted:* 09 September 2016 *Published:* 23 September 2016

#### *Citation:*

Dufour K, Maps F, Plourde S, Joly P and Cyr F (2016) Impacts of Intraguild Predation on Arctic Copepod Communities. Front. Mar. Sci. 3:185. doi: 10.3389/fmars.2016.00185 Keywords: intraguild predation, copepods, *Metridia longa*, *Calanus hyperboreus*, Arctic regions, numerical modeling

### INTRODUCTION

Arctic and subarctic marine food webs are characterized by the presence of large calanoid copepods that channel primary production toward secondary consumers. Copepods have developed life cycle strategies that allow them to thrive in these highly seasonal environments. In the Arctic Ocean, several species of Calanus dominate the mesozooplankton biomass (Head et al., 2003; Hopcroft et al., 2010). During the short productive period in spring and summer, copepods feed on ice algae (when available in ice-covered regions) and phytoplankton and concentrate this energy into lipids, mostly stored as wax ester in hypertrophied oil sacs (Lee et al., 2006). In winter, they survive thanks to those lipid reserves that fuel their reduced metabolism during an extended period of dormancy (the diapause). All year long, copepods are an essential food source for many predators such as bowhead whale, little auk, and above all Arctic cod, a cornerstone component of the Arctic food web (Fort et al., 2010; Falardeau et al., 2013; Pomerleau et al., 2014). Thus, communities of large copepods form a critical hub of matter and energy fluxes in Arctic and subarctic marine food webs.

In the Arctic, copepod community biomass is mainly composed of the large species Calanus hyperboreus and Calanus glacialis (adult female median prosome length of 6.7 and 4.1 mm, respectively), the medium-sized Metridia longa (2.8 mm) and the small Pseudocalanus spp. (1.1 mm) (Darnis et al., 2012). Following the current dynamics, the boreal species C. finmarchicus is also regularly found in marginal Arctic seas, especially in the eastern Greenland Sea and Barents Sea (Conover and Huntley, 1991). Moreover, C. finmarchicus' biogeographic distribution in the surface layer is projected to move even farther northward in response to surface circulation and temperature forcing induced by climate change (Reygondeau and Beaugrand, 2011). The structure and functions of copepod communities are critical from an energetic point of view for marine ecosystems and depend on the actual assemblage of species. From one species to the other, the oil sac size is different and therefore the energetic content differs. C. hyperboreus and C. glacialis are bigger and contain more lipids than the boreal C. finmarchicus. Consequently, many small visual predators such as fish larvae and juveniles, would reap a larger energetic reward for a similar harvesting effort, making these Arctic copepod species the preys of choice. Hence, changes in the assemblage of copepods communities could impact marine predators' recruitment, resulting in a form of bottomup control (Mills et al., 2013; Greene and Pershing, 2014). For example, along the West coast of the Spitsbergen island in the Svalbard archipelago, the increase of warm Atlantic water masses that bring along abundant C. finmarchicus may have a negative impact on the reproductive success of little auks by reducing the relative abundance of its preferred prey, C. glacialis (Kwasniewski et al., 2010). In order to understand and predict impacts of environmental changes on Arctic marine ecosystems, it is necessary to better understand the mechanisms responsible for the specific assemblages of copepod communities.

In addition to physical forcing, relationships occurring within copepod communities can influence their structures and functions. Species that follow each other and co-occur in a community not only share food and space resources, but also develop complex interactions between them. Intraguild predation (IGP) has been proposed as an ecological strategy that could structure copepod communities (Irigoien and Harris, 2006; Plourde et al., 2009; Darnis, 2013; Melle et al., 2014). This particular type of predation occurs between members of a group of species that share the same food resources (Polis et al., 1989). This phenomenon is widespread across a variety of marine and terrestrial ecosystems and through all taxonomic and trophic levels (Polis et al., 1989; Holt and Polis, 1997; Arim and Marquet, 2004). This complex interaction is particularly interesting since it results in an immediate energy gain for the predator as well as a long term reduction of its competition (Hiltunen et al., 2013).

In copepod populations, survival rate to adulthood is strongly influenced by egg and nauplii mortality (Davis, 1984; Plourde et al., 2009). Egg mortality is particularly high in broadcast spawning species that release their eggs in the water column (Ohman et al., 2004), such as Calanusspp and M. longa. Although predominantly considered to be herbivorous, most calanoid copepod species have a flexible diet and can be omnivorous or even cannibalistic (Landry, 1981; Ohman and Hirche, 2001; Bonnet, 2004; Basedow and Tande, 2006). These species usually generate a filtration current to obtain small prey, essentially phytoplankton and micro-zooplankton, or cruise through the water and attack when a prey is detected (Kiørboe, 2013). Thus, they can consume eggs and young nauplii stages with limited mobility.

Cannibalism on eggs and nauplii can control the phenology of C. finmarchicus recruitment (Ohman and Hirche, 2001). It is therefore likely that IGP can impact recruitment as well as influencing the temporal succession of dominant species (Irigoien and Harris, 2006). In environments as contrasted as the Beaufort Sea and the St-Lawrence estuary, reduced C. hyperboreus recruitment and abundance co-occurred with an increase in M. longa abundance (Plourde et al., 2002; Darnis, 2013). During the time of peak egg production by C. hyperboreus, the gut of individual M. longa is often observed to be orange, a particularity linked to the probable ingestion of lipid-rich C. hyperboreus eggs (Conover and Huntley, 1991). Hence it has been hypothesized that M. longa individuals that remain active at intermediate depths throughout winter (no diapause) could intercept and ingest buoyant C. hyperboreus eggs that are spawned in deep waters (Plourde et al., 2003; Darnis, 2013). Given that M. longa population dynamics resources are scarce in winter, lipid-rich eggs could represent an important energy source for such an omnivorous (opportunistic) species. Later in early spring, numerous C. hyperboreus and C. glacialis that emerge from diapause and ascend toward the surface ahead of the phytoplankton bloom could also be feeding on eggs and young nauplii stages. Consequently, IGP could impact the recruitment of the true Arctic C. hyperboreus.

Surprisingly, only few studies have been conducted on predation within calanoid copepod communities (Landry, 1981; Huntley and Escritor, 1992; Bonnet, 2004; Basedow and Tande, 2006; Vestheim et al., 2013). The majority of the studies targeted cannibalism and while none was focused on IGP between the dominant Arctic species M. longa and C. hyperboreus, Huntley and Escritor (1992) reported ingestion rates of the vicariant species M. gerlachei on eggs of the dominant Antarctic Calanoides acutus in the Austral Ocean. In all experiments, ingestion rates on eggs (and nauplii) vary according to their concentration. The influence of alternative food source on ingestion produced ambiguous experimental results. On one hand, experiments with female C. pacificus suggest a switch between herbivorous and carnivorous behavior that depends on the relative abundances of phytoplankton and their own nauplii (Landry, 1981). On the other hand, experiments with C. finmarchicus have shown that ingestion rates on its own nauplii are independent of the ambient algae concentration (Basedow and Tande, 2006).

Copepod community models have been developed with a focus on development, growth and competition for food resources (Record et al., 2012, 2013). However, community level processes involving interspecific interactions such as IGP have not yet been implemented into these models. In order to provide a better understanding of IGP and to provide a better parameterization for models of copepod communities, we conducted laboratory experiments that quantified the ingestion of copepod eggs by some of the dominant Arctic copepod species, M. longa and C. hyperboreus. We further conducted a simple numerical experiment in order to assess the potential ecological implications of our findings in Arctic marine ecosystems. Copepods were sampled in the Lower St-Lawrence estuary (LSLE) and feeding experiments on eggs were conducted under different conditions of temperature, egg concentration, and alternative food availability.

### METHODS

### Area of Study and Sampling

The LSLE is the southernmost sea directly influenced by Arctic water masses and that presents Arctic features in the North Atlantic (**Figure 1**). Arctic water masses enter in the Gulf of St-Lawrence (GSL) by the Strait of Belle Isle in the North, transporting Arctic copepods species such as C. hyperboreus, C. glacialis, and M. longa. Warmer North Atlantic water masses enter the system by Cabot Strait in the South and carry along boreal species such as C. finmarchicus. Both Arctic and temperate species thrive in the GSL system where cold and warm water masses are segregated vertically between the thin seasonal surface layer, the cold intermediate layer renewed locally each winter (core temperatures can be negative) and the deep Atlantic layer (between 4 and 5◦C). Colder water masses dominate the eastern and northern parts of the Gulf and the deep lower Estuary where upstream tidal pumping brings cold and nutrient-rich waters to the surface, whereas warm surface waters (up to 20◦C) develop throughout the summer over the shallow southern half of the Gulf (Saucier et al., 2003; Le Fouest et al., 2005). These particular water masses and species mix make the LSLE an exceptional experimental model to study IGP in the context of the rapid environmental changes that the Arctic is currently facing. Zooplankton was sampled in the LSLE (48◦ 40′N, 68◦ 35′W) in October 2014 with a vertical plankton net (158 µm mesh size, 1 m diameter) at 125 or 200 m from the surface at a towing speed of 0.5 m s−<sup>1</sup> . The catch was diluted into 4 L jars filled with filtered seawater and maintained close to ambient temperature at 5 to 6 ◦C in coolers during transport to the laboratory (less than an hour).

In a subsequent numerical experiment, we applied our observations to a truly Arctic environment, the Amundsen Gulf. The Amundsen Gulf is located in the Canadian territory of Nunavut at about 71◦N and bordered by Banks Island and Victoria Island. It connects south-eastern Beaufort Sea to the Canadian archipelago (**Figure 1**). The Amundsen Gulf water masses are generally cold (around 0◦C) and are mainly discriminated by their different salinities: the Polar-Mixed Layer from the surface to c.a. 50 m (S ∼ 31.6), the Pacific Halocline below until 200 m (32.4 < S < 33.1) and the slightly warmer Atlantic Layer below 200 m (S ∼ 34) (Carmack and Macdonald, 2002). The Gulf covers about 60,000 km<sup>2</sup> and the maximum

depth of this large channel is 630 m. In winter, it is entirely ice-covered except for sporadic polynyas and flaw leads and the spring ice-breakup his highly variable (Galley et al., 2008).

### Live Animal Sorting

Owing to the harsh conditions at sea during winter over the LSLE, copepods were sampled at the end of October 2014 prior to the beginning of C. hyperboreus reproduction and the formation of dense sea ice. Plourde et al. (2003) have previously shown, for a similar experimental setup, that capture and handling of C. hyperboreus females triggered gonad maturation, leading to egg production a few weeks after collection and approximately a month earlier than expected according to the in situ timing. A visual inspection of appendages and behavior under a binocular microscope allowed us to select adult female M. longa and C. hyperboreus in good condition from the live samples, within 48 h of the catch. Animals were kept in the dark between 3 and 5 ◦C in groups of 25 to 50 in 1 L beakers equipped with egg separators (mesh size = 333 µm) and filled with filtered seawater. Female M. longa were fed with solutions of concentrated diatoms Thalassiosira weissflogii (Instant Algae <sup>R</sup> TW 1200), whereas female C. hyperboreus where not fed since egg production is entirely fuelled by internal lipids during the dormant part of their life cycle. The beakers were inspected daily for egg production for about a month until female C. hyperboreus spawned enough eggs to start the experiments.

### Predation Experiments

Within 48 h of the start of the experiment, individuals used as predators were photographed laterally using a PixeLINK camera of 5 Mb (PL-E425CU) mounted on a LEICA MZ6 stereoscope. In order to minimize stress, individuals were kept in cooled seawater until the very moment that the picture was taken and gently manipulated with handling needles. Prosome length (distance between the tip of the cephalosome and the tip of the last thoracic segment), prosome area, oil sac length, and area were measured with the software ImageJ v. 1.49. The condition index was estimated as the oil sac area divided by the prosome area of the individual in order to give an indication of its lipid content. Predators' carbon content was estimated from species and stagespecific seasonal relationships between individual carbon mass and prosome length (Forest et al., 2010). The photographed animals were then placed individually in 45 mL Petri dishes filled with filtered seawater and equipped with egg separator (mesh size = 333 µm) for acclimation at the experimental temperatures.

Experiments were carried in an atmosphere-controlled chamber in November 2014 with female M. longa fed with C. hyperboreus eggs. Predators were placed individually in a bottle (1.35 or 2.37 L) filled with filtered seawater containing a precise number of eggs spawned within the previous 48 h. Bottles were turned upside down once per minute on a rotating wheel in order to maintain the eggs in suspension. Manipulations were conducted under a dimmed red light and the experiments were carried in the dark. Incubation time was kept relatively short (less than 24 h) in order to avoid a complete consumption of the eggs and hence a failure to accurately estimate ingestion rates. It also varied according to incubation conditions, with longer incubation times for lower egg concentration (lower encounter probability between eggs and the predator). After 4 to 22 h, the contents of the bottles were filtered with a 73 µm sieve and the remaining eggs were counted. A minimum of two controls without predator for each treatment was set up in order to check the accuracy of the egg recovery method. The status of each individual was verified at the end of the experiment. Ingestion rates were discarded for the few dead individuals, and the sluggish or unhealthy-looking ones as well.

We tested the effect of temperature on M. longa ingestion of C. hyperboreus eggs. Incubations were carried at 1, 4, and 8 ◦C to reflect the potential range of in situ water temperature encountered by this species between the Arctic and subarctic regions. Unfortunately, we could not test for negative water temperatures. In order to characterize functional responses, we tested the effect of C. hyperboreus egg concentration on M. longa ingestion rate. We were not aware of actual data about in situ C. hyperboreus egg concentrations in the water column, but we estimated it to be low (Huntley and Escritor, 1992). Hence we chose concentrations of 5, 10, 20, and 30 egg L−<sup>1</sup> . Finally, we checked whether there was an influence of alternative food availability, by adding an additional food source in the form of concentrated diatoms T. weissflogii (Instant Algae <sup>R</sup> TW 1200) in half of our replicates. Algae were offered at about 50 µg C L −1 according to cell concentration determined with a Hausser Bright-Line Hemacytomer (couting chamber) and carbon to volume relationships for diatoms (Menden-Deuer and Lessard, 2000).

### Estimation of Ingestion Rates

The instantaneous feeding rate on eggs g (h−<sup>1</sup> ) was derived from an exponential equation (Båmstedt et al., 2000):

$$\lg = \frac{\ln\left(\frac{E\_f}{E\_0}\right)}{t} \tag{1}$$

where E<sup>0</sup> and E<sup>f</sup> are respectively the egg concentration at beginning and the end of experiment (egg L−<sup>1</sup> ) and t is incubation time (h). The number of C. hyperboreus eggs obviously did not increase during the experiments, and experiment duration was not long enough for hatching to occur (no nauplii was ever found in any of the control or experiment bottles).

We deduced the clearance rate F (L ind−<sup>1</sup> h −1 ), which corresponds to the volume of water processed assuming 100% capture efficiency and a homogeneous food concentration, from both g and the volume of the incubation bottle V (L):

$$F = \text{g} \times V \tag{2}$$

Finally, we obtained the ingestion rate I (egg ind−<sup>1</sup> h −1 ) with:

$$I = F \times \left[E\right] \tag{3}$$

where [E] is the average egg concentration as given by:

$$\mathbf{E}[E] = \mathbf{(E\_0 \times \frac{1 - e^{\left(-\mathbf{g} \times t\right)}}{\mathbf{g} \times t})} \tag{4}$$

Daily ingestion rates where assumed to be 24 times the hourly rates since M. longa is known to be active and swimming almost continuously (Hirche, 1987). Egg ingestion rates were then converted in carbon units using an egg carbon content of 0.84 (µg C egg−<sup>1</sup> ; Plourde et al., 2003). The proportion of daily metabolic needs (%) satisfied by egg ingestion was estimated from the ratio of carbon ingestion rate I<sup>C</sup> = 0.84 <sup>∗</sup> I (µg C ind−<sup>1</sup> d −1 ) and a mean and constant respiration rate (µg C ind−<sup>1</sup> d −1 ) measured by Seuthe et al. (2006).

### Data Analysis

The number of ingested eggs followed a Poisson distribution (an asymmetric right-skewed distribution of discrete values). Hence, in order to minimize estimating errors, a generalized linear model (GLM) for Poisson distribution was used to predict the number of eggs ingested (EI) (the raw data) according to temperature (T), egg concentration (E), presence of additional food source (AC), prosome length (PL), and condition index (CI) of the predator. Bottle volume (V) and duration of experiment (D) were taken into account by using them in an offset term. Several models were tested (with and without interactions) and we computed Akaike's information criterion corrected for overdispersion (QAIC) as a decision-support metric. The GLMs formulae were of the form (here is the one with all the independent variables but no interactions):

$$\log\left(\frac{EI}{D \times V}\right) = \beta\_0 + (\beta\_T \times T) + (\beta\_E \times E) \tag{5}$$

$$+ (\beta\_{AC} \times AC) + (\beta\_{PL} \times PL) + (\beta\_{CI} \times CI)$$

where β<sup>i</sup> are the coefficient estimates for each variable. The number of eggs ingested per unit of time and volume can easily be obtained from this model results.

### Model of Egg Vertical Distribution

In order to assess the implications of our findings in the context of Arctic marine ecosystems, we developed a simple water column (1D) model of the vertical distribution of C. hyperboreus eggs in the Amundsen Gulf. The model computed the time evolution of egg concentration at a given depth according to advection and diffusion, gains by egg production and losses by development and predation (**Figure 4**). The rate of change of egg concentration followed the classical advection-diffusion-reaction formulation (Soetaert and Herman, 2009):

$$\frac{\partial E}{\partial t} = -\mathbf{w}\frac{\partial E}{\partial z} + K\frac{\partial^2 E}{\partial z^2} + P\_z - I \ast M + 1/H \ast E \tag{6}$$

where the first right-hand side term represents the effect of egg vertical velocity, the second the effect of diffusion and the others several biological reaction terms. More specifically, E was the egg concentration (egg m−<sup>3</sup> ), t the time (h), w the egg velocity (m h−<sup>1</sup> ) defined positive downward, z the depth (m), K the vertical eddy diffusivity coefficient (m<sup>2</sup> h −1 ), P<sup>Z</sup> the depth-dependent egg production rate (egg m−<sup>3</sup> h −1 ), H the egg hatching time (h), M the females M. longa concentration (ind m−<sup>3</sup> ) and I the ingestion rate by other copepods (egg ind−<sup>1</sup>

h −1 ). The egg velocity w was given by Stokes' law (Visser and Jónasdóttir, 1999):

$$\omega = \Re 600 \times \frac{\text{g} \times d^2 \times (\rho\_{\text{egg}} - \rho\_{\text{water}})}{18 \times \mu} \tag{7}$$

where g is the gravitational constant (9.81 m s−<sup>2</sup> ), d is the egg diameter (m), ρegg is the egg density (g m−<sup>3</sup> ), ρwater is the water density (g m−<sup>3</sup> ) and µ is the dynamic viscosity of the seawater (1.85 g m−<sup>1</sup> s −1 ), here taken as a constant (**Table 1**).

The source term for eggs (PZ) came from the average daily production of C. hyperboreus population (30,000 eggs m−<sup>2</sup> ) observed between February and April 2008 in the Amundsen Gulf (Darnis, 2013). C. hyperboreus females released more than 90% of their eggs during this 3 month-period, while remaining at depths between 200 and 300 m (Darnis, 2013). As a result, we computed the vertical profile of egg production rate P<sup>Z</sup> according to a normal distribution whose mean was centered at 250 m, its standard deviation 15 m and its integral equal to 30,000 eggs m−<sup>2</sup> (99.9% of the eggs were released between 200 and 300 m).

The IGP rate I (h−<sup>1</sup> ) exerted on C. hyperboreus eggs was simply the product of M. longa females' abundance (ind m−<sup>3</sup> ) and the individual filtration rate (m<sup>3</sup> ind−<sup>1</sup> h −1 ) found in our grazing experiments.

Egg hatching time H (h) followed an empirical Belehrádek's ˇ function obtained from observed hatching times of C. hyperboreus eggs (Jung-Madsen et al., 2013):

$$H = a \times \left(T - \alpha\right)^{-b} \tag{8}$$

where T was water temperature (◦C), a (d ◦C −1 ), α ( ◦C) and b constants.

A simple ordinary differential equation framework was not optimal for the modeling of developing eggs because of the "numerical diffusivity" caused by the hatching rate (Gentleman et al., 2008). Simply put, with a development (hatching) rate, the progression through development stages is treated as a continuous process within the population, instead of a discrete event highly synchronized among many individuals. This can

#### TABLE 1 | Model parameters and references.


VJ1999, Visser and Jónasdóttir (1999); D2013, Darnis (2013); JM2013, Jung-Madsen et al. (2013)

lead to unrealistic and spurious results, such as a small fraction of the simulated egg population that has already hatched after the first time step! In order to prevent this, we used the simple approach of spreading the egg development over 20 numerical stages of equal length (Gentleman et al., 2008) and we further integrated the development throughout theses stages with a flux limiting numerical scheme (Record and Pershing, 2008).

### Simulations

The 1D water column model was split into 5 m vertical layers between 0 and 300 m, and the time step of integration was 12 h. For the model forcing, we used physical and biological datasets from the Circumpolar Flaw Lead System Study (CFL; Barber et al., 2011). We only selected profiles from stations that were at least 300 m deep and located within the Amundsen Gulf. As a result, the physical forcing came from mean vertical profiles of eddy diffusivity coefficient (K), temperature (T), and water density (ρwater) obtained at 20 different stations. These stations were sampled in November and December 2007 under dense sea-ice cover with a vertical microstructure profiler (VMP500, Rockland Scientific International). For two long-term stations the number of casts used in the average profile were respectively 24 and 25, whereas at least 5 profiles were used to build the 18 other mean profiles. Missing values in averaged profiles (e.g., near the surface or below 250 m) were dealt with according to Equation (1) from Bourgault et al. (2011). Further details about this dataset can be found in their study.

We also used 18 vertical profiles of M. longa female abundance obtained with a Hydrobios <sup>R</sup> multinet sampler. Details of the sampling procedure can be found in Darnis and Fortier (2014). We selected the stations sampled between February and April 2008, during the peak of C. hyperboreus reproduction. The layer thickness for the vertical sampling ranged from 10 to 144 m, with a median of 20 m.

In order to test the sensitivity of the model to both the physical properties of the water column and the vertical distribution of the predators (M. longa) we ran 360 simulations, one for each possible combination of the physical and biological forcing fields. In addition, we ran this ensemble of simulations for three different scenarios of egg density in order to verify the impacts of different egg velocities: the mean (scenario D0), minimum (Dmin) and maximum (Dmax) egg densities observed by Jung-Madsen et al. (2013). Simulations ran for 15 days in order to reach a quasi-steady state where the maximum local rate of change in egg concentration δE/δt was less than 10−<sup>6</sup> .

### RESULTS

### Egg Ingestion Rates

Predation of C. hyperboreus eggs by female M. longa occurred in each of the incubation experiments. However, in each experiment there was high individual variability and several individual incubations showed no egg ingestion. After discarding incubations within which dead or unhealthy individuals were found at the end of the experiment, for each treatment approximately 8 individual replicates out of the initial 10 were used for further analyses. The frequency distribution of ingestion rates was positively skewed, i.e., the median value was lower than the mean. The global mean ingestion rate of C. hyperboreus eggs by M. longa was 5.8 eggs ind−<sup>1</sup> d −1 (SE = 0.57, n = 141) and the median was 3.7 eggs ind−<sup>1</sup> d −1 (**Figure 2**). In terms of carbon, the mean ingestion rate was 4.9 µg C ind−<sup>1</sup> d −1 and the median 3.1 µg C ind−<sup>1</sup> d −1 (SE = 0.48, n = 141; **Figure 2**). C. hyperboreus eggs constituted an energy-rich food source (0.84 µg C egg−<sup>1</sup> ; (Plourde et al., 2003) and the average daily ration of M. longa females feeding on C. hyperboreus eggs was 37% of their estimated metabolic needs based on respiration rates (SE = 4, n = 141). Individual variability resulted in a contrasted pattern where about a quarter of M. longa did not ingest any eggs, while an equivalent proportion filled more than 50% of their daily energetic requirements through egg ingestion. Some individuals actually largely exceeded their daily metabolic needs (i.e., over 100%, **Figure 2**), even when eggs were offered at low concentrations.

### Influence of Incubation Conditions

According to the GLM analysis, presence of additional food source, prosome length, or condition index of the individuals had no discernable effect on egg ingestion (**Table 2**). The only predictor that improved the model and that significantly affected the number of eggs ingested by M. longa was egg concentration (**Figure 3**). In the full model with no interactions, temperature seemed to have a significant negative effect on ingestion rates (**Table 2**). However, in the model that only kept egg concentration and temperature as independent variables, the influence of temperature and the interaction term between them did not remain significant. Moreover, the size effect of the temperature and interaction term coefficients was small compared to the impact of egg concentration and the QAIC values were very close between the models. Hence, we decided to use the simplest model with only egg concentration as predictor of egg ingestion (**Figure 3**). We did not observe any feeding saturation for the range of egg concentrations offered.

### Simulated Egg Vertical Distribution

The velocity of C. hyperboreus eggs estimated with Equation (7) ranged between −9 and −4.1 m d−<sup>1</sup> for the mean egg density scenario (D0) over the 20 physical forcing profiles. Negative velocities meant that eggs were positively buoyant, from the bottom of the water column up to the surface. Egg velocity was dependent on the water density profile and it decreased slowly with decreasing depth (**Figure 4**). This pattern was conserved among the 20 physical forcing profiles whose overall variability was low. Egg velocity was strongly influenced by egg density itself. C. hyperboreus egg density is highly variable, both between individual females and within clutches of the same female (Jung-Madsen et al., 2013). When we used the minimal egg density (scenario Dmin) the velocity tripled to range between −26.2 and −21.3 m d−<sup>1</sup> , whereas for maximal egg density (scenario Dmax) the associated velocity was not negative throughout the water column. The egg velocity ranged between −2.3 and 2.6 m d−<sup>1</sup> with a converging depth of neutral buoyancy around 100 m.

Egg velocity was critical for egg vertical distribution. In the ensemble of simulations for scenario D0, egg vertical

distributions showed higher concentrations between 150 and 275 m and peaked around 225 m to reach about 3000 eggs m−<sup>3</sup> (or 3 eggs L−<sup>1</sup> ) once the simulation reached its steady state (**Figure 4**). For scenario Dmax, the denser eggs ascend only slightly in the water column before hatching. They remained concentrated between 200 and 300 m with a maximum egg concentration a little less than 4000 eggs m−<sup>3</sup> near 250 m (**Figure 4**). Contrarily, in the Dmin scenario, eggs moved rapidly upward and some even managed to reach the first 5 m of the water column to attain a concentration of a little less than 300 eggs m−<sup>3</sup> (**Figure 4**). Eggs where spread over the entire column and concentration peaked above 160 m at about 1200 eggs m−<sup>3</sup> .

### Impact of *M. longa* Predation on *C. hyperboreus* Eggs

For each egg density scenario tested, the proportion of egg biomass eaten by M. longa was more sensitive to the profiles of M. longa abundance than to the physical forcing (see **Figure 5** for scenario D0). Over the ensemble of 360 simulations of the D<sup>0</sup> scenario, the percentage of C. hyperboreus egg standing stock ingested by M. longa ranged between 0.1 and 1.1% with most of the values being in the low end (**Figure 6**). The percentage of egg standing stock ingested by M. longa varied between 0.2 and 3.2% for scenario Dmin and between 0 and 0.8% for maximal egg density (scenario Dmax; **Figure 6**).

This modest impact of M. longa IGP is hardly noticeable between the egg concentration profiles simulated with and without egg predation, even for the combination of physical conditions and M. longa profiles that lead to the maximum difference (**Figure 7**). The corresponding daily egg ingestion of the whole population of M. longa ranged between a little more than 1 to almost 20 eggs m−<sup>3</sup> d −1 (**Figure 7**). It is noticeable, though, that such egg ingestion values could allow M. longa individuals to satisfy almost 10% of their metabolic TABLE 2 | Results from the generalized linear models (GLM) fitted to predict the number of *C. hyperboreus* eggs ingested by female *M. longa* according to egg concentration (*E*), temperature (*T*), alternative food source (*AC*), condition index (*CI*), prosome length (*PL*), and interactions between the terms.


Estimated coefficients b, standard error SE, P-values (\*\*\*P < 0.001;\*\*P< 0.01; \*P < 0.1; ns not significant) and Akaike's information criterion corrected for overdispersion QAIC. Model entry in bold indicates the one selected for further numerical experiments.

needs according to respiration rates from Seuthe et al. (2006), or up to 37% if we consider the lower respiration rates reported by Hirche (1987).

### DISCUSSION

### Individual Variability

Our results show high individual variability of egg ingestion rates, with a quarter of all the individuals not ingesting any eggs and about the same proportion satisfying more than half of

FIGURE 3 | Ingestion rates of female *M. longa* on *C. hyperboreus* eggs according to the presence of alternative food source (left panel), temperature (middle panel), and egg concentration (right panel). Points are jittered to reduce overlap. Black and white line is the prediction of the mean from the selected generalized linear model (see text); dotted black lines are the corresponding 95% confidence intervals.

simulated for mean egg density (scenario D0) of 19.4 kg m−<sup>3</sup> are presented in the right panel. Dashed line is the egg velocity (m d−<sup>1</sup> ) computed according to Stokes' law. Dotted line is at the initial condition corresponding to the spawned eggs profile. Solid line is the egg concentration distribution after 15 days of simulation. Gray area is the female M. longa abundance (ind m−<sup>3</sup> ).

their daily metabolic needs from egg grazing. This asymmetric and widely spread distribution has a geometric coefficient of variation of 149%. This pattern is consistent across the range of incubation conditions we tested, and this level of variability is common in any experimental setting measuring individual biological features (size, structural or storage weight, swimming behavior, etc.) and physiological rates (respiration, ingestion, growth, etc.) (e.g., Basedow and Tande, 2006). We do not have clear explanations for the level of variability we observed, but it is a useful observation to report (see Supplementary Material for a spreadsheet of individual observations). Individual variability has long been recognized as a key property of plankton ecology since population dynamics and trophic interactions (that are of primary interest for marine ecologists) are emerging properties of individual characteristics and behaviors (Båmstedt, 1988). Modern experimental and in situ observation methods

are providing increasingly detailed and abundant individuallevel data (e.g., Schmid et al., 2016), while current numerical approaches allow for testing how and how well individual-based models can effectively represent emerging properties at higher organizational levels (Neuheimer et al., 2010; Morozov et al., 2013).

### Dynamical Interactions in the Water Column

This modeling exercise provided insight on the physical and biological dynamical processes interacting in the water column and their relative importance for the vertical distribution of C. hyperboreus eggs.

We first performed a scale analysis of the two first terms on the right-hand side of Equation (7), i.e., egg buoyancy and vertical turbulence. For the simulation scenario illustrated in **Figure 4**, we can estimate the vertical gradient in egg concentration <sup>∂</sup><sup>E</sup> <sup>∂</sup><sup>z</sup> ≈ 15 egg m−<sup>4</sup> near the maximum egg concentration at 250 m (an approximate increase of 750 egg m−<sup>3</sup> over 50 m) and <sup>∂</sup> 2E ∂z <sup>2</sup> ≈ 1 egg m−<sup>5</sup> ( ∂E ∂z varies between ± 15 egg m−<sup>3</sup> over about 30 m from both sides of the maximum concentration), simple arithmetic suggests that

and

$$K \frac{\partial^2 \mathbf{E}}{\partial \mathbf{z}^2} \approx 10^{-5} \text{egg } \text{m}^{-3} \text{ s}^{-1}$$

egg m−<sup>3</sup>

s −1

≈ [1, 3] × 10−<sup>3</sup>

with w ε [4, 9.3] m d−<sup>1</sup> (see Results) and K = 3.4×10 m−<sup>6</sup> s −1 (background turbulent diffusivity) from (Bourgault et al., 2011). This suggest that from a physical point of view, the buoyant vertical displacement of eggs is dominant over the turbulent diffusion mechanism, and only turbulent events about a 100 times above the background value could effectively influence their distribution. The role of turbulent mixing in egg distribution (aggregation or spreading) is likely minimal and the use of a parameterization such as the one presented in Bourgault et al. (2011) could have been sufficient here. The effect of turbulence may only become important for denser eggs rising very slowly toward the surface or directly after the spawning if it occurs in a thin layer pattern, hence producing a high concentration gradient. This effect could be studied more efficiently with new in situ sampling devices such as the LOKI underwater imaging system that can provide highly resolved vertical distribution of adult females C. hyperboreus, their eggs, a whole suite of potential other intraguild predators beyond M. longa and the physical properties of the water column as well (Schmid et al., 2016).

From a biological point of view, egg density had an overwhelming impact on egg vertical distribution patterns (**Figure 7**). Egg density defined their vertical velocity w and as a result both the range of depth they could reach before hatching and their corresponding concentration. For two out of three egg density scenarios, eggs laid at depth did not manage to reach and accumulate within the surface layer. Even for the minimum density scenario Dmin, the amount of eggs reaching the surface remained marginal. This is coherent with the generally accepted idea that C. hyperboreus nauplii, rather than eggs, accumulate under the ice in advance of the phytoplankton bloom (Conover and Huntley, 1991). Meanwhile, the maximum egg concentration reached was about 4 eggs L−<sup>1</sup> , close the minimal egg concentration used in our grazing experiments. Depth and concentration were crucial for the interaction with female M. longa whose vertical position and abundance vary a lot, and whose ingestion rate depends on the surrounding egg concentration. As a result, it appeared that the probability of encounter between a predator and an egg of C. hyperboreus was determined essentially by the density of the latter.

### Impact of Intraguild Predation on *C. hyperboreus* Recruitment

If we consider thin layer effects to remain marginal, our results suggest that impacts on C. hyperboreus population dynamics may remain limited in space and time since M. longa IGP was limited to a little more than 3% of C. hyperboreus egg biomass. However, young nauplii stages could also be preyed upon by M. longa and thus our figures could underestimate the actual impact of M. longa on C. hyperboreus recruitment. M. longa is a cruising feeder, i.e., it cruises through water searching for food and prey and captures them upon detection. Moreover, motile preys such as nauplii can generate a hydrodynamic trail while swimming that could render them be easier to detect by M. longa than nonmotile preys such as eggs (Kiørboe, 2011). This assumption is supported by feeding experiments with M. lucens and M. longa in which phytoplankton and much larger nauplii Artemia were offered together, illustrating selective feeding on Artemia nauplii (Haq, 1967).

In addition to females M. longa, other development stages of this species and other copepod species could also exert IGP on

w ∂E ∂z

(scenario Dmax) (right panel).

C. hyperboreus eggs. As already mentioned, adults and advanced copepodite stages of the large C. glacialis emerge from diapause and initiate ascent to surface layers prior the spring bloom to feed on ice algae (Daase et al., 2013). Therefore, they could also benefit from the energy rich C. hyperboreus eggs (and potentially the nauplii) and add to the predation pressure. Thus, we likely have underestimated IGP pressure on C. hyperboreus and its impact on its recruitment in several ways. However, it may remain very dependent on the seasonal timing of the feeding activity of these potential predators, as well as their vertical position in the water column as already demonstrated.

It seems that there is actually an ecological trade-off for C. hyperboreus females to lay low (lipid-rich) or high-density (lipid-poor) eggs. On one hand the obvious metabolic advantage for lipid-rich eggs is that the offspring can rely on abundant reserves to develop. The downside however could be that low-density eggs reach faster and "en masse" the layer where M. longa and other species are abundant, hence increasing their mortality risk. On the other hand, dense eggs ascend very slowly and actually hatch before having reached these dangerous depths. The wide range in egg density that has been observed among eggs from different C. hyperboreus females but also within the same egg clutch (Jung-Madsen et al., 2013) could actually be part of a strategy that mitigates predation risk by spreading the eggs across a range of ascent speeds. However, the delicate balance of both opposing effects on offspring fitness could only be assessed in a more detailed modeling study supported by finely resolved and concurrent observation of the zooplankton community vertical distribution.

### *C. hyperboreus* Importance in the Arctic System

Our results could offer an interesting contrast with the earlier study of Huntley and Escritor (1992) on a couple of homologous species from Antarctica, M. gerlachei and C. acutus. They showed from incubations of a group of individuals that M. gerlachei could reach daily rations ranging between 4 to 11% of its body weight when offered 1000 egg L−<sup>1</sup> . The authors further estimated that this concentration was about three orders of magnitude higher than what it could be in situ (1 egg L−<sup>1</sup> ) and thus concluded that this type of predation is likely insignificant. However, our experimental results showed that M. longa individuals could meet up to 75% of their daily metabolic requirements on eggs of C. hyperboreus offered at a concentration of 5 L−<sup>1</sup> , based on respiration rates observed in Amundsen Gulf (Seuthe et al., 2006). We also simulated that the mean in situ ration of eggs for M. longa females should vary between 8 and 37% of their metabolic needs, depending on the respiration rate. The lower boundary is based on Seuthe et al. (2006), whereas the upper boundary is based on lower respiration rates (Hirche, 1987). Neither value is sufficient to ensure complete metabolic maintenance, but during wintertime it could be combined to some level of lipid stores to cope with the otherwise scarce food background available to these copepods. Lipid-rich C. hyperboreus eggs (and potentially nauplii) are a reliable and valuable food source that at least some M. longa individuals seem prone to take advantage of during several months of the year.

Our study stresses the importance of C. hyperboreus as a linchpin of Arctic marine trophic network. This key species has adapted to the extreme environment by evolving its ability to store considerable amounts of lipids. C. hyperboreus efficiently concentrate the energy from the short-lived primary production bloom and supports the entire marine trophic network. Higher trophic levels rely heavily on its large copepodite and adult development stages, while zooplankton species from a similar trophic level (from the same guild) also benefit from the smaller packaging of the bounty within its eggs. Moreover, since C. hyperboreus reproduction occurs for several months during a period of the polar year when primary production has shut down, it likely provides a precious and unparalleled resource for several species of planktonic predators that remain active in the dead of winter. Hence, IGP should not only be considered as an extra mortality source that could affect recruitment of the species that is preyed upon, but also as a crucial survival strategy that could shape the life cycle strategies of some opportunistic species.

IGP needs to be studied further as we move toward an integrated approach of marine ecology that recognizes the influence of both individual variability and community-level interactions. Other implications of IGP than those evoked in our study could be important. In the North Atlantic for example, the survival of C. finmarchicus early stages follows different seasonal patterns in areas where it is the dominant Calanus species than in areas where its larger congeners, C. glacialis and C. hyperboreus, co-occur. In such areas where all three species live together, the C. finmarchicus recruitment peak can occur several weeks after the spring bloom, much later than it usually does (Melle et al., 2014). In early spring, C. hyperboreus and C. glacialis, that are already active when C. finmarchicus initiates its reproduction fuelled by the phytoplankton bloom, could ingest C. finmarchicus eggs and affect its recruitment. Interestingly, IGP could contribute to the resistance of marginal Arctic marine ecosystems to the northward advance of the boreal C. finmarchicus under the pressure of climate change.

### AUTHOR CONTRIBUTIONS

KD designed and ran the laboratory experiments, participated to the in situ sampling, did the statistical analysis, ran the modeling experiment, and wrote most of the paper. FM contributed to the design of the laboratory experiment, contributed to the data analysis, designed, and executed most of the modeling experiment and contributed to the writing. SP contributed to the design of the laboratory experiment, provided access to the laboratory facility, and contributed to the writing. PJ contributed to the design and the execution of the laboratory experiment, and ran the in situ sampling. FC contributed to the design of the numerical experiment, provided data from Amundsen Gulf, and contributed to the writing.

### FUNDING

This work has been supported by an NSERC Discovery grant to FM, DFO, and Québec-Océan.

### ACKNOWLEDGMENTS

KD is grateful to PJ for his invaluable help in the field and in the laboratory, Geneviève Parent for her help with image analysis, Michel Starr and Liliane St-Amand for their help with laboratory analysis, David Levasseur for his assistance in the laboratory experiments and Daniel Bourgault for the Amundsen Gulf physical data. KD also thanks FM, SP, and Maurice Levasseur for the stimulating and constructive discussions and finally FC and Jeffrey Runge for their help on the manuscript. This is a contribution to the research programs of Québec-Océan, ArcticNet and UMI Takuvik.

### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fmars. 2016.00185

The R code and forcing fields for the model can be found online at: https://github.com/NEOLab-Git/Chyp\_Egg\_1D.git

The detailed table of individual observations is provided.

### REFERENCES


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Dufour, Maps, Plourde, Joly and Cyr. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Modeling Plankton Mixotrophy: A Mechanistic Model Consistent with the Shuter-Type Biochemical Approach

Caroline Ghyoot <sup>1</sup> \*, Kevin J. Flynn<sup>2</sup> , Aditee Mitra<sup>2</sup> , Christiane Lancelot <sup>1</sup> and Nathalie Gypens <sup>1</sup>

<sup>1</sup> Ecologie des Systèmes Aquatiques, Université libre de Bruxelles, Brussels, Belgium, <sup>2</sup> Biosciences, Swansea University, Swansea, United Kingdom

Mixotrophy, i.e., the ability to combine phototrophy and phagotrophy in one organism, is now recognized to be widespread among photic-zone protists and to potentially modify the structure and functioning of planktonic ecosystems. However, few biogeochemical/ecological models explicitly include this mode of nutrition, owing to the large diversity of observed mixotrophic types, the few data allowing the parameterization of physiological processes, and the need to make the addition of mixotrophy into existing ecosystem models as simple as possible. We here propose and discuss a flexible model that depicts the main observed behaviors of mixotrophy in microplankton. A first model version describes constitutive mixotrophy (the organism photosynthesizes by use of its own chloroplasts). This model version offers two possible configurations, allowing the description of constitutive mixotrophs (CMs) that favor either phototrophy or heterotrophy. A second version describes non-constitutive mixotrophy (the organism performs phototrophy by use of chloroplasts acquired from its prey). The model variants were described so as to be consistent with a plankton conceptualization in which the biomass is divided into separate components on the basis of their biochemical function (Shuter-approach; Shuter, 1979). The two model variants of mixotrophy can easily be implemented in ecological models that adopt the Shuter-approach, such as the MIRO model (Lancelot et al., 2005), and address the challenges associated with modeling mixotrophy.

Keywords: constitutive mixotroph (CM), non-constitutive mixotroph (NCM), modeling, phytoplankton, zooplankton

## INTRODUCTION

Traditionally, planktonic protists are separated into two distinct functional groups: the phototrophic phytoplankton and the phago-heterotrophic microzooplankton. However, many protists assigned to these two groups are recognized as capable of combining phototrophy and phago-heterotrophy (Flynn et al., 2013). These mixotrophic protists have been reported in all planktonic functional groups (with the notable exception of the diatoms) and they include a large diversity of mixotrophic types (Flynn et al., 2013). In some mixotrophs, growth is mainly supported by phototrophy (e.g., Cryptomonas ovata; Tranvik et al., 1989) while in others, growth

#### Edited by:

Michael Arthur St. John, Institute for Aquatic Resources, Danish Technical University, Denmark

#### Reviewed by:

Peter Allan Thompson, Commonwealth Scientific Industrial Research Organisation, Australia Alberto Basset, University of Salento, Italy

> \*Correspondence: Caroline Ghyoot cghyoot@ulb.ac.be

#### Specialty section:

This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Ecology and Evolution

> Received: 21 June 2016 Accepted: 30 June 2017 Published: 18 July 2017

#### Citation:

Ghyoot C, Flynn KJ, Mitra A, Lancelot C and Gypens N (2017) Modeling Plankton Mixotrophy: A Mechanistic Model Consistent with the Shuter-Type Biochemical Approach. Front. Ecol. Evol. 5:78. doi: 10.3389/fevo.2017.00078 is mainly supported by phagotrophy (e.g., Poterioochromonas malhamensis; Sanders, 1991). Some mixotrophs are forced to use both trophic modes to grow and survive because some essential metabolites come specifically from one of the two metabolic pathways (e.g., the ciliate Laboea strobila; Stoecker et al., 1988); others are facultative mixotrophs (e.g., the dinoflagellate Fragilidium duplocampanaeforme; Park et al., 2015). Some mixotrophs use their second trophic mode to fulfill carbon requirements (e.g., the haptophyte Chrysochromulina brevifilum; Stoecker, 1998); for others, it is a means to fulfill nutrient requirements (e.g., the dinoglagellate Prorocentrum minimum; Stoecker, 1998); and for others yet, it is a mechanism to get specific metabolites (as phospholipids; Kimura and Ishida, 1989).

Among this large diversity of mixotrophic types, a major distinction can be made between mixotrophs depending on whether they photosynthesize using their own chloroplasts or using chloroplasts acquired from their phototrophic prey (Mitra et al., 2016). Mixotrophs that actively synthesize and maintain their own chloroplasts are called constitutive mixotrophs (CMs). Mixotrophs that do not constitutively synthesize chloroplasts but photosynthesize using chloroplasts acquired from their phototrophic prey are called non-constitutive mixotrophs (NCMs). The acquired chloroplasts in NCMs remain functional for periods ranging from hours to days, depending on the type of NCM (Mitra et al., 2016). Generalist NCMs, i.e., those that acquire chloroplasts from a broad range of phototrophic prey, have a poor ability to maintain functional chloroplasts (Dolan and Pérez, 2000). By contrast, specialist NCMs, i.e., those that need to acquire chloroplasts from specific phototrophic prey, can maintain a photosynthetic activity for long periods (Stoecker et al., 2009; Hansen et al., 2013). Specialist NCMs can further be divided into those that retain the entire photosynthetic prey (endosymbiosis) and those that only retain the chloroplasts (kleptochloroplasty; Mitra et al., 2016). In a functional capacity, the CMs are closer to the strict phototrophs while the NCMs are closer to the strict phago-heterotrophs.

While mixotrophy has been reported for a long time, it is now appreciated as being much more widespread in aquatic ecosystems than initially thought. Previously, the mixotrophic status was only accorded to some dinoflagellates, forams, radiolarian, and acantheria while now, mixotrophy has been acknowledged in all eukaryote planktonic microorganism groups, except diatoms (Sanders and Porter, 1988; Burkholder et al., 2008; Flynn et al., 2013). In addition, these species are not limited to a specific habitat: mixotrophs are observed in both freshwater and marine (Sanders, 1991; Stoecker et al., 2009), oligotrophic and eutrophic systems (Burkholder et al., 2008), and from polar to equatorial regions (Zubkov and Tarran, 2008; Stoecker et al., 2009; Sanders and Gast, 2012). In coastal areas, mixotrophic flagellates can account for some 50% of the pigmented biomass (Havskum and Riemann, 1996) and chloroplast-containing ciliates can account for 40–>60% of the planktonic ciliates in summer (Stoecker et al., 1987; Bernard and Rassoulzadegan, 1994). In oceanic waters, mixotrophs account for 40–95% of the bacterivory in the euphotic layer (Zubkov and Tarran, 2008).

Constitutive mixotrophy is suggested to play an important ecological role when inorganic nutrients are low (e.g., in oligotrophic systems; e.g., Arenovski et al., 1995) or unbalanced (e.g., in eutrophied systems; e.g., Nygaard and Tobiesen, 1993; Burkholder et al., 2008), and when light is limiting (e.g., during the polar night or occasionally in eutrophied systems; e.g., Bird and Kalff, 1986; Roberts and Laybourn-Parry, 1999; Jones et al., 2009). In such systems, prey ingestion provides nutrients and energy. Similarly, non-constitutive mixotrophy may be advantageous in "high light–low prey" ecosystems (e.g., in oligotrophic systems; e.g., Skovgaard, 1998; Hansen et al., 2013) because acquired phototrophy supplies carbon by photosynthesis. Finally, mixotrophy is worthy of interest in an environmental perspective because most marine harmful algae have been reported as mixotrophs (Stoecker et al., 2006; Burkholder et al., 2008; Jeong et al., 2010).

Several models have been developed with the specific aims of exploring planktonic mixotrophy from an ecophysiological or ecological (species competition) perspective. Most interest has been leveled at the potential impact of mixotrophs on the microbial food web structure and functioning, and the conditions under which mixotrophs may likely coexist with strict phototrophs and heterotrophs (Thingstad et al., 1996; Baretta-Bekker et al., 1998; Stickney et al., 2000; Jost et al., 2004; Hammer and Pitchford, 2005; Hood et al., 2006; Flynn and Mitra, 2009; Crane and Grover, 2010; Ward et al., 2011; Våge et al., 2013). By far the greater effort has been applied to CM organisms. The complexity of the model structure varies widely among such studies. The simplest models describe mixotrophy as the ability to combine both phototrophy and heterotrophy without any feedbacks or trade-offs between the two nutritional modes and organisms have a fixed stoichiometry (e.g., Hammer and Pitchford, 2005). At the other extreme, the most complex model explicitly describes the main regulative processes that occur between phototrophy and heterotrophy in the mixotroph and allows for a variation of the cellular stoichiometry (Flynn and Mitra, 2009).

Despite the potential significance of mixotrophy in aquatic systems and the existence of mathematical models describing this trophic mode, few ecological/biogeochemical models consider it explicitly (e.g., Mitra et al., 2014). Those models that do include mixotrophs demonstrate the potential for mixotrophy to significantly impact the flow of energy and nutrients in the system. In particular, primary production can potentially be increased by a factor 2 compared to a system in which mixotrophy is not considered, thanks to a shortened and more effective chain from nutrient regeneration to primary production (Mitra et al., 2014).

Considering mixotrophy in biogeochemical/ecological models is however challenging due to the large diversity of mixotrophic types, the scarcity of data allowing the parameterization of physiological processes, and the need to make the inclusion of mixotrophy into existing ecosystem models as simple as possible. Indeed, the addition of a mixotroph functional type description into ecosystem models will inevitably be tempered by the structure of the extant ecosystem model.

Regarding the diversity of mixotrophic types, this paper proposes a flexible mechanistic model featuring the two main types of mixotrophy: constitutive and non-constitutive. The two mixotrophic types have indeed different ecophysiology and different relation to their prey (the NCM being strictly dependent on the presence of prey); therefore, they affect differently the ecosystem dynamics (Mitra et al., 2016). In addition, the version describing constitutive mixotrophy can be configured to represent either CMs that favor either phototrophy or heterotrophy. Simulations have been performed to compare each mixotrophic type with the strict trophic type it most closely resembles from a functional perspective (the CM with the strict phototroph and the NCM with the strict heterotroph) in order to explore the competitive advantage of mixotrophy over strict forms.

As for the explicit inclusion of mixotrophy into existing biogeochemical/ecological models, we were mainly interested in introducing mixotrophy in a form consistent with the mechanistic structure of the AQUAPHY model (Lancelot et al., 1991); this model has been used to describe primary production via phytoplankton growth physiology within several biogeochemical models (Billen et al., 1994; Lancelot et al., 2000, 2005). A feature of AQUAPHY is that the total cellular carbon is divided into separate classes of components on the basis of their function: these comprise synthetic and structural material (i.e., photosynthetic apparatus, ribosomes, genetic material, membranes, etc.), stored carbon (i.e., carbohydrates, lipids), and carbon monomers (i.e., photosynthetic products and precursors of complex molecules). This mechanistic approach was suggested by Shuter (1979) as a means to successfully describe the observed behavior of a variety of unicellular algal species, qualitatively and quantitatively. The work is thus a first step in the implementation of mixotrophy in the biogeochemical models that adopt a "Shuter mechanistic approach" to describe the phytoplankton physiology.

### METHODS

### Constitutive Mixotrophy

The model of constitutive mixotrophy was constructed on the basis of the following hypotheses, summarizing the main qualitative observations related to CMs : (i) the CM is preferentially phototrophic but it can supplement its nutrient requirements (under inorganic nutrient limitation) or its carbon requirements (under light limitation) by ingesting prey (e.g., in Jones et al., 1995; Carvalho and Granéli, 2010; McKie-Krisberg et al., 2015); (ii) the maximum mixotrophic growth is not allowed to exceed the maximum phototrophic growth; (iii) the phototrophic growth has to account for at least 10% of the mixotrophic growth, such that we describe an obligate phototroph (Caron et al., 1993; Brutemark and Granéli, 2011); (iv) the nutrients regenerated by heterotrophic activity (PO3<sup>−</sup> 4 , NH<sup>+</sup> 4 ) are re-assimilated to sustaining phototrophic growth with any surplus being excreted (Flynn and Mitra, 2009).

The model combines an adaptation of the AQUAPHY model (Lancelot et al., 1991; Ghyoot et al., 2015) for the phototrophic pathway, coupled to a simple zooplankton model (Lancelot et al., 2005) for the phago-heterotrophic path. It is important to note that, in keeping with the formulation of the AQUAPHY model, the description of mixotrophy given here describes biomass growth (i.e., molC m−<sup>3</sup> time−<sup>1</sup> ) rather than per capita growth (i.e., C C−<sup>1</sup> time−<sup>1</sup> ) as in some other models (e.g., Flynn and Mitra, 2009). **Figure 1A** shows the schematic representation of the CM growth physiology, linking the phototrophic (dark gray) and heterotrophic (light gray) components. The CM model contains six state variables (**Table 1**) describing intracellular components on the basis of their function: the functional and structural metabolites (e.g., nucleic acids, proteins) synthesized by phototrophic and heterotrophic activities (Fphot and Fhet , respectively), soluble carbon monomers (i.e., early products of photosynthesis; SC), carbon reserves (i.e., carbohydrates, fatty acids; RC), intracellular soluble phosphate (SP), and intracellular soluble inorganic nitrogen (SN). The total C-cell biomass (mmolC m−<sup>3</sup> ) is given by the sum of Fphot, Fhet, SC, and RC. The Fphot and Fhet pools are assumed to have a fixed C:N:P stoichiometry, based on biochemical constraints (Geider and Laroche, 2002). Variable cellular stoichiometry is enabled by considering the additional C, P, and N accumulated as carbon monomers (SC), carbohydrates and fatty acids (RC), soluble inorganic phosphorus (SP), and soluble inorganic nitrogen (SN). The model of constitutive mixotrophy is linked to three state variables describing external inorganic nutrients—dissolved inorganic nitrogen (DIN = NO<sup>−</sup> <sup>3</sup> <sup>+</sup> NH<sup>+</sup> 4 ) and phosphate (PO3<sup>−</sup> 4 )—and also the prey which in reality expresses a variable C:N:P stoichiometry (though here prey stoichiometry is fixed as the emphasis is on the description of the autecology of the mixotrophs, rather than system ecology).

**Tables 2**, **3** show, respectively, the nine conservation equations related to the state variables and the associated processes. Phototrophic growth (µ phot; Equation 17) is controlled by the concentration of the structural and functional metabolites related to phototrophic activity (Fphot), by the limitation in carbon monomers SC—either directly produced by photosynthesis (ϕ; Equation 20) or indirectly by R<sup>C</sup> catabolism (catRC; Equation 10)—and by the limitation in internal soluble inorganic nutrients (S<sup>N</sup> and SP). The S<sup>C</sup> limitation is formulated by a Michaelis–Menten equation in which the substrate concentration is expressed by XS<sup>C</sup> − kS<sup>C</sup> , with XS<sup>C</sup> = SC F phot and kS<sup>C</sup> , which is the minimum value for XS<sup>C</sup> (assumed to be equal to the half-saturation constant for S<sup>C</sup> assimilation). The inorganic nutrient limitation is formulated by the Liebig's minimum law in which the limitation for each nutrient is expressed by a hyperbolic function depending on XSN,<sup>P</sup> (the ratio between SN,P and the N,P contained in Fphot). The uptake of inorganic nutrients (uptDIN and uptPO4; Equations 26 and 27) depends on the external nutrient concentration and the status of the internal nutrient reserve. The phototrophic respiration (respphot; Equation 22) includes costs for cellular maintenance and for synthesis of new Fphot .

Prey ingestion (graz; Equation 14) is controlled by the concentration of the structural and functional metabolites related to heterotrophic activity (Fhet) and by prey availability; the latter

FIGURE 1 | Schematic representation of functioning of constitutive mixotroph (CM; A) and non-constitutive mixotroph (NCM; B). Total mixotroph biomass is divided into six components: structural and functional metabolites related to phototrophic activity (Fphot) and heterotrophic activity (Fhet), carbon monomers (SC), carbon reserves (RC), soluble inorganic nitrogen (SN), and soluble inorganic phosphorus (SP). The "dark gray part/solid lines" is the phototrophic part and the "light gray part/dashed lines" is the heterotrophic part.



is controlled by a sigmoid (type III) function. From the ingested prey, a non-assimilated fraction is egested (egest; Equation 11) as dissolved and particulate organic matter (loss terms), a fraction is respired to meet the heterotrophic metabolic costs and is released as carbon dioxyde (resphet; Equation 21), and the last fraction is assimilated and contributes directly to the heterotrophic growth (µ het; Equation 16). If the nutrient content of the prey is higher than the nutrient required by Fhet, the surplus is regenerated as NH<sup>+</sup> 4 and PO3<sup>−</sup> 4 (reg<sup>i</sup> with i = N, P; Equation 23). These regenerated nutrients can be retained up to a maximum level in the inorganic nutrient reserves S<sup>N</sup> and S<sup>P</sup> (ret<sup>i</sup> ; Equation 24), contributing to the phototrophic growth. If the reserve capacity is full, the surplus is excreted to the environment (excr<sup>i</sup> ; Equation 12).

TABLE 2 | Conservation equations for the constitutive mixotroph (CM).


Mixotrophic growth is computed as the sum of the phototrophic and the heterotrophic growth rate, but limited by the maximum mixotrophic growth. The latter is computed differently according to whether phagotrophy is used to offset a lack of carbon or a lack of nutrients. When the 24 h-average S<sup>C</sup> limitation is below a threshold value (threshSClim) set here as 0.15, we assumed that the mixotroph switches to perform increasing levels of phagotrophy to acquire carbon (in addition to nutrients if also nutrients limited) and, therefore, the maximum mixotrophic growth is equal to the phototrophic growth obtained with no limitation (µ mix max; Equation 18). When the 24 h-average S<sup>C</sup> limitation is above this threshold value, we assumed that the CM undertakes phagotrophy to acquire nutrients and, therefore, the maximum mixotrophic growth is equal to the phototrophic growth obtained with no nutrient limitation (µ mix max; Equation 19). If the sum of the phototrophic and the heterotrophic growth is higher than the maximum mixotrophic growth, either the grazing or the photosynthesis rate is regulated to TABLE 3 | Equations that describe the processes occurring in the constitutive mixotroph (CM).


limit the mixotrophic growth to its maximum. In other terms, the mixotroph can favor either phototrophic or heterotrophic growth. The model offers the possibility to test either of these two configurations: the CM that regulates its grazing rate (i.e., tends to grow phototrophically) hereafter referred to as "Reggraz" and the CM that regulates its photosynthesis (i.e., tends to grow heterotrophically) hereafter referred to as "Regphot." In either case, we assumed that phototrophic growth has to represent at least 10% of the mixotrophic growth. This implies that phagotrophy cannot sustain growth under prolonged dark conditions because of an obligatory demand for products of photosynthesis.

Parameter values were selected here to describe constitutive mixotrophic nanoflagellates that graze on bacteria to fulfill nutrient or energy requirements (**Table 4**). Parameters related to phototrophic carbon pathways are those of phototrophic nanoflagellates as used in the MIRO model (the MIRO model being a biogeochemical model that uses AQUAPHY to represent phytoplankton growth and that describes the planktonic ecosystem of the Southern North Sea; Lancelot et al., 2005). Parameters related to phototrophic P-pathways are similar to those presented in Ghyoot et al. (2015). Parameters related to phototrophic N-pathways and parameters related to heterotrophic activity were estimated by implementing the mixotrophy model into the MIRO model and by tuning the model against observations reported in the Belgian coastal zone (Ghyoot et al., submitted). Observations used in that tuning included plankton biomass (bacteria, nanoflagellates, diatoms, Phaeocystis colonies, microzooplankton, and copepods) and nutrient concentrations [NO<sup>−</sup> 3 , NH<sup>+</sup> 4 , PO3<sup>−</sup> 4 , and dissolved silica (DSi)].

Single parameter steady-state model sensitivity to parameters values was studied with the method of Haefner (1996). The model was run under "low DIN–high prey" chemostat-type conditions and a normalized sensitivity index (SI; Equation 28) based on steady-state biomass was calculated for each parameter:

$$SI = \frac{\left(R - R\_{ref}\right) / R\_{ref}}{\left(p - p\_{ref}\right) / p\_{ref}} \tag{28}$$

Where Rref is the value of CM biomass reached at steady-state with the reference parameter value pref (**Table 4**) and R is the value of CM biomass reached at steady-state with p, the reference parameter increased/decreased by 25%. The SI-value is thus a measure of the relative variation of CM biomass compared to the relative variation of the parameter.

### Non-constitutive Mixotrophy

We constructed the model of non-constitutive mixotrophy on the basis of available qualitative observations specific to this type of mixotrophy: (i) the photosynthetic capacity of the ingested phototrophic prey is retained for some time in the food vacuole so that it provides carbon to the mixotroph (Skovgaard, 1998); (ii) in the food vacuole, there is no replication of the functional metabolites related to phototrophy; they are only supplied by phagotrophy on phototrophic prey; (iii) the digestion rate of the ingested phototrophic prey is constant; (iv) nutrients regenerated through heterotrophic activity (PO3<sup>−</sup> 4 , NH<sup>+</sup> 4 ) can be retained for the phototrophic activity while the excess is excreted outside the cell; (v) there is no inorganic nutrient uptake (we assume these NCMs are generalist rather than specialist NCMs; the latter, such as Mesodinium and Dinophysis, are capable of using externally supplied inorganic nutrients; Hansen et al., 2013); (vi) the organism does not require some level of phototrophy to grow, meaning that we describe a facultative mixotroph (but a minimum level of phagotrophy is required for obtaining chloroplasts).

As for the model of constitutive mixotrophy, the model of non-constitutive mixotrophy combines the AQUAPHY model for the phototrophic path and a simple zooplankton model for the heterotrophic path. **Figure 1B** shows the schematic representation of the NCM growth physiology, showing the heterotrophic (light gray) and phototrophic (dark gray) components. While the model of non-constitutive mixotrophy deploys the same six state variables as the model of constitutive mixotrophy and operates with the same external factors (**Table 1**), some conservation equations (**Table 5**) and processes (**Table 6**) differ. The differences mainly rely on the fact that NCMs acquire their phototrophic capacity by ingesting phototrophic prey and they are not able to permanently maintain this capacity.

The phototrophic prey biomass (prey) is characterized by the five phototrophic compounds usually used within AQUAPHY: F phot, SC, RC, SN, and S<sup>P</sup> (we have therefore: prey<sup>F</sup> phot , preyS<sup>C</sup> , preyR<sup>C</sup> , preyS<sup>N</sup> , and preyS<sup>P</sup> ). The grazing on each of these five compounds (graz<sup>i</sup> with i = F phot, SC, RC, SN, SP; Equation 41) is computed as the grazing on the total prey biomass (prey = prey<sup>F</sup> phot + preyS<sup>C</sup> + preyR<sup>C</sup> ) relative to the compound concentration. Once ingested by the NCM, the five compounds are distributed to their corresponding pools. As there is no mechanism for synthesis or maintenance of Fphot in the NCM configuration, Fphot is exclusively supplied via grazing on photrophic prey<sup>F</sup> phot (Equation 30). SC, RC, SN, and S<sup>P</sup> are supplied by the grazing but also by other (phototrophic and heterotrophic) processes (Equations 31–34). Photosynthesis and R<sup>C</sup> catabolism supply S<sup>C</sup> in the same way as in the model of constitutive mixotrophy (ϕ; cf. Equation 20 and catRc; cf. Equation 10). R<sup>C</sup> synthesis supplies RC, as in the model of constitutive mixotrophy (synthRc; cf. Equation 25), while nutrient retention supplies S<sup>N</sup> and S<sup>P</sup> (ret<sup>i</sup> with i = N, P; cf. Equation 24).

The phototrophic components obtained by grazing enables phototrophic growth to be computed as for the model of constitutive mixotrophy (µ phot; cf. Equation 17) but now the phototrophic growth supports the production of Fhet instead of F phot (Equation 29). As there is no synthesis and maintenance of Fphot, phototrophic respiration includes only costs for the synthesis of Fhet (respphot; Equation 44).

The phototrophic components in NCMs (Fphot, SC, RC, SN, SP) are continuously degraded (de facto digested) at a constant rate (dig<sup>i</sup> with i = F phot, SC, RC, SN, SP; Equation 39). The digested material has three possible fates: the nonassimilated material is egested outside the cell (egest; Equation 40) as dissolved and particulate organic matter, a fraction of the assimilated material is respired (resphet; Equation 43) to meet the heterotrophic metabolic costs, and the remaining fraction is used for heterotrophic growth (µ het; Equation 42). If the C:N:P stoichiometry of the digested prey is higher than the C:N:P stoichiometry of Fhet, NH<sup>+</sup> 4 , and PO3<sup>−</sup> 4 are regenerated (reg<sup>i</sup> with i = N, P; Equation 45). These nutrients can be retained in S<sup>N</sup> and S<sup>P</sup> and contribute to the phototrophic growth (ret<sup>i</sup> with i = N, P calculated as in CM; cf. Equation 24). As we assumed that inorganic nutrient uptake does not occur in NCMs, these retained inorganic nutrients are the only ones that allow phototrophic growth. If the reserves S<sup>N</sup> and S<sup>P</sup> are full, the regenerated nutrients are excreted outside the cell (excr<sup>i</sup> with i = N, P calculated as in CMs; cf. Equation 13).



Values were taken from Lancelot et al. (2005), Ghyoot et al. (2015) and Ghyoot et al. (submitted).


With the selected parameters values (**Table 4**), the model describes a generalist non-constitutive mixotrophic microzooplankton (ciliate) that feeds on phototrophic nanoflagellates and uses their chloroplasts to photosynthesize. The value of the constant rate of degradation of acquired photosystems is 0.03 h−<sup>1</sup> , the same as in Flynn and Hansen (2013). The other parameters related to heterotrophic processes were estimated by implementing the mixotrophy models into the MIRO model that describes the planktonic ecosystem of the Southern North Sea and by tuning the model against observations reported in this area (Ghyoot et al., submitted). Parameters values involved in phototrophic processes are those of the phototrophic prey, i.e., the nanoflagellates, as in the model of constitutive mixotrophy.

TABLE 6 | Equations that describe the processes occurring in the non-constitutive mixotroph (NCM).


Model sensitivity to the parameter values was studied with the method of Haefner (1996) as described above for the model of constitutive mixotrophy (Equation 28).

### RESULTS

### Constitutive Mixotrophy

In order to explore the qualitative behavior of the CM under different environmental conditions, we ran the model of constitutive mixotrophy under steady-state conditions with various values of DIN (ranging from 0 to 20 mmolN m−<sup>3</sup> ) and prey (bacteria) biomass (ranging from 0 to 20 mmolC m−<sup>3</sup> ). These simulations were run under two contrasting photon flux densities (30 and 200 µmol quanta m−<sup>2</sup> s −1 ). Conditions are such that P never limits the growth and the prey is considered as "inert" (i.e., bacteria growth and metabolism is not described). The two possible regulation mechanisms (photosynthesis "Regphot" vs. grazing "Reggraz") limiting the mixotrophic growth to its maximum were tested. The performance of the two CMs ("Reggraz" and "Regphot") is compared with that of the strict phototrophic nanoflagellate when growing under the same growth conditions.

Under high photon flux density (**Figure 2**), the growth rate of the strict phototroph decreases to zero as DIN decreases to zero because phototrophic growth is prevented by the lack of DIN (**Figure 2A**). By contrast, when prey concentration is higher than 4 mmolC m−<sup>3</sup> , the growth rate of the two CM configurations ("Reggraz" and "Regphot") does not vary as a function of DIN because the lack of DIN is offset by bacteria ingestion (**Figures 2F,K**). De facto, the model captures correctly the competitive advantage of the mixotrophs at low inorganic nutrient concentration and high prey concentration. The grazing rate of the two CMs varies in function of the external conditions: it increases when prey concentration increases and when DIN decreases (**Figures 2H,M**). Thanks to their grazing activity, at low DIN, the photosynthesis rate of the two CMs decreases less than the photosynthesis rate of the strict phototroph (**Figures 2B,G,L**). When mixotrophs ingest prey under high photon flux density, the entire part of the regenerated DIN is retained inside the cell to sustain phototrophic activity (**Figures 2J,O**); there is no NH<sup>4</sup> excretion (**Figures 2I,N**). Under this photon flux density, there is no noticeable difference between the two mixotrophic configurations (CM "Reggraz" vs. CM "Regphot").

Under low photon flux density (**Figure 3**), the strict phototroph cannot grow in any nutrient conditions because the carbon monomers (SC) limitation (which is controlled by the light limitation) is too high to allow steady-state growth rates above zero (**Figure 3A**). In function of its configuration, the CM behaves differently: the CM "Reggraz" is able to grow under specific DIN and prey conditions (**Figure 3F**) while the CM "Regphot" has a zero steady-state growth in all conditions (**Figure 3K**). This different behavior is explained by the initial hypothesis used to construct the model, i.e., a minimum level of phototrophic growth (involving inorganic nutrient assimilation) is needed to allow prey ingestion. When the "Regphot" configuration is used, the CM down-regulates its photosynthesis when the maximum mixotrophic growth is attained, instead of its grazing. Therefore, phototrophy is more constrained in this "Regphot" configuration and the minimum level of phototrophic growth required to allow prey ingestion is not attained. The hypothesis of a minimum level of phototrophy also explains that the CM "Reggraz " cannot take advantage of its ability to ingest prey at low DIN, as phototrophy involves inorganic nutrient assimilation (**Figure 3F**). By comparison with the high photon flux density conditions, the regenerated DIN related to phagotrophic activity is not entirely retained inside the cell; a significant part is

excreted outside the cell (**Figure 3I**) because the demand is lower due to the low photosynthesis rate (**Figure 3G**). Without the hypothesis of a minimum level of phototrophic growth, the behavior of the two CMs is similar a steady-state growth rate is reached around 0.3 day−<sup>1</sup> when prey is available (not shown).

The sensitivity analysis conducted on the physiological parameters involved in the model of constitutive mixotrophy shows that parameter rankings constructed on the basis of the sensitivity index (SI; Equation 28) differ according to the model configuration selected, i.e., "Reggraz" or "Regphot" (**Figures 4A,B**). Because grazing is the process that is regulated when the configuration "Reggraz" is selected, the parameters related to phago-heterotrophy have proportionally a higher impact on the model response (as shown on the left part of the ranking; **Figure 4A**). By contrast, if the configuration "Regphot" is selected, the parameters related to phago-heterotrophy are located on the right part of the ranking, indicating that they have a lower impact than parameters related to phototrophic processes (**Figure 4B**). Despite the difference of parameter appearance in the ranking, the two model configurations are generally low-sensitive to most of parameters in the range of the tested values; 17 out of 22 parameters have a SI < 0.4 for "Reggraz" and 15 out of 22 parameters have a SI < 0.4 for "Regphot", meaning that a 25% change of their reference value induces <10% change of the mixotroph biomass reached at steady-state.

### Non-constitutive Mixotrophy

To study the behavior of the NCM, we ran the model under steady-state conditions for various prey (a phototrophic nanoflagellate) biomass (ranging from 0 to 20 mmolC m−<sup>3</sup> ) and for various DIN-values (ranging from 0 to 20 mmolN m−<sup>3</sup> ). These simulations were run under two contrasting photon flux densities (30 and 200 µmol quanta m−<sup>2</sup> s −1 ). As for the model of constitutive mixotrophy, we considered the prey as inert, meaning that the metabolism of the phototrophic prey is not active. The behavior of the NCM is compared with that of a strict heterotrophic microzooplankton under the same growth conditions.

Under high photon flux density (**Figure 5**), the NCM can grow at lower prey concentrations than the strict heterotroph (**Figures 5A,F**) because the NCM takes advantage of the photosynthetic capacity of the prey retained in the food vacuole for C supply (**Figures 5B,G**) and of inorganic nutrient retention from heterotrophic regeneration (**Figures 5E,J**). DIN concentration has no impact on the NCM growth rate because we assumed that the NCM is not able to take up inorganic nutrients; the inorganic nutrients required for phototrophic growth are only provided by nutrient recycling from prey digestion. As photosynthesis in the NCM relies exclusively on the acquired prey chloroplasts, when prey concentration is lower than 5 mmolC m−<sup>3</sup> , the NCM cannot grow so well because the grazing is limited by the low prey availability (**Figures 5F–H**). With the model configuration used, the grazing rate of the NCM is lower than the grazing rate of the strict heterotroph at prey concentration higher than 8 mmolC m−<sup>3</sup> (**Figures 5C,H**). The difference is explained by the phototrophic growth that contributes to the mixotrophic growth by providing photoassimilated C (**Figure 5G**) and inorganic nutrient from nutrient retention (**Figure 5J**). This illustrates the benefit of the close interactions that occur between phototrophy and heterotrophy inside the mixotrophic cell. At high prey concentrations, NH<sup>4</sup> excretion is substantially lower for the NCM than for the strict heterotroph (**Figures 5D,I**). Given the low N retention observed for the NCM (**Figure 5J**), the difference cannot be only explained by the ability of the NCM to retain a part of the regenerated N for its phototrophic growth. The difference is actually due to a different N regeneration for the strict heterotroph and the NCM (N regeneration being defined here as the sum of NH<sup>4</sup> excretion and N retention). As the grazing rate of the NCM is lower than that of the strict heterotroph at high prey concentration, N regeneration is lower for the NCM. In addition, when the NCM photosynthesizes thanks to the chloroplasts acquired from its prey, it can use a part of the N inorganic pool (SN) of the prey to grow phototrophically. This process tends to increase the C/N stoichiometry of the prey so that N regeneration issued from prey digestion is lower (Equation 45). The latter effect is particularly important at high photon flux density because the nutrient demand for phototrophic growth is higher.

Under low photon flux density (**Figure 6**), the growth rates of the NCM are the same as those obtained under high photon flux density (**Figures 6A,F**) because the decrease of photosynthesis rate in the NCM (**Figure 6G**) associated with the lower photon flux density is offset by an increase of grazing rate (**Figure 6H**). As we assumed that the NCM was a facultative mixotroph (i.e., does not require some level of photosynthesis to grow), it is not impacted by the low light. Due to its higher grazing rate, NH<sup>4</sup> excretion and N retention by the NCM are slightly higher than under high photon flux density (**Figures 6I,J**).

The sensitivity analysis conducted on the physiological parameters involved in the model of non-constitutive mixotrophy (**Table 4**) shows that the parameters that have the highest impact on the model response (here, in terms of steady-state biomass) are those related to heterotrophic activity (**Figure 4C**). As the grazing directly controls the heterotrophic growth as well as the phototrophic growth, it is not surprising to observe that the half-saturation constant for grazing (k<sup>g</sup> ) and the maximum grazing rate (gmax) are the two first parameters in the ranking. Among parameters related to heterotrophic activity, the half-saturation constant for prey digestion (k dig ) is the most problematic to measure experimentally. Further, it is an important parameter because it directly controls the extent to which the organism is able to use phototrophy, as a low k dig means that the organism maintains the kleptochloroplasts active during a long period while a high k dig means that the organism rapidly digests the kleptochloroplasts and thus, approaches the strict heterotrophic organism. However, the model is rather robust against k dig changes because SI = 0.4, meaning that a 25% change of its reference value only induces a 10% change of the mixotroph biomass reached at steadystate.

Parameters related to phototrophic activity are generally of lower importance as most of them have a SI < 0.003, meaning that a 25% change of the parameter value induces a 0.075% change of the mixotroph biomass reached at steadystate. The parameter of light adaptation (α) and the maximum photosynthesis rate (kmax), i.e., the two parameters directly involved in the photosynthesis (Equation 20), are the only parameters related to phototrophy that have a visible impact on the model response. However, their impact is minor as the SIs are, respectively, 0.33 and 0.19.

### DISCUSSION

Many field, experimental and modeling studies have highlighted the potential, if not real significance, of planktonic mixotrophy in aquatic systems (e.g., Bird and Kalff, 1986; Estep et al., 1986; Bockstahler and Coats, 1993; Hall et al., 1993; Nygaard and Tobiesen, 1993; Arenovski et al., 1995; Havskum and Riemann, 1996; Stoecker et al., 1997; Stickney et al., 2000; Carvalho and Granéli, 2010; Hartmann et al., 2012; Mitra et al., 2014). In addition, experimental studies have shown that there is a large diversity among mixotrophs, in terms of (i) planktonic groups in which mixotrophic species have been observed, (ii) prey

ingested, (iii) obligation to feed on a specific prey (specialist or generalist mixotroph), (iv) obligation to use the two trophic modes (obligate or facultative mixotrophy), (v) proportion of phototrophy and heterotrophy involved in growth, and (vi) factors inducing the use of the additional trophic mode (carbon limitation or nutrient limitation). However, despite the large diversity, a major distinction can be made among mixotrophs according to the origin of their chloroplasts: either constitutive or acquired from ingested phototrophic prey (Mitra et al., 2016). All mixotrophic protists can, therefore, be divided between being CMs or NCMs. The aim of this work is thus to offer a model able to represent the two contrasting forms of mixotrophy and that can be easily implemented in biogeochemical/ecological models. Specifically, the offering here facilitates the implementation of these groups into the AQUAPHY model that deploys the Shuter (1979) concept. The aim was not to develop descriptions for specific organisms, but rather to provide flexible constructs in which key parameters could be safely varied (as demonstrated by sensitivity analyses, **Figure 4**) to enable applications as appropriate for different ecosystem scenarios.

We adopted a model structure in which the organism biomass is divided into different components (on the basis of their function in the cell, i.e., structure, synthesis, or reserve) that interact and explain the main features related to microalgae metabolism (as in Shuter, 1979). This kind of model structure offers the advantage to be particularly appropriate to represent the main interactions that occur between phototrophic and heterotrophic activities in a mixotroph. Mitra and Flynn (2010) have indeed shown that descriptions integrating physiological processes, with some degree of feedback to modulate the processes of phototrophy and heterotrophy, are needed to properly represent the qualitative behavior of mixotrophs. Among existing mixotrophic models, only those of Stickney et al. (2000) and the "perfect beast" of Flynn and Mitra (2009) take the interactions between the two trophic modes into account; the others rely on additive descriptions of phototrophy and heterotrophy (Thingstad et al., 1996; Baretta-Bekker et al., 1998; Jost et al., 2004; Hammer and Pitchford, 2005; Crane and Grover, 2010; Ward et al., 2011; Våge et al., 2013).

In this work we presented descriptions of the two mixotroph forms: the CMs and NCMs. The two versions, describing

fundamentally different mixotroph functional types, differ in the models by the processes linking the different components (i.e., the state variables) though they do share a common structure, with similar components in most respects. In the tested conditions, the model of constitutive mixotrophy was

able to reproduce the expected observed behaviors of CMs: under light limitation or nutrient limitation (here, DIN), the CM has a growth rate substantially higher than its equivalent strictly autotroph (**Figures 2**, **3**). This is consistent with field and experimental observations showing that mixotrophs are generally dominants under these conditions (Nygaard and Tobiesen, 1993; McKie-Krisberg et al., 2015). Regarding the model of non-constitutive mixotrophy, it properly captures the competitive advantage of NCMs over the strict heterotrophs

s

).

under light conditions, when prey are limiting (**Figure 5**), in accordance with the observations (Skovgaard, 1998).

In this work, we configured the CM as a nanoflagellate able to feed on bacteria while the NCM was illustrated by a microzooplankton (ciliate) that feeds on autotrophic nanoflagellates. However, parameters values can easily be adapted to describe other planktonic group or other prey. To consider another prey, the only parameter that has to be changed in the CM model is the prey C:N:P ratio (if assumed fixed). In the NCM model, all parameters values related to phototrophy have to be changed in order to be the same as those of the prey. The type of prey will have an impact on the amount of inorganic nutrients that is retained inside the cell or excreted outside the cell (for the CM and the NCM), and also impacts on the phototrophic capacity for the NCM. We did not consider the fact that some specialists NCMs (i.e., acquiring photosynthetic capabilities from a specific prey) are capable of replicating their acquired photosystems (Hansen et al., 2013). It has been reported, for instance, that Mesodinium rubrum had the potential to synthesize and replicate new chloroplasts at least 3–5 times when starved of prey (Hansen et al., 2013). To take this specificity into account, the constant degradation rate of ingested prey (k dig ) can be lowered to maintain the kleptochloroplasts for a longer period.

By imposing a minimum level of phototrophy to mixotrophic growth, we assumed that the CM is an obligate phototroph, but a facultative mixotroph. The fact that our CM cannot maintain a positive growth rate when both light and DIN are limiting, despite the high prey concentration, stems directly from the assigned 10% minimum level of phototrophic growth in the mixotrophic growth. However, to describe an obligate mixotroph, the only thing to do is imposing a minimum level of heterotrophy in the mixotrophic growth, in addition to the minimum level of phototrophy. A similar approach was enacted by Flynn and Mitra (2009). In the NCM configuration, we also assumed that mixotrophy is facultative but we assumed that phototrophy is facultative too (in contrast to the CM configuration). The NCM configuration could, however, be modified to match that of the CM in respect of the minimum level phototrophic growth required in the mixotrophic growth.

To take account that the proportion of phototrophy and heterotrophy involved in mixotrophic growth is not the same for all mixotrophs, we distinguished two model configurations for the model of constitutive mixotrophy: one that describes CMs using phototrophy as a priority (e.g., C. ovata; Tranvik et al., 1989) and another that describes CMs using heterotrophy as a priority (e.g., P. malhamensis; Sanders, 1991). The appropriate configuration can therefore be selected as appropriate for the

### REFERENCES

Arenovski, A. L., Lim, E. L., and Caron, D. A. (1995). Mixotrophic nanoplankton in oligotrophic surface waters of the Sargasso Sea may employ phagotrophy to obtain major nutrients. J. Plankton Res. 17, 801–820. doi: 10.1093/plankt/17.4.801

application. When comparing the two CM model configurations (i.e., "Reggraz" vs. "Regphot") results show that they behave similarly under high photon flux density. The different behaviors under low photon flux density are more explained by a combination of the model configuration and the hypothesis of a minimum level of phototrophy, than by the configuration controlling the dominance of heterotrophy vs. phototrophy itself.

When constructing the model of constitutive mixotrophy, we assumed that both carbon and nutrient limitations could induce phagotrophy. If only one of these factors was to be considered, the formulation of µ mix max (**Table 3**, Equations 18–19) can be changed to take only account of the factor inducing phagotrophy. For instance, if only nutrient limitation is assumed to induce phagotrophy, the formulation of µ mix max would be restricted to Equation (19).

In conclusion, the model structure presented in this work is able to take account of the main features and interactions between phototrophy and phago-heterotrophy in mixotrophs, and has enough flexibility to represent the observed diversity among mixotrophs. The mechanistic model of mixotrophy developed by Flynn and Mitra (2009)—the "perfect beast" has these two characteristics as well. The main difference between the two models lies in the model structure; the "perfect beast" of Flynn and Mitra (2009) is based on cell quotas and results from the merging between C:N:P zooplankton and photoacclimative models, while the models presented here are based on the Shuter approach of a division of the biomass between components chosen on the basis of their function in the cell. The type of biogeochemical/ecological model in which mixotrophy will be implemented could guide the choice between either of these model structures; the models presented in this work are particularly adapted to be implemented in those biogeochemical models that use the "Shuter" mechanistic approach to describe the phytoplankton compartment but that do not take mixotrophy into account yet.

### AUTHOR CONTRIBUTIONS

All five authors contributed to the model conception and test design. CG conducted the model analyses and prepared the manuscript while AM, CL, KF, and NG revised it.

### FUNDING

CG was supported by a Ph.D. scholarship funded through the Fonds de la Recherche Scientifique (F.R.S.-FNRS, Belgium). This work was partly enabled by support for an International Network grant from the Leverhulme Trust (UK) to KF and AM.

Baretta-Bekker, J. G., Baretta, J. W., Hansen, A. S., and Riemann, B. (1998). An improved model of carbon and nutrient dynamics in the microbial food web in marine enclosures. Aquat. Microb. Ecol. 14, 91–108. doi: 10.3354/ame014091

Bernard, C., and Rassoulzadegan, F. (1994). Seasonal variations of mixotrophic ciliates in the northwest mediterranean sea. Mar. Ecol. Prog. Ser. 108, 295–301. doi: 10.3354/meps108295


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2017 Ghyoot, Flynn, Mitra, Lancelot and Gypens. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Key Drivers of Seasonal Plankton Dynamics in Cyclonic and Anticyclonic Eddies off East Australia

Leonardo Laiolo1, 2 \*, Allison S. McInnes <sup>1</sup> , Richard Matear <sup>2</sup> and Martina A. Doblin<sup>1</sup>

*<sup>1</sup> Climate Change Cluster, University of Technology Sydney, Ultimo, NSW, Australia, <sup>2</sup> Oceans and Atmosphere, CSIRO, Hobart, TAS, Australia*

#### Edited by:

*Christian Lindemann, University of Bergen, Norway*

#### Reviewed by:

*Kemal Can Bizsel, Institute of Marine Sciences and Technology, Turkey Bruno Buongiorno Nardelli, National Research Council, Italy*

> \*Correspondence: *Leonardo Laiolo Leonardo.Laiolo@gmail.com*

#### Specialty section:

*This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Marine Science*

Received: *10 June 2016* Accepted: *16 August 2016* Published: *30 August 2016*

#### Citation:

*Laiolo L, McInnes AS, Matear R and Doblin MA (2016) Key Drivers of Seasonal Plankton Dynamics in Cyclonic and Anticyclonic Eddies off East Australia. Front. Mar. Sci. 3:155. doi: 10.3389/fmars.2016.00155* Mesoscale eddies in the south west Pacific region are prominent ocean features that represent distinctive environments for phytoplankton. Here, we examine the seasonal plankton dynamics associated with averaged cyclonic and anticyclonic eddies (CE and ACE, respectively) off eastern Australia. We do this through building seasonal climatologies of mixed layer depth (MLD) and surface chlorophyll-a for both CE and ACE by combining remotely sensed sea surface height (TOPEX/Poseidon, Envisat, Jason-1, and OSTM/Jason-2), remotely sensed ocean color (GlobColour) and *in situ* profiles of temperature, salinity and pressure from Argo floats. Using the CE and ACE seasonal climatologies, we assimilate the surface chlorophyll-a data into both a single (WOMBAT), and multi-phytoplankton class (EMS) biogeochemical model to investigate the level of complexity required to simulate the phytoplankton chlorophyll-a. For the two eddy types, the data assimilation showed both biogeochemical models only needed one set of parameters to represent phytoplankton but needed different parameters for zooplankton. To assess the simulated phytoplankton behavior we compared EMS model simulations with a ship-based experiment that involved incubating a winter phytoplankton community sampled from below the mixed layer under ambient and two higher light intensities with and without nutrient enrichment. By the end of the 5-day field experiment, large diatom abundance was four times greater in all treatments compared to the initial community, with a corresponding decline in pico-cyanobacteria. The experimental results were consistent with the simulated behavior in CE and ACE, where the seasonal deepening of the mixed layer during winter produced a rapid increase in large phytoplankton. Our model simulations suggest that CE off East Australia are not only characterized by a higher chlorophyll-a concentration compared to ACE, but also by a higher concentration of large phytoplankton (i.e., diatoms) due to the shallower CE mixed layer. The model simulations also suggest the zooplankton community is different in the two eddy types and this behavior needs further investigation.

Keywords: data assimilation, mesoscale features, phytoplankton dynamics, zooplankton dynamics, biological oceanography, size based model

### INTRODUCTION

Mesoscale eddies play crucial roles in ocean circulation and dynamics, stimulating phytoplankton growth and enhancing the global primary production by ∼20% (Falkowski et al., 1991; McWilliams, 2008). Usually, eddies occur where there are strong currents and oceanic fronts (Robinson, 1983) and hence are a common feature of western boundary currents (Chelton et al., 2011). The direction and resulting temperature of an eddy circulation can be categorized as either cyclonic cold core or anticyclonic warm-core (Robinson, 1983). The cyclonic eddies (CE) are associated with low sea level anomalies, doming of the isopycnals and shoaling of the nutricline (Falkowski et al., 1991; McGillicuddy, 2015). The shoaling of the nutricline helps supply nutrient-rich waters to the euphotic zone when mixed layer depth (MLD) undergoes seasonal deepening (Dufois et al., 2014; McGillicuddy, 2015) and, thereby stimulating phytoplankton growth (Jenkins, 1988; Falkowski et al., 1991; McGillicuddy and Robinson, 1997). In contrast, anticyclonic eddies (ACE) are associated with high sea level anomalies, depression of the isopycnals and deepening of the nutricline (McGillicuddy, 2015). The MLD of ACEs is generally deeper than CEs (Dufois et al., 2014) and this changes the supply of nutrients to the euphotic zone when the eddy undergoes seasonal deepening of the MLD with additional impacts to light levels (Dufois et al., 2014; McGillicuddy, 2015). While representing different physical and nutrient conditions, the characteristics of CE and ACE can also differ because of differences in how these eddies form. The process called "eddy trapping" (McGillicuddy, 2015) was used to describe how composition of the water trapped in an eddy depends on the process of eddy formation as well as on the local gradients in physical, chemical, and biological properties. One example is the formation of eddies off Western Australian where the Leeuwin Current generates ACE initialized with high Chl-a derived from the coastal water (Moore et al., 2007).

CE and ACE represent two distinct environments because of differences in their physical properties and in the physical processes that form them, which can lead to different phytoplankton abundance, biomass, and composition (Angel and Fasham, 1983; Arístegui et al., 1997; Arístegui and Montero, 2005; Moore et al., 2007; Everett et al., 2012, **Table 1**). In addition, sub-mesoscale processes can affect phytoplankton dynamics in mesoscale eddies (Klein and Lapeyre, 2009); in particular smallscale upwellings and downwellings seem to have a significant impact on phytoplankton subduction and primary production (Levy et al., 2001).

Multiple processes can impact phytoplankton composition and growth in mesoscale eddies. Oceanographic studies show that large photosynthetic eukaryotes (>3 µm, diatoms in particular) appear confined to the center of CE (Rodriguez et al., 2003; Brown et al., 2008). In comparison, higher concentrations of cyanobacteria (<3 µm) are located in the surrounding oligotrophic waters (Olaizola et al., 1993; Rodriguez et al., 2003; Vaillancourt et al., 2003; Brown et al., 2008) and in adjacent ACEs (e.g., Haury, 1984; Huang et al., 2010). However, we still have very limited understanding about the phytoplankton communities TABLE 1 | Schematic representation of main physical and biological differences between CE and ACE off East Australia.


that characterize eddy environments because they remain largely under-sampled.

Phytoplankton are limited by two primary resources in marine environments: light and nutrients (Behrenfeld and Boss, 2014). Eddies represent an interesting resource paradox because, through physical processes, they influence light and nutrient concentrations simultaneously. Indeed, the seasonal deepening of the MLD can bring nutrient-rich water from depth into the euphotic zone but decrease the total photon flux to cells. Due to the differing nutrient requirements of phytoplankton, the water mass below the MLD could therefore play an important role in determining eddy phytoplankton concentration and composition (Bibby and Moore, 2011; Dufois et al., 2016). Furthermore, the shallower MLD that characterizes CE leads to higher light levels in the surface mixed layer, while ACE have lower light levels (Tilburg et al., 2002). Understanding what the primary driver of phytoplankton dynamics in these two environments is an important question, given the uncertainty in regional predictions of primary production under projected ocean change (Bopp et al., 2013).

Floristic shifts in phytoplankton at a regional level will play an important role in determining the marine ecosystem response to future climate change (Boyd and Doney, 2002). Representation of phytoplankton in biogeochemical models ranges in complexity from a single phytoplankton compartment to multi-phytoplankton compartments that can be separated into different functional groups and/or sizes (Fennel and Neumann, 2004). To advance knowledge about the physical-biological interactions in mesoscale features and reduce uncertainty, McGillicuddy (2015) suggests coupling in situ observations, remote sensing, and modeling. Here, we follow such an interdisciplinary approach.

Our study area is eastern Australia (**Figure 1**), a region strongly influenced by the southward flowing Eastern Australian Current (EAC), which forms both CE and ACE (Hamon, 1965; Tranter et al., 1986). EAC waters are low in nutrients and any subsurface nutrients are rarely upwelled to the euphotic zone (Oke and Griffin, 2011). However, increases in phytoplankton biomass occur in this region as a response to occasional upwelling-favorable wind events, the separation of the EAC from the shelf or the formation of CE (Tranter et al., 1986; Cresswell, 1994; Roughan and Middleton, 2002). Both eddy types form from meanders in the EAC and move into adjacent water with different

physical, chemical, and biological characteristics (Lochte and Pfannkuche, 1987).

Here, we characterize phytoplankton dynamics in CE and ACE off East Australia using a combination of in situ observations, remote sensing, and modeling. We firstly explore the level of phytoplankton complexity required to estimate the phytoplankton chlorophyll-a (Chl-a) for eddies in the East Australian system, using a single (WOMBAT) and a multi-phytoplankton class model (EMS). Models were used to simulate the observed Chl-a concentrations obtained from satellites (MERIS, SeaWiFS, and MODIS-Aqua). Shifts in phytoplankton composition and size distribution were also examined using a manipulative ship-board experiment and comparing outcomes with simulations. Results show that CE and ACE off eastern Australia are not only characterized by a different Chl-a concentration but also by different phytoplankton composition. Both models suggest these differences are related to distinct zooplankton dynamics. Furthermore, simulation results are consistent with the ship-based experiment, highlighting the important role of MLD and irradiance in driving eddy phytoplankton dynamics off eastern Australia.

### MATERIALS AND METHODS

### Study Region and Location of Voyage Experiment

The eastern Australian ocean region is significant for Australia's economy and marine ecology (Hobday and Hartmann, 2006). This area is adjacent to capital cities, major shipping lanes and regions of environmental significance (e.g., Great Barrier Reef World Heritage area). Pelagic offshore fisheries, including the valuable Bluefin tuna, are strongly influenced by the EAC, the major western boundary current of the South Pacific subtropical gyre (Mata et al., 2000; Ridgway and Dunn, 2003; Hobday and Hartmann, 2006; Brieva et al., 2015). Furthermore, the ocean circulation of this region has a crucial role in removing heat from the tropics and releasing it to the mid-latitude atmosphere (Roemmich et al., 2005). In this region, climate change is projected to increase eddy activity and hence primary productivity (Matear et al., 2013). Due to its importance, the area selected for this study is located between 30◦ and 40◦ S, and 150◦ and 160◦E (**Figure 1**).

### Description of Biogeochemical Models

To explore the level of complexity required to represent seasonal phytoplankton dynamics associated with mean MLD variations in CE and ACE within the domain, two biogeochemical models were used. The first model, "WOMBAT" (Whole Ocean Model of Biogeochemistry And Trophic-dynamics) is a Nutrient, Phytoplankton, Zooplankton and Detritus (NPZD) model, with one zooplankton and one phytoplankton class (i.e., total Chl-a concentration) characterized by a fixed C:Chl-a ratio (Kidston et al., 2011, **Figure 2A**). WOMBAT has a total of 14 different parameters. The second NPZD biogeochemical model, Environmental Modeling Suite (EMS), is a more complex size-dependent model characterized by a total of 104 parameters (CSIRO Coastal Environmental Modelling Team, 2014). EMS has been developed to model coupled physical, chemical, and biological processes in marine and estuarine environments (CSIRO Coastal Environmental Modelling Team, 2014) and can be implemented in a wide range of configurations. We set it up with two phytoplankton and two zooplankton classes, characterized by different sizes, growth, mortality, and grazing rates (zooplankton only; **Figure 2B**). The two EMS phytoplankton classes can adjust their C:Chl-a ratio daily, to attain the ratio that allows optimal phytoplankton growth (Baird et al., 2013).

Both biogeochemical models are configured as 0D to represent a well-mixed MLD with a prescribed seasonal cycle of nutrient levels below the MLD. Phytoplankton and zooplankton concentrations are uniformly distributed in the MLD. The MLD climatology was the only environmental factor differing between the CE and ACE systems. The time series of temperature in the MLD and nutrients below the MLD from the CSIRO Atlas of Regional Seas dataset (CARS; http://www.marine.csiro. au/~dunn/cars2009/; Ridgway et al., 2002) were used in the simulations, with no distinction between the eddy environments. The surface incident irradiance comes from seasonal climatology of the region (Large and Yeager, 2008). Because other physical phenomena, such as upwelling or downwelling were not explicitly represented, the only supply of nutrients to the MLD occurs with the deepening of the MLD (i.e., when the MLD is shoaling there is no new supply of nutrients to the MLD). In both models, when the MLD is deepening from a time step to the next one, the nutrient concentration (calculated from the nitrate dataset below the MLD obtained from CARS; Ridgway et al., 2002) is added to the MLD. Following Matear (1995) approach the nutrients concentration added in the MLD is calculated as:

$$\mathbf{N}\_{t+1} = \frac{\mathbf{8h} \cdot \mathbf{N}\_{\mathbf{b}} + \mathbf{h} \cdot \mathbf{N}\_{m}}{\mathbf{h} + \mathbf{8h}}$$

where h represents the MLD, δh the difference in the MLD between the time t and t+1, N<sup>b</sup> represent the nutrient

concentration below the MLD, N<sup>m</sup> the nutrient concentration in the MLD.

To evaluate the sensitivity of the model to higher-frequency variations in the MLD, we added Gaussian random noise to the CE and ACE daily MLD dataset, where the standard deviation of the random noise was estimated from the standard error of the CE and ACE MLDs (i.e., ACE 1.3 m; CE 1.2 m).

### Input Data and Implementation to Biogeochemical Models

Because of their different dynamical balances, ACE and CE can be identified through sea surface height anomalies (SSH) detected by satellites (Lee-Lueng et al., 2010). A 17 year, 8-day composite dataset of SSH anomalies (2 September, 1997–26 September, 2014), was downloaded from AVISO (Delayed-Time Reference Mean Sea-Level Anomaly; http://www.aviso.altimetry. fr/en/data/products/sea-surface-height-products.html). Eddies were identified by prescribing ±0.2 m SSH anomaly threshold that characterizes ACE and CE, respectively (Pilo et al., 2015). Satellite-derived Chl-a measurements (25 km spatial resolution, 8-day average) were downloaded from GlobColour (an ocean color product that combines output from MERIS, SeaWIFS, and MODIS; http://hermes.acri.fr/index.php?class=archive). Using this kind of product ensures data continuity, improves spatial and temporal coverage and reduces noise (ACRI-ST GlobColour Team et al., 2015). To obtain MLD measurements, Argo data (temperature, salinity, time, pressure, location for every Argo Float) were downloaded from the GODAE (Global Ocean Data Assimilation Experiment; http://www.usgodae.org/cgi-bin/argo\_select.pl). The MLD value was defined as the depth where temperature changed by 1◦C and density by 0.05 kg m−<sup>3</sup> from the surface value (Brainerd and Gregg, 1995; de Boyer Montegut et al., 2004; Dong et al., 2008). The climatology of surface water (5 m) temperature and nitrate concentration below the MLD was obtained from CARS (**Figure 3**; Ridgway et al., 2002); while we obtained the irradiance from the seasonal climatology of the downward short wave radiation at the surface of the ocean (Large and Yeager, 2008). Before inputting to the models, all data were filtered to exclude locations shallower than 1000 m, to avoid including data from coastal systems.

The Chl-a and MLD datasets obtained from GlobColour and GODAE were mapped in time and space onto the 8-day averaged CE and ACE SSH fields. Thus, we obtained surface Chla concentrations and MLDs for CE and ACE off East Australia occurring from 1 December 2002 to 1 December 2014 in an 8 day averaged dataset (Argo data are not available before 2002 in our domain). Chl-a concentration and MLD were averaged over time periods (n = 546) at their original resolution, obtaining a Chl-a and a MLD 8-day averaged seasonal climatology for an idealized CE an ACE of the selected East Australia region (**Figure 4**). The datasets extracted from CARS (nitrogen, temperature, and light) were used in the two biogeochemical models without any distinction between CE and ACE, as the available data from CARS are an average of the whole area of study.

### Statistical Analysis and Goodness of the Fit

The student t-test was performed to assess statistical differences between the CE and ACE Chl-a climatologies, calculated from the GlobColour dataset. The same approach was applied to the MLD climatology derived from the GODAE Argo dataset. The same test was used to asses if there were statistical differences between the average of the observed and modeled data (i.e., GlobColour Chl-a climatology vs. simulated Chl-a), with significance for all tests defined as p < 0.05.

and Yeager, 2008).

The goodness of the fit between simulated and observed seasonal climatology of Chl-a was assessed through the Chisquared misfit (χ 2 ):

$$\chi^2 = \frac{1}{\nu} \sum\_{t=1}^{T} \frac{\left(Q\_m^t - Q\_o^t\right)^2}{\sigma^t}$$

of the Chl-a climatology. The degrees of freedom are represented by ν:

$$\nu = n\_o - n\_{\mathcal{P}}$$

where Q t <sup>m</sup> is the value of the modeled data at time t and Q t o is the observed value of Chl-a at time t, while σ t is the variance at time t where n<sup>o</sup> is the number of observations, and n<sup>p</sup> is the number of fitted parameters. A χ 2 value of ∼1 represents an acceptable model fit to the observations.

### Data Assimilation

The observed CE and ACE Chl-a seasonal climatologies were used for the data assimilation, with the purpose of finding parameter sets that best fitted the observations from the two environments (e.g., Matear, 1995). The observed Chl-a climatology was assumed to represent the Chl-a concentration in the MLD (i.e., Chl-a uniformly distributed in the MLD). Although this assumption is commonly made, caution needs to be used when interpreting results because a chlorophyll maximum below the surface mixed layer may be not be detected by satellites (e.g., Sallée et al., 2015). To quantify the difference between the simulated and observed Chl-a concentrations we used a cost function (x) defined as:

$$\kappa = \sum\_{t=1}^{T} \frac{\left(\ln \mathbf{Q}\_{\mathbf{m}}^{t} - \ln \mathbf{Q}\_{\mathbf{o}}^{t}\right)^{2}}{n}$$

where Q<sup>t</sup> <sup>m</sup> is the value of the modeled data (total Chl-a concentration) at time t, Q<sup>t</sup> o is the observed value of Chl-a at time t and n is the number of samples over time. The "ln" transformation was applied to achieve normal distribution of the Chl-a concentrations around the mean seasonal value, thus allowing us to employ statistical parametric methods.

To estimate the optimized parameter set for WOMBAT, we used a simulated annealing algorithm based on the likelihood cost metric (x). This approach has been previously used in marine ecosystem models and can solve optimization problems with a small number of unknown parameters (e.g., Matear, 1995; Kidston et al., 2013). The simulated annealing algorithm was run for 200 iterations to allow the algorithm to converge to the minimum cost function value. The data assimilation was performed with WOMBAT, fitting CE and ACE seasonal climatology independently by allowing eight parameters that controlled plankton growth to vary (**Table 3**). Data assimilation was also used to fit both the environments with one parameter set to determine if the one-phytoplankton class model was sufficiently complex to represent both eddy types.

The data assimilation was then performed with EMS, fitting the CE and ACE Chl-a seasonal climatology independently and fitting both the environments with one parameter set. Because the simulated annealing algorithm computational requirements are large and EMS is a much more complex model than WOMBAT, we estimated EMS parameters with the conjugategradient algorithm because it was more computationally efficient. Although this algorithm is sensitive to the choice of the initial model parameters, it is used to solve optimization problems with



*Results at significance values are highlighted: N.S, indicates not significant (p* > *0.05);* \**indicates p* < *0.05;* \*\**p* < *0.01; and* \*\*\**p* < *0.001.* χ 2 *indicates the Chi-squared misfit value: the closer* χ 2 *is to 1, the more accurate the simulation. In this table, "p" and "* χ 2 *intervals represent the minimum and the maximum value obtained from acceptable solutions. Simulations were considered acceptable when both p* > *0.05 and* χ <sup>2</sup> > *2.5.*

marine biogeochemical models as well (e.g., Fasham et al., 1995; Evans, 1999). Advantages and disadvantages of using simulated annealing or conjugate-gradient algorithms are discussed in Matear (1995). The phytoplankton size classes in EMS were fixed, with the purpose of representing two distinct phytoplankton types to examine if their abundance was different between CE and ACE: 2 µm diameter for small phytoplankton cells and 40 µm diameter for large phytoplankton cells. With EMS, the data assimilation was allowed to vary 12 parameters—like WOMBAT, they were the parameters controlling plankton growth (**Table 4**).

To recognize that there was not one unique solution, rather a range of parameter values could produce acceptable solutions, we show a range of simulated behavior to reflect the non-uniqueness of the solution. From data assimilation results, only acceptable solutions are shown, which were simulations where both 0 < χ <sup>2</sup> < 2.5 and there was no significant difference between the annual mean simulated and observed Chl-a concentration (with 95% confidence in the equivalence test; Wellek, 2010).

### Shipboard Manipulation Experiment

To investigate the potential shift in phytoplankton size and abundance in a CE we examined phytoplankton responses to increased light and nutrients by performing an experiment during an oceanographic research voyage. The experiment was carried out on board the RV Investigator (voyage IN2015\_V03), with water sampled from a station located in the EAC (32.7◦ S and 153.6◦E), inside the modeling domain (**Figure 1**). This site was representative of potential source water for eddies, allowing us to evaluate the effect of light and nutrients on the phytoplankton community prior to the seasonal shoaling of the MLD. Water was sampled a few meters below the MLD (∼110 m, water temperature ∼20.9◦C) and exposed to increased light and nutrients. Sampled seawater was transferred directly from the CTD-rosette into 15 acid-cleaned 4 L polycarbonate vessels. Vessels were sealed, randomly assigned to three light treatments, with half the bottles being amended with inorganic nutrients and the other half remaining unamended, before they were all placed in a deck-board incubator which had continuous flow of surface seawater of ∼21.5◦C. The nutrient enrichment consisted of daily nutrient addition of dissolved inorganic Fe III 0.005 µmol L−<sup>1</sup> , N as nitrate 1.2 µmol L−<sup>1</sup> , Si as silicate 1.2 µmol L−<sup>1</sup> , P as phosphate 0.075 µmol L−<sup>1</sup> , in Redfield proportion (McAndrew et al., 2007; Ellwood et al., 2013). The experimental treatments included control (CON; ambient light i.e., ∼1% incident light, no nutrient amendment), low light (LL; 20% incident light), high light (HL; 40% incident light), low light and nutrients (LL+N), high light and nutrients (HL+N), and were made in triplicate. Incident light was attenuated using shade cloth. Pigment samples for Ultra-High Performance Liquid Chromatography (UPLC) analysis were collected from each bottle at the end of the 5-day experiment, as well as the initial phytoplankton community.

Samples for UPLC analysis were filtered through 25 mm glass fiber filters (Whatman GF/F), filters were placed in cryotubes, flash frozen in liquid nitrogen, and stored in a −80◦C freezer. The pigment extraction was carried out following a modified method used by Van Heukelem and Thomas (2001). Each filter was placed into an individual 15 mL falcon tube with 1.5 mL of chilled 90% acetone. Each filter was then disrupted using a 40 W ultrasonic probe for ∼30 s, keeping the tube in ice; then the samples were stored at 4◦C overnight. The sample slurry was vortexed for 10 s and clarified by passing through a 0.2 µm PTFE 13 mm syringe filter before storage in UPLC glass vials, followed by analysis. The dataset obtained from the UPLC analyses was analyzed following Barlow et al. (2004) formulae and Thompson et al. (2011) for the pigment quality control.

### RESULTS

### Characterization of CE and ACE

The physical environment of the CE and ACE show important differences in their seasonal climatologies. For ACE, the MLD is deeper than CE throughout the seasonal cycle (**Figure 4A**; n = 365, p<0.01, **Table 2**). Conversely, the surface Chl-a concentrations are higher in CE than ACE for most of the year (**Figure 4B**, n = 365, p < 0.001, **Table 2**). Both Chl-a and MLD show the greatest differences between CE and ACE in the May and October period (austral winter/spring); while for the rest of the year (November to April) Chl-a concentrations and MLD are similar (**Figure 4**).

### WOMBAT and EMS Simulations

Data assimilation to independently determine WOMBAT parameter sets for the CE and ACE environments produced acceptable simulations of the Chl-a seasonal climatology



#### TABLE 4 | EMS parameter set for CE and ACE.


*EMS contains a total of 104 different parameters, in this table are shown only the parameters that were allowed to vary during the data assimilation analyses (except large and small phytoplankton cells diameter, remineralization rate, and sinking velocity).*

(**Figures 5A,B**). Acceptable simulations are demonstrated by the χ 2 values and the non-significant t-student test (ACE p > 0.12; CE p > 0.22, 95% confidence that the two dataset are equivalent), confirming that there are no significant differences between the average of the modeled and observed data (**Table 2**).

The data assimilation carried out with the single phytoplankton model WOMBAT for the two eddy environments yielded distinct parameter sets (**Table 3**). For acceptable solutions, the main difference between the parameter sets relate to zooplankton (quadratic) mortality, where CE shows ∼130% greater values than ACE (**Table 3**). From the acceptable solutions, we show the primary production and zooplankton concentrations for the two types of eddies (**Figures 5C–F**). When the data assimilation tries to fit both the environments with a single parameter set there is a significant probability (ACE p = 0.003; CE p = 0.005, **Table 2**) the annual mean Chl-a differs between the observed and simulated value.

The data assimilation carried out with EMS for the two environments leads to acceptable simulation of Chl-a (**Table 2**), with the simulated annual mean Chl-a consistent with the observed value (ACE p > 0.13; CE p > 0.24, 95% confidence that the two dataset are equivalent; **Figure 6**, **Table 2**). However, no acceptable solutions were found fitting both the environments with one parameter set (**Table 2**). The data assimilation with EMS produced distinct parameter sets for the CE and ACE environments, with main differences

related to the large zooplankton parameters: large zooplankton quadratic mortality rate is ∼1.8 times greater in CE and large zooplankton maximum growth rate is ∼2.1 times greater in CE (**Table 4**). For the acceptable EMS solutions we show the primary production for large and small phytoplankton and the seasonal evolution of the small and large zooplankton concentrations (**Figures 6C–H**). The development of the winter/spring (May– October) phytoplankton bloom is driven by increased production of large phytoplankton, that is considerably greater in the CEs than the ACEs.

Simulations carried out to evaluate higher-frequency variations in the MLD (i.e., with the inclusion of random noise), produce plankton dynamics within the range of the acceptable solutions (**Figures 5**, **6**).

### Shipboard Manipulation Experiment

The initial phytoplankton community sampled below the EAC MLD, at ∼110 m in June was composed mainly of picophytoplankton (<2 µm) and nanophytoplankton (2-20 µm) while the microphytoplankton (>20 µm) was the least abundant phytoplankton size class (**Figure 7A**). Prochlorococcus (as indicated by the concentration of divinyl chlorophylla) and haptophytes (hex-fucoxanthin) were the dominant phytoplankton classes in the initial community (**Figure 7B**). At the end of the shipboard experiment, the phytoplankton composition (as determined by pigment analyses) was similar in all treatments (**Figure 7**). By the end of the experiment, there was a large change in the phytoplankton community, highlighting a shift from nano and picophytoplankton to the larger microphytoplankton (**Figure 7A**) and from Prochlorococcus and haptophytes to diatoms (**Figure 7B**). The pigment concentrations in the control vessels at the end of the experiment were below detection (>0.004 µg L−<sup>1</sup> ), and are hence shown as zero in **Figure 7**.

### DISCUSSION

### The Role of Mixed Layer Depth and Light on Phytoplankton

Statistical analysis of the MLD and Chl-a seasonal climatologies clearly shows that CE and ACE off eastern Australia are two distinct environments (**Figure 4**, **Table 2**). Similarities in

FIGURE 6 | EMS acceptable solutions from the data assimilation. Left column shows ACE seasonality and right column CE seasonality. The red solid lines in plots (A,B) show the Chl-a observed seasonal climatology with the red shading denoting the standard deviation variability. Patterns of the two EMS phytoplankton classes (Chl-a) are represented in plot (C; ACE) and (D; CE), where red areas represent the large phytoplankton class (40 µm diameter) and blue areas represent the small phytoplankton class (2 µm diameter). Plots (E; ACE) and (F; CE) represent the total primary production (g C m−<sup>2</sup> ) in black and the primary production for small (blue) and large phytoplankton (red). The total zooplankton biomass (g C m−<sup>2</sup> ) is represented in black on plots (G; ACE) and (H; CE), while the small and large zooplankton biomass is represented in blue and red, respectively.

the MLD and Chl-a seasonal climatology dynamics (**Figure 4**) suggest the MLD could be a key environmental driver of differences in Chl-a between these two environments. The importance of MLD deepening to Chl-a seasonality in subtropical water is consistent with a recent study of Chl-a variability in eddies of the Indian Ocean (Dufois et al., 2016).

In both the single and multiple box phytoplankton models, the MLD seasonal climatology was enough to drive the phytoplankton dynamics and reflect the observed differences between the CE and ACE environments (**Figures 5A,B**, **6A,B**). Although our simulations did not take physical dynamics (i.e., sub-mesoscale events) directly into account, these processes are indirectly accounted for by the implementation of observed CE and ACE MLD.

WOMBAT and EMS simulations confirm that MLD dynamics play an important role in driving the Chl-a concentration in both eddy types. The evolution of the MLD leads to a change in both the nutrient concentration and the light available for photosynthesis, which in turn influences the phytoplankton abundance and community composition (Officier

and Ryther, 1980; Pitcher et al., 1991; Tilburg et al., 2002). The differences in Chl-a and MLD between CE and ACE are greatest in the austral winter/spring when surface light irradiance are near their seasonal minimum (**Figure 3B**). During the winter/spring period the MLD is deep and it has been shown to cause strong light limitation of phytoplankton growth (Behrenfeld and Boss, 2014). McGillicuddy (2015) hypothesized that in such a light-limited regime, the shallower MLD of the CE than ACE could lead to higher Chl-a concentration in CE.

The shipboard manipulation experiment clarifies the effect of light and nutrients on the phytoplankton community sampled in the same area as our modeling study. The water collected in austral winter from below the MLD (110 m) originally contained a low abundance of phytoplankton (total Chl-a concentration 0.068 ± 0.003 µg L−<sup>1</sup> , mean ± standard deviation). After being exposed to 1% surface light (ambient irradiance at the sampling depth) for 6 days, phytoplankton were undetectable (<0.004 µg Chl-a L−<sup>1</sup> ), confirming they did not have enough light to remain viable. The same phytoplankton community exposed to 20 and 40% surface irradiance resulted in growth and showed a similar shift in community structure whether nutrients were added or not (**Figure 7A**). The shipboard experiment reveals that, in this region, during winter while the MLD is still deepening (**Figure 4A**), the phytoplankton growth is limited by light rather than by nutrients.

## Phytoplankton Composition and Size Structure

During the shipboard experiment with elevated light, the phytoplankton community shifted from picophytoplankton (<2 µm; ∼49% of the initial community) and nanophytoplankton (2– 20 µm; ∼35% of the initial community) to microphytoplankton (>20 µm; ∼90% of the final community; **Figure 7A**). The microphytoplankton appear most light-limited because they are initially in lowest abundance and then dominate the community when exposed to elevated light. The microphytoplankton are almost totally composed of fucoxanthin-containing cells, most likely reflecting diatoms (**Figure 7B**).

Data assimilation with WOMBAT and EMS showed that both models could represent the seasonal evolution of Chla in the two types of eddies if the two environments had different parameter values (**Table 2**). The physical and chemical environment that characterizes the CE in oligotrophic oceans, generally drives the accumulation of large phytoplankton species such as diatoms, while small phytoplankton species and cyanobacteria are more characteristic of the surrounding waters and ACE (Jeffrey and Hallegraeff, 1980; Olaizola et al., 1993; Rodriguez et al., 2003; Vaillancourt et al., 2003; Brown et al., 2008). EMS simulations are consistent with such behavior where different phytoplankton dominate CE and ACE (**Figure 6**). In particular, EMS simulations show the differences between CE and ACE Chl-a concentrations are attributed to the large phytoplankton class, while the small phytoplankton class has similar dynamics in both the systems (**Figures 6C,D**). The greatest difference in the EMS simulated large phytoplankton occurs between May and October when observed Chl-a shows the greatest differences between the ACE and CE Chl-a (**Figure 6**).

Trying to get WOMBAT to use one parameter set to represent both CE and ACE failed to satisfactorily represent Chla observations (**Table 2**). WOMBAT's failure to represent the two environments with a unique parameter set may be expected for a model that does not resolve different plankton sizes. However, the parameter values from fitting the two environments separately are very similar. Furthermore, EMS with its two sizes of phytoplankton shows a similar pattern to WOMBAT, where model simulations are unable to produce an acceptable Chl-a simulation using one parameter set to represent both ACE and CE. This suggests that it is more than phytoplankton size that is driving differences between Chl-a in CEs and ACEs.

### Zooplankton

For both WOMBAT and EMS, the optimized parameter sets suggest that the zooplankton in CE have twice the mortality rate and nearly double the growth rate compared to the ACE (**Tables 3**, **4**). Hence, in both models, the phytoplankton grow better in CE than in ACE, because of the higher mortality of their grazers which reduces top-down grazing pressure. Bakun (2006) suggests that an enhanced primary production (typical of CEs) improves zooplankton growth but comes at a cost of increased zooplankton predator abundance; this concept is consistent with the higher zooplankton mortality and growth rate obtained from the parameter optimization in the CE system (**Tables 3**, **4**). Another possible explanation is that two distinct zooplankton communities characterize CE and ACE, with higher grazing pressure in CE environments. Such behavior is consistent with the water in CEs from this region tending to have more coastal organisms than ACEs (Macdonald et al., 2016). However, the interpretation of the difference in zooplankton behavior requires some caution because it may be related to eddy dynamics not directly considered in our simulations (i.e., sub-mesoscale interactions). While the differences in zooplankton properties between CE and ACE is a robust feature of the model simulations, additional observations are needed to confirm this result, and determine the mechanism responsible.

### CONCLUSION

Biogeochemical models are increasingly considering phytoplankton composition to characterize elemental cycles in the contemporary and future ocean (Finkel et al., 2009; Follows and Dutkiewicz, 2011). This study shows that inclusion of multiple phytoplankton groups provides useful, and potentially unexpected, insights about ecosystem dynamics, demonstrating divergent accumulation of biomass in different phytoplankton and zooplankton size classes in CE and ACE.

To put the impact and relevance of these mesoscale features in eastern Australian waters into perspective, an average of 13 CE and 15 ACE with a lifetime ≥10 weeks occur annually in the study region (obtained from Chelton et al., 2011 eddy database, yearly average from 1 December 2002 to 4 April 2012). Given that the primary productivity in East Australia is projected to increase 10% by the 2060s due to an increase in eddy activity (Matear et al., 2013), it is therefore critical to quantify plankton concentration, composition, and functioning within eddies and adjacent water masses to advance our understanding of their ecological and trophic roles and impacts to regional fisheries and biogeochemical cycling.

### AUTHOR CONTRIBUTIONS

LL, AM, RM, and MD conceived and designed the experiment. LL and RM acquired the data, performed the modeling work, and analyse the data. LL, AM, and MD performed the ship-based experiment. LL drafted the work, prepared figures, and tables; all authors critically revised the work.

### FUNDING

This research was supported by the Australian Research Council Discovery Projects funding scheme (DP140101340), the Marine National Facility, and the School of Life Science, University of Technology Sydney (postgraduate scholarship to LL), and the Climate Change Cluster research institute (operational support).

### ACKNOWLEDGMENTS

We would like to acknowledge the valuable reviews provided by the two reviewers, which has helped improve the clarity and focus of the manuscript. LL would like to thank Mark Baird, Farhan Rizwi, and Mathieu Mongin (CSIRO) for their useful suggestions and explanations about the Environmental Modeling Suite (EMS), Olivier Laczka (UTS) for his assistance with setting up the experiment aboard the RV Investigator and Gabriela Semolini Pilo (UTAS) for the useful conversations about eddy dynamics. This research was supported by the Australian Research Council Discovery Projects funding scheme (DP140101340 awarded to MD and RM), the Marine National Facility, and the School of Life Science, University of Technology Sydney (postgraduate scholarship to LL) and the Climate Change Cluster research institute (operational support). The authors would like to acknowledge the captain and crew of the IN2015\_V03 voyage, as well as the chief scientist, Prof. Iain Suthers. Furthermore, we would like to thank GlobColour, AVISO and the International Argo Program for the production and distribution of the dataset used in this study.

## REFERENCES


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Laiolo, McInnes, Matear and Doblin. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Modeling Larval Connectivity of Coral Reef Organisms in the Kenya-Tanzania Region

#### C. Gabriela Mayorga-Adame1, 2 \*, Harold P. Batchelder 1, 3 and Yvette. H. Spitz <sup>1</sup>

*<sup>1</sup> College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis, OR, USA, <sup>2</sup> National Oceanography Centre, Liverpool, UK, <sup>3</sup> North Pacific Marine Science Organization, Sidney, BC, Canada*

Most coral reef organisms have a bipartite life-cycle; they are site attached to reefs as adults but have pelagic larval stages that allow them to disperse to other reefs. Connectivity among coral reef patches is critical to the survival of local populations of reef organisms, and requires movement across gaps that are not suitable habitat for recruitment. Knowledge of population connectivity among individual reef habitats within a broader geographic region of coral reefs has been identified as key to developing efficient spatial management strategies to protect marine ecosystems. The study of larval connectivity of marine organisms is a complex multidisciplinary challenge that is difficult to address by direct observation alone. An approach that couples ocean circulation models with individual based models (IBMs) of larvae with different degrees of life-history complexity has been previously used to assess connectivity patterns in several coral reef regions [e.g., the Great Barrier Reef (GBR) and the Caribbean]. We applied the IBM particle tracking approach to the Kenya-Tanzania region, which exhibits strong seasonality in the alongshore currents due to the influence of the monsoon. A 3-dimensional (3D) ocean circulation model with 2 km horizontal resolution was coupled to IBMs that track virtual larvae released from each of 661 reef habitats, associated with 15 distinct regions. Given that reefs provide homes to numerous species, each with distinctive, and in aggregate very diverse life-histories, several life-history scenarios were modeled to examine the variety of dispersal and connectivity patterns possible. We characterize virtual larvae of *Acropora* corals and *Acanthurus* surgeonfish, two coral reef inhabitants with greatly differing pelagic life-histories, to examine the effects of short (<12 days) and long (>50 days) pelagic larval durations (PLD), differences in swimming abilities (implemented as reef perception distances), and active depth keeping in reef connectivity. *Acropora* virtual larvae were modeled as 3D passive particles with a precompetency period of 4 days, a total PLD of 12 days and a perception distance of 10 m. *Acanthurus* virtual larvae were characterized by 50 days precompetency period, a total PLD of 72 days and a perception distance of 4 km. *Acanthurus* virtual larvae were modeled in two ways—as 3D passive particles and including an idealized ontogenetic vertical migration behavior. A range of distances within which larvae were able to perceive reefs and directionally swim to settle on them during the competency period were evaluated. The influence of interannual environmental variations was assessed for 2 years (2000, 2005) of contrasting physics. The spatial scale of connectivity is much smaller for the short

#### Edited by:

*Christian Lindemann, University of Bergen, Norway*

#### Reviewed by:

*Louis Worth Botsford, University of California, Davis, USA Anne Chenuil, Centre National de la Recherche Scientifique (CNRS), France Guillem Chust, AZTI-Tecnalia, Spain*

> \*Correspondence: *C. Gabriela Mayorga-Adame gmaya@noc.ac.uk*

#### Specialty section:

*This article was submitted to Marine Ecosystem Ecology, a section of the journal Frontiers in Marine Science*

Received: *05 August 2016* Accepted: *15 March 2017* Published: *13 April 2017*

#### Citation:

*Mayorga-Adame CG, Batchelder HP and Spitz YH (2017) Modeling Larval Connectivity of Coral Reef Organisms in the Kenya-Tanzania Region. Front. Mar. Sci. 4:92. doi: 10.3389/fmars.2017.00092* PLD coral, with successful connections restricted to a 1◦ radius (∼100 km) around source reefs. In contrast, long distance connections from the southern to the northernmost reefs (∼950 km) are common for virtual *Acanthurids.* Successful settlement for virtual *Acropora* larvae was <0.3%, and within region settlement (local retention) was 0.38%, substantially greater than inter-region settlement (ca. 0.2%). Settlement of *Acanthurus* virtual larvae was >20% overall, with cross-region recruitment much increased compared to the coral larvae. Approximately 8% of *Acropora* larvae that successfully settled, recruited to their source reef (self-recruitment), an important proportion compared to only 1–2% selfrecruitment for *Acanthurus.* These rates and dispersal distances are similar to previous modeling studies of similar species in other coral reef regions and agree well with the few observational studies within the Kenya-Tanzania region.

Keywords: larval connectivity, coral reefs, Western Indian Ocean, individual based modeling, particle tracking, ocean modeling

### INTRODUCTION

Tropical coral reef ecosystems are very important from both the ecological and economical points of view (Spalding et al., 2001). However, they are also particularly fragile, and have been declining in recent years in most regions of the world (Hughes et al., 2003; Pandolfi et al., 2003; Melbourne-Thomas et al., 2011), since they are highly susceptible to anthropogenic stressors operating at global scales (e.g., global warming and ocean acidification) and local scales (e.g., pollution/eutrophication, fishing, over-commercialization for recreation). Coral reef ecosystems are complex communities with very high species diversity. Most reef species have bipartite life histories with a planktonic larval stage and a benthos associated adult life. As adults, coral reef organisms exhibit various degrees of site attachment ranging from completely sessile, like corals and sponges, to highly mobile, like fish and crustaceans. Generally, even fish capable of swimming several kilometers in a few hours have restricted home ranges, since they are relatively territorial and are associated with specific reef habitats that are patchily distributed (Sale, 2006). Most adult reef organisms are distributed in metapopulations connected by pelagic larvae that disperse subject to the ocean currents (Bode et al., 2006; Cowen and Sponaugle, 2009).

Coral reefs extend along the coast of East Africa from the equator to ∼14◦ S, being absent only at major river outflows or Pleistocene river valleys. Fringing reefs are the most common type, but complex formations occur around islands and other regions where the continental shelf extends more than a few kilometers from shore. Reefs are absent on the Somali coast north of the equator due to seasonal upwelling of cold water associated with the monsoon winds. The southernmost reef is found in Mozambique at 26◦ S; but scattered colonies of scleractinian corals occur as far south as 34◦ S, in South Africa (Day, 1974 cited in Hamilton and Brakel, 1984). Western Indian Ocean coral reef communities are characterized by high levels of species diversity and may be centers of biodiversity (Spalding et al., 2001). Coastal communities of Kenya and Tanzania depend on the reef for food. Since there is little regulation on the use of these resources through formal resource management strategies, reef areas in Kenya and Tanzania have been degraded due to overfishing, destructive fishing techniques, coastal pollution and other activities affecting the coastal environment (Hamilton and Brakel, 1984; Spalding et al., 2001). Increasing interest in coral reef tourism is simultaneously leading to increased pressure on some coral reefs while providing a powerful local incentive for conservation (Spalding et al., 2001). There are 26 Marine Protected Areas (MPAs) in Kenya and Tanzania reported in the Protected Planet Database (http://www.protectedplanet.net/; accessed July 2016) that encompass coral reef habitat; some of these were established as recently as 2010. Eight of the 26 MPAs are no-take areas, while 18 of them allow extraction using traditional fishing methods like handlines and traps (Muthiga et al., 2008). The benefits of MPAs for biodiversity conservation and fisheries management are well known (McClanahan and Mangi, 2000; Gell and Roberts, 2003; Roberts et al., 2005; Lester et al., 2009; Micheli et al., 2012); however, the design (spacing, size and separation distance) of effective MPA networks is not trivial (e.g., Botsford et al., 2003; McLeod et al., 2009; Edgar et al., 2014). Many studies (e.g., Botsford et al., 2009; McCook et al., 2009; Hogan et al., 2011; Rossi et al., 2014) emphasize the importance of larval connectivity on the performance of MPA spatial management for meeting conservation and fisheries yield objectives.

Larval connectivity is vital to the survival of marine metapopulations, both at ecological and evolutionary time scales (James et al., 2002; Cowen and Sponaugle, 2009; Burgess et al., 2014). Population connectivity plays a fundamental role in local and metapopulation dynamics, community dynamics and structure, genetic diversity, ecosystem responses to environmental changes, and the resiliency of populations to human exploitation (Cowen et al., 2007). Connectivity among marine metapopulations is controlled by physical transport and dispersion, temperature, and biological processes such as the timing of spawning, pelagic larval duration (PLD), larval behavior, and mortality. The net combined effect of these processes determines the spatial scales over which a population is connected (Gawarkiewicz et al., 2007). Connectivity is therefore a function of several interacting variables including species, geographical area, and ocean conditions, and is highly variable in both time and space (e.g., Cowen and Sponaugle, 2009; Christie et al., 2010b; Domingues et al., 2012). Often, little is known about the connections among different coral reef regions (Cowen et al., 2000; Mora and Sale, 2002; Sponaugle et al., 2002) and the degree to which local populations are open (dependent on recruits from external sources) (e.g., Saenz-Agudelo et al., 2011) or closed (self-replenishing) (e.g., Schultz and Cowen, 1994).

Observational approaches for studying connectivity use genetic techniques (Baums et al., 2005; Jones et al., 2005; Christie et al., 2010a,b; Hogan et al., 2011; Harrison et al., 2012), spatially varying natural bio-markers leaving a geochemical signature in calcified structures (i.e., otoliths and statoliths) (Thorrold et al., 1998, 2007) or tagging otoliths of larvae (Jones et al., 1999; Almany et al., 2007). These techniques are limited in the spatiotemporal scales they can resolve and some of them are restricted to specific species or environments (Gawarkiewicz et al., 2007; Hedgecock et al., 2007; Thorrold et al., 2007). Challenges of applying observational techniques to larval connectivity in the Kenya-Tanzania (KT) region are that these methods are expensive, time-consuming and require highly specialized equipment and expertise (Thorrold et al., 2007). Individual based Lagrangian particle tracking models (IBM) coupled to realistic ocean circulation models are a less limiting method to study potential connectivity among East-African coral reefs. So long as the ocean circulation model reasonably depicts the timevarying flows, IBMs can resolve time varying 3-dimensional (3D) potential dispersion of planktonic larvae over large spatial scales with high spatio-temporal resolution (Werner et al., 2007). Results of numerical simulations can only provide estimates of potential connectivity, that need to be validated with empirical measurements (i.e., Foster et al., 2012; Soria et al., 2012) and scaled by observed reproductive input (Watson et al., 2010) and settlement (i.e., Sponaugle et al., 2012). Even in the absence of empirical confirmations, estimates of potential connectivity from modeling studies provide a comprehensive understanding of the spatial-temporal dynamics of marine populations, that inform the design of more efficient MPAs (Willis et al., 2003; Sale et al., 2005). With the exception of a few studies (McClanahan, 1994; McClanahan et al., 1994; Mangubhai, 2008; Yahya et al., 2011; Kruse et al., 2016), knowledge of reef biota ecology is lacking for much of the Western Indian Ocean region, due to the lack of infrastructure and local expertise, combined with problems of national security in some areas (Spalding et al., 2001). Few studies have examined larval supply and connectivity in coral reefs in the Western Indian Ocean (Kaunda-Arara et al., 2009; Crochelet et al., 2013, 2016). Genetic techniques have been used to study connectivity at evolutionary time scales of several reef fish (Dorenbosch et al., 2006, Lutjanus fulviamma; Visram et al., 2010, Scarus ghobban; and Muths et al., 2012, Lutjanus kasmira). High gene flow and weak genetic structure were found in these fish, even among sites as distant as 4000 km (Muths et al., 2012). Recently, van der Ven et al. (2016) used genetic techniques to examine connectivity at evolutionary time scales of the branching coral Acropora tenuis in the Kenya-Tanzania region. They report high but variable connectivity among sample sites spanning 900 km along the coast. These studies do not address ecologically significant timescales of a few generations, and are in general concerned with large spatial scales (∼1000 s of km), therefore they cannot provide insights on population demography at temporal and spatial scales relevant to the implementation of management and conservation strategies at national and regional levels. Only Souter et al. (2009) used genetic techniques to examine both evolutionary and ecological connectivity of the coral Pocillopora damicornis in the MPAs of the KT region. They identified the Mnemba Conservation area northeast of Zanzibar Island as a potential source for the P. damicornis population, and Malindi Marine National Park and Reserve in north Kenya as a genetically isolated reef.

For decades the spatial connectivity of larval fish and invertebrates was thought to be a passive process governed primarily by the ocean physics and the duration of the larval period (e.g., Shanks, 2009). The PLD of coral reef organisms varies greatly; from a few hours for some coral species to a few months for some fish and crustaceans (Shanks, 2009). Recent studies (i.e., Leis and Carson-Ewart, 2003; Paris and Cowen, 2004; Shanks, 2009; Pineda et al., 2010) have shown that larval transport of most marine organisms is not strictly passive and that there is an uncoupling between dispersal distance and PLD due to larval behavior, such as active depth selection and directional swimming. Discrepancies between the passive transport hypothesis and observed patterns of recruitment point to the importance of biological factors (i.e., behavior, predation, starvation, etc.) in the control of larval dispersal and connectivity (Paris and Cowen, 2004; Cowen et al., 2006; Leis et al., 2007; Cowen and Sponaugle, 2009; Sponaugle et al., 2012). Even excluding mortality, the degree to which biological factors influence connectivity is greater than originally hypothesized (Shanks, 2009). Recent studies have shown the importance of physiological and behavioral characteristics of larvae on influencing the connectivity and dispersal of species with a planktonic larval stage (i.e., Kingsford et al., 2002). Growth rates (e.g., Bergenius et al., 2002), ontogenetic and diel vertical migrations (Paris et al., 2007; Drake et al., 2013), swimming ability (e.g., Stobutzki and Bellwood, 1997; Wolanski et al., 1997; Leis and Carson-Ewart, 2003; Leis et al., 2007), orientation through olfaction (Atema et al., 2002, 2015; Gerlach et al., 2007; Paris et al., 2013) and audition (Tolimieri et al., 2000; Leis et al., 2003; Simpson et al., 2005; Heenan et al., 2009; Vermeij et al., 2010), and settlement strategies (Leis and Carson-Ewart, 1999; Lecchini, 2005) are important in controlling connectivity of coral reef organisms. Observational studies suggest that marked ontogenetic vertical zonation is important for larval transport (Boehlert and Mundy, 1993; Cowen and Castro, 1994). In modeling studies, vertical migration often promotes local retention and recruitment of pelagic larvae to suitable habitat. A modeling study of the California Current System (CCS) by Drake et al. (2013) showed that larvae that remained below the surface boundary layer were 500 times more likely to be retained within 5 km of the coast after 30 days than larvae that remained near the surface. Settlement in the CCS increased by an order of magnitude when larvae remained at 30 m depth. Similarly,

settlement success in different regions of the Caribbean increased when a shallow ontogenetic vertical migration (OVM) behavior was added to the virtual larvae (Paris et al., 2007). Potential settlement estimates increased up to 190% in the southern Florida Keys with the OVM (Paris et al., 2007). The influence of larval physiology and behavior on connectivity and dispersal of coral reef species is now well established (Kingsford et al., 2002; Paris et al., 2007; Wolanski and Kingsford, 2014). However, biological characteristics are known with certainty only for a handful of species.

The hydrodynamics of the KT coastal ocean is highly variable at seasonal and subseasonal time scales, due to the influence of the monsoons and complex tidal interactions. The coastal circulation is mainly influenced by: (1) the northward flowing East African Coastal Current (EACC) fed by (2) the regionally westward flowing North East Madagascar Current (NEMC), (3) the seasonally reversing Somali Current (SC), (4) tides and (5) local winds (see Figure 1 of Mayorga-Adame et al., 2016). SW monsoon conditions are characterized by strong continuous northward flow along the coast and relatively cool (∼24◦C) sea surface temperatures (SST) that prevail from May to October. During the NE monsoon, from January to March, a strong north-south SST gradient is caused by the intrusion of the shallow, southward flowing, cold and salty Somali Current that meets the slow northward flowing, warm and fresh EACC. The convergence of the two currents forms the eastward flowing South Equatorial Counter Current. The inter-monsoon seasons, in between these two periods, are characterized by strong mixing and slow currents.

The relative lack of physiological and behavioral data for larvae of coral reef species in the Kenya-Tanzania region led us to examine connectivity among coral reefs using idealized particle tracking experiments that simulate larvae with characteristics of two ubiquitous and ecologically important species groups: the Acropora branching corals with short PLD (ca. 12 days; Babcock and Heyward, 1986; Nishikawa et al., 2003; Nozawa and Harrison, 2008) and the Acanthurus surgeon fish with long PLD (72 days; Rocha et al., 2002) (See Mayorga-Adame, 2015 for a review of the genus life histories). Particle tracking of individual organisms using the output of ocean circulation models is a suitable, cost effective tool to examine larval connectivity among coral reefs in large areas and at fine spatiotemporal scales relevant to the population ecology of coral reef species (Werner et al., 2001, 2007; Cowen and Sponaugle, 2009). Insight developed from connectivity matrices generated from this study could aid local managers and decision makers tasked with regulating the use of marine resources in the Kenya-Tanzania region. Hindcasting the connections among reefs in the strongly dynamical Kenya-Tanzania region is challenging and the level of uncertainty is high. The results presented are a first attempt at assessing connectivity in the region and should be treated as a regional result suitable for comparison with similar studies in other coral reef regions [Great Barrier Reef (GBR); Mesoamerican Caribbean Reef]. In addition, these model results should be useful for developing hypotheses and designing observational campaigns aimed at validating or improving the described connectivity patterns.

### METHODS

### Hydrodynamic Model

A 2 km horizontal resolution Regional Ocean Model System (ROMS) (Haidvogel et al., 2008) that includes tides, the 2 km Kenyan-Tanzanian Coastal Model (hereafter 2KTCM), was used to generate (3D) ocean velocity fields. This model is an enhanced resolution version of the 4 km Kenyan-Tanzanian Coastal Model (KTCM) (Mayorga-Adame et al., 2016). The model domain is a rectangular grid extending from 38◦ to 47◦E and from the equator to 10◦ S (**Figure 1**). It has 31 terrain following vertical levels. The model bathymetry comes from the 30 s global GEBCO product (http://www.gebco.net/data\_and\_ products/gridded\_bathymetry\_data/; accessed April 2011). The model coastline was manually edited to retain as many features as the 2 km resolution allowed. Only Pate Island in north Kenya, and Pemba, Zanzibar and Mafia Islands in Tanzania are included as dry cells in the land mask. The atmospheric forcing (wind stress, heat and freshwater fluxes) is calculated by ROMS bulk formulation using atmospheric variables from the daily NCEP/NCAR reanalysis (Kalnay et al., 1996). The model is initialized and forced at the boundaries by monthly fields of T, S and velocity from the KTCM (Mayorga-Adame et al., 2016) and tides are provided by the TPXO6 global tidal model (Egbert et al., 1994; Egbert and Erofeeva, 2002). Freshwater runoff and diurnal wind variability are not included in the model. The ocean model was run continuously for 8.25 years from October 1999 to December 2007. Three-hourly averages of the velocity fields

FIGURE 1 | Study area with coral reefs grouped by color into 15 regions. sS, south Somalia; nK, north Kenya; sK, south Kenya; wP, west Pemba; eP, east Pemba; nP, north Pemba; nT, north Tanzania; wZ, west Zanzibar; eZ, east Zanzibar; cT, central Tanzania; DP, Dar es Salaam Peninsula; oR, offshore Reef; wM, west Mafia; eM, east Mafia; sT, south Tanzania.

for 2000 and 2005 were stored and used for the particle tracking experiments.

### Lagrangian Particle Tracking

An Individual Based Model (IBM) (Batchelder, 2006) was run offline using previously stored 3-h averages of the 3D-2KTCM velocity fields. The IBM interpolates tri-linearly in space and linearly in time the velocity fields from the ROMS simulation. Particle trajectories are computed using a 4th order Runge-Kutta algorithm. No explicit diffusion (e.g., random walk applied to the individual's position) is invoked since the 2 km horizontal resolution of the ocean circulation model is enough for significant eddy formation and horizontal mixing to occur around reefs, and the terrain following coordinates provide very high vertical resolution (<15 cm) in the shallow regions. A 3D advection-only version of the IBM was used to track forward in time the dispersal of particles (virtual larvae) originating from all reef polygons. The tracking was done using a 30 min time step. Coral larvae were tracked using the 3D passive advection scenario only. For surgeonfish, with longer PLDs and greater ability to control depth in the water column, an idealized ontogenetic vertical migration scenario was implemented.

### Biological Assumptions

In the model experiments all reefs were seeded randomly with a density of 50 particles per square kilometer of reef. Reefs smaller than 1 km<sup>2</sup> were seeded with 50 particles. A total of 129 184 particles were released for each modeled spawning day, using identical seeding locations for all simulations. Spawning was assumed to take place at 5:30 p.m. local time (∼sunset) during February and March, the months of peak spawning for coral reef species in the Western Indian Ocean (Mangubhai, 2008; Mangubhai and Harrison, 2008). All particles were released at 3 m depth. For the 3D passive experiments (reference experiments) virtual larvae were spawned at the release locations at 3 day intervals starting on February 2nd for a total of 20 releases. PLD for Caribbean species of Acanthurus range from 45 to 70 days (Rocha et al., 2002). The Indo-Pacific species A. triostegus has a mean PLD of 54 days (range of 44–83 days) (Randall, 1961; McCormick, 1999; Longenecker et al., 2008). Acanthurus virtual larva were tracked for 72 days and considered competent to settle 50 days after their release, giving them a competency period of 22 days. Acropora virtual larvae were tracked for 12 days and considered competent after 4 days giving them a competency period of 8 days. These assumptions were made considering the results of laboratory rearing studies that reported a minimum pre-competency period of 3 to 4 days for A. muricata, A. valida (Nozawa and Harrison, 2008), and A. tenuis (Nishikawa et al., 2003), and up to 97% settlement 10 days after spawning (Babcock and Heyward, 1986; Nishikawa et al., 2003; Nozawa and Harrison, 2008). The ability of reef larvae to sense nearby reefs and swim toward settlement habitat is often represented in models as a sensory zone based on perception distance (Paris et al., 2007; Sponaugle et al., 2012), a buffer distance around suitable habitat that defines how far away from a reef larvae are able to successfully settle. Based on observational studies of sensing, swimming and settling ability (Leis and Carson-Ewart, 1999; Leis and Fisher, 2006; Atema et al., 2015), perception distance for competent Acanthurus larvae was assumed to be 4 km, which is consistent with the distance used to model other coral reef fish (Paris et al., 2007; Sponaugle et al., 2012). Perception distance for competent Acropora larvae was assumed to be much shorter, only 10 m, because despite their ability to perceive sounds (Vermeij et al., 2010) and chemical cues (Dixson et al., 2014) emanating from reefs they have very limited swimming ability and are unlikely to overcome water speeds (Baird et al., 2014). Virtual larvae were evaluated each night during their competency period to determine if reefs were within their perception distance. If so, they were assumed to settle on the first reef they encountered. Sensitivity analysis to evaluate whether the destination reef of settled larvae was affected by the time of evaluation during the dark hours indicated little temporal variation within a night. Therefore, settlement of virtual larvae was evaluated once per night at 11:30 p.m. local time. The Acanthurus ontogenetic vertical migration (OVM) experiment included passive dispersal for 20 days, then larvae were shifted to 50 m (or 3 m above the bottom at locations shallower than 50 m). Virtual larvae at 50 m continued to be passive in their horizontal movement but were kept at fixed depth for 20 days. At day 40, the larvae migrated back to 3 m depth to find suitable reef habitat when reaching competency (50 days after spawning). After the upward migration, larvae are advected passively in three dimensions until day 72, when the trajectory was terminated. Successful settlement was assessed as described in the reference experiment. OVM experiments were run for the February to March period as the passive experiments, but with larvae released only every sixth day (for a total of 10 release dates).

### Seascape Analysis

Kenya and Tanzania have very narrow continental shelves, with the 200 m isobath only 12 km offshore, except at the Mafia and Zanzibar Channels. The shores of Kenya and Tanzania are bordered by a virtually continuous chain of fringing coral reefs that stretches along the coast, only breaking at river mouths and estuaries. The coral reef polygons in the model domain were extracted from the Global Distribution of Coral Reefs 2010 database available at the Ocean Data Viewer webpage (http://data.unep-wcmc.org/). After simplifying the polygons using ArcGIS, by merging adjacent reefs (separated by <20 m), and discarding individual reefs smaller than 25 m<sup>2</sup> , a total of 661 individual reef polygons identified reef habitat for larval settlement (**Figure 1**). A connectivity matrix showing the origin locations on one axis and destination locations on the other axis is used to visualize the geographic connections among habitat patches for simple alongshore linear systems. However, the two dimensional nature of the reef systems bordering East Africa, with multiple reefs at the same latitude (e.g., mainland fringing reefs, atolls or patch reefs in the channels between the islands and mainland, fringing reefs on the west and east coast of the islands), make the reef to reef connectivity matrices organized by the latitude of the centroid of the reef polygons insufficiently informative regarding inshore-offshore connections. Due to the spatial complexity of the reef habitat, we simplified the connectivity matrices by assigning individual reefs to one of fifteen geographic subregions (**Figure 1**). Geographic regions considered mainland continuity of reefs, but also national borders and offshore island masses, many of which have both shoreward facing and offshore facing fringing reefs (**Figure 1**). This allowed a more meaningful visualization of the results. Based on the number of particles released within a region, the percentage of particles that successfully connect from region to region was calculated. Summing the percentages in the horizontal direction (all destination regions) on the connectivity matrices shows the percent of successful recruits from each region of origin.

The term local retention refers to the ratio of virtual larvae settling at their released location and the total number of virtual larvae released at that location, while self-recruitment is the ratio of virtual larvae settling at their released location and the total number of larvae settling at that location. In the results section the comparatives "weaker" and "stronger" are used to refer to the magnitude of connections between two specific sites, indicating the proportion of particles connecting from one reef or region to another. Strong connections appear as large color-coded circles in the connectivity matrices, while weak connections are small black circles. Conversely "few" and "more/lots" are used to refer to the number of sites that are connecting to a reef or region. The number of connections for a region will be represented by the number of circles on each row or column for origin and destination regions, respectively.

We use the terms "source" and "origin" interchangeably to refer to reefs or regions from which virtual larvae are released. Similarly, we use the terms "sinks" and "destinations" interchangeably to refer to reefs or regions into which virtual larvae successfully settle. We are not referring to population source/sinks according to the classical population ecology definition, since we do not consider spatially variable reproductive input nor variable mortality during the settlement phase. In this case we are referring only to source/sinks of the planktonic pool of successful virtual larvae, and therefore the terms only refer to the diversity of origins/destinations of the virtual larvae that are assumed to successfully settle.

### Sensitivity Analysis

Complementary analysis and "in silico" experiments were carried out to determine the sensitivity of the resulting connectivity matrices linking origins and destinations to the perception distance assumption and to the inclusion of vertical diffusion. To investigate the sensitivity of settlement success to perception distance, the coral and surgeonfish reference runs of 2000 were re-analyzed with perception distances of 10, 500, and 4000 m. This analysis was performed for particle releases every sixth day for a total of 10 spawning days within February and March. The percent of larvae that successfully settled on reef habitat and the standard deviation among the 10 release dates was calculated.

In order to assess the effects of vertical diffusion on connectivity, and to investigate if an important proportion of reef-to-reef connections is being missed by considering advective only experiments, additional experiments similar to the advective only Acanthurus reference runs, but with the addition of vertical diffusion processes, were carried out for 26 selected reefs (Supplementary Figure 5). In order to perform these simulations with the same computer resources used for the advective only simulations the number of release locations had to be greatly reduced; we subsampled 10% (a total of 2694 release locations) from the 26938 release locations used for the advection only scenario for these 26 reefs. For each advection-diffusion release location 100 replicate particles were released on each of 3 release dates; at the beginning, middle and end of the presumed spawning season (February 2nd, March 1st, and March 31st, respectively) of 2000 and 2005. Vertical diffusion was implemented as a vertical random walk scaled by the vertical viscosity coefficient of the ocean model according to the model detailed by Batchelder et al. (2002). The connectivity provided by the advection-diffusion simulations was compared to advection only results from the same 26 reefs to investigate the potential role of vertical diffusion in either enhancing or reducing connectivity and modifying the general patterns observed in the advective only experiments. Comparisons were done at the reef scale. Magnitude of the connections was calculated as the percentage of particles released per reef that settled. The number of particles released was an order of magnitude higher in the experiments with diffusion, while the number of release locations was 10 times greater in the advective only experiments (e.g., 1 particle from each of 50 different locations from a 1 km<sup>2</sup> reef in the advection only case vs. 500 particles from each of only 5 release locations within the same reef in experiments including vertical diffusion). The results of all 6 release dates (three in each of 2000 and 2005) were aggregated on a binary reef to reef connectivity matrix, which neglects the magnitude of the connections, and compared to the advective only counterpart. The subtraction of the matrices eliminates connections present in both scenarios and provides an estimate of how many connections were missed by one or the other experimental set ups. Trajectories and connectivity patterns were also visualized and compared to gain understanding of the observed differences, but are not shown.

### RESULTS

## Acanthurus and Acropora 3-D Passive Advective Experiments

### Settlement Success

Larvae that find a reef within their perception distance during their competency period are assumed to successfully settle. The percentage of successful settlers differs greatly between the two modeled genera. For virtual larvae characterized as Acanthurus surgeonfish the mean settlement success of the 40 releases during February and March of 2000 and 2005 is 24.4 ± 4.7% while for the Acropora coral virtual larvae the mean is 0.28 ± 0.04% (**Figure 2**). Settlement success variability around the mean is similar between the two species groups. Changes in yearly mean settlement success are opposite for the two modeled genera (Acanthurus 25.5% in 2000 and 23.3% in 2005, Acropora 0.27% in 2000 and 0.28% in 2005).

#### Region to Region Connectivity Matrices

The region to region connectivity matrices allow an easier visualization of the main connectivity patterns, synthesizing the information of reef to reef connectivity matrices (Supplementary Figure 6). Regional connectivity matrices with reefs grouped into 15 regions (**Figure 1**) show a dominant South to North connectivity pattern along the Kenya-Tanzania coast (**Figure 3**), as represented by the predominance of circles below the 1:1 diagonal line, which indicates sites where local retention occurred (larvae released in a region settled in the same region). This pattern is prevalent in both modeled years (2000 and 2005) for both larvae types (Acanthurus and Acropora) (**Figure 3**), and reflects the strong south to north flows that prevail along most of the Kenya-Tanzania region, which is influenced by the northward flowing EACC year round. Most of the small number of circles above the 1:1 line of the connectivity matrices indicate north to south connections [a few of them represent west to east connections, for example west Zanzibar (wZ) to east Zanzibar (eZ)], which are much less common but occur in the northern part of the domain due to the influence of the southward flowing Somali Current during the Northeast monsoon (December-March), or to small scale recirculation features, such as eddies, in a few other locations. The magnitude and location of north to south connections is particularly variable interannually. For the 2000 Acanthurus simulation (**Figure 3A**) small proportions of north to south connections occur in most regions, but mainly at the northern-most (Somalia [sS], Kenya regions [nK, sK]) and southern-most regions (east Mafia [eM]) and in some central regions (Dar es Salaam Peninsula [DP] and central Tanzania [cT]). In 2005 (**Figure 3C**) north to south connections are weak at the northern and southern limits of the domain, but somewhat stronger in the central region (Dar es Salaam Peninsula [DP], western Zanzibar [wZ] and central Tanzania [cT]).

In Acropora corals (**Figures 3B,D**) most of the connections are due to within region recruitment, and strong connections are restricted to a 1 degree (∼100 km) radius around the reef of origin. The reef offshore of Dar es Salaam (oR), east Mafia (eM) and south Tanzania (sT) regions show the longest distance connections. Interannual variability in north to south connections is similar to that of Acanthurus virtual larvae.

Regional connectivity matrices enable differentiation among across-shore reefs at the same latitude, and yield insights about well-connected and isolated reef regions. At a regional scale, the Kenya (sK, nK) and Somali (SS) reefs receive Acanthurus virtual larvae from all other reef regions in both modeled years. In contrast reef regions adjacent to Pemba Island (eP, nP, wP) receive very few Acanthurus larvae from any other reef habitats within the model domain (**Figures 3A,C**). The reef offshore of the Dar es Salaam peninsula (oR at ca. 7◦ S), due to its oceanic location and exposure to the strong northward flowing EACC, has potential for long distance connections. Settlement of Acanthurus from oR was very different in the two modeled years. In 2000 it was a source for larvae settling on distant Kenyan (sK, nK) and Somali (sS) reefs only; in 2005 it exported larvae to Kenyan (sK, nK) and Somali (sS) reefs, but also to some nearer Tanzania regions (central and north Tanzania and east Zanzibar regions; cT, nT, eZ). This offshore reef (oR) is not a large sink reef for Acanthurus larvae, but the origin of its arriving larvae is diverse, coming from reefs to the south of it in 2000 and from all regions except east Zanzibar (eZ) in 2005. The Somalia (sS) and Kenya (sK, nK) regions are the sink regions with the greatest diversity of source reefs, followed by the north Tanzania (nT) region. Larvae from Dar es Salaam Peninsula (DP) region settling in the north Tanzania region represented the strongest connection in 2000, followed in magnitude by the connection from the east Zanzibar (eZ) region to the south Kenya (sK) region. In 2005 the strongest connection remains the same but the second strongest connection was between east Zanzibar (eZ) and the north Tanzania (nT) region. During 2005 source reefs around Zanzibar Island (eZ, wZ) and the central Tanzania (cT) region had more connections to southern destination reefs. However, local retention of Acanthurus surgeonfish virtual larvae at the regional scale was larger in 2000.

For Acropora corals (**Figures 3B,D**) the highest proportion of recruitment is due to local within region recruitment at the

nT, north Tanzania; wZ, west Zanzibar; eZ, east Zanzibar; cT, central Tanzania; DP, Dar es Salaam Peninsula; oR, offshore Reef; wM, west Mafia; eM, east Mafia, and sT, south Tanzania. Color and size of the circles are proportional to the percentage of successful connections from source (origin) to sink (destination) reefs according to the colorbars to the right of the panels.

west Zanzibar (wZ) and west Pemba (wP) regions in both 2000 and 2005. In all regions except east Pemba (eP) and the offshore reef (oR), the probability of recruiting locally is higher than the probability of connecting to another reef region. Similar to Acanthurus, more north to south connections of Acropora are observed in the regions between north Tanzania (nT) and the Dar es Salaam Peninsula (DP) in 2005 than in 2000, when substantial north to south connection occurred only between Dar es Salaam (DP) and west Mafia (wM). In 2000, the offshore reef (oR) connects to all Pemba regions (eP, wP, nP) and north Kenya (nK), while in 2005 it connects to all regions north of Dar es Salam except north and west Pemba (nP, wP). This offshore reef is the only source of Acropora larvae for the east Pemba (eP) region. North and west Pemba get recruits from all Pemba regions in both years.

The variable number of north to south connections between the two modeled years is explained by the influence of the mesoscale circulation on the shelf circulation pattern. In 2000 the northward flowing East African Coastal Current (EACC) was weak during the spawning months (<0.5 m s−<sup>1</sup> ) as is typical during the NE monsoon season. The Somali Current (SC) that flows southward at this time of the year was strong in February (∼0.68 m s−<sup>1</sup> ) and its subsurface influence prevailed until April (Supplementary Figure 1). The strong influence of the southward flowing SC current in the northern part of the domain is responsible for the north to south connections in that region. In the rest of the domain the weak EACC generates slower northward velocities on the shelf during the spawning months, especially February (Supplementary Figure 2), allowing for some north to south connections at most latitudes, more evident in the reef to reef connectivity matrices (Supplementary Figure 6).

In contrast, in 2005, the SC was weaker and only present during February and March since the transition to SW monsoon conditions happened very early in the year, with strong northward flow (>1 m s−<sup>1</sup> ) established in March and already re-established in the upper 300 m by April (Supplementary Figure 3). The weak SC only promotes a few north to south connections in the northern part of the domain. The strong EACC intensifies the flow reversal north of the Mafia and Zanzibar Channels, which is generated as the northward flow overshoots and turns southward into the channels when trying to follow the curved bathymetric contours past the islands (Supplementary Figure 4). This small scale circulation pattern is responsible for the north to south connections observed on regions around the north and south entrances of the Zanzibar Channel in 2000 for both Acanthurus and Acropora virtual larvae (Supplementary Figure 6).

### Acanthurus Ontogenetic Vertical Migration (OVM) Experiments

#### Acanthurus OVM Settlement Success

Experiments that include an idealized OVM exhibit greater variability in Acanthurus settlement success among release dates within a year and between the two modeled years compared to the passive larvae experiments (**Figures 2A**, **4**). Mean settlement success is 34.5% ± 14.6 for 2000 and 17.7% ± 8.3 in 2005, but due to the large variability among release dates, the year to year difference is not statistically significant. There is a marked decrease in settlement success from earlier to later spawning dates in the OVM scenario, going from 46.8% for particles released in February 2nd to 7.2% for those released on March 31th in 2000 and from 34.0 to 15.9% for those same dates

in 2005. The decrease in settlement success occurred earlier in 2005 than during 2000, associated with the rapid transition to SW monsoon conditions in 2005 (Supplementary Figure 4). In the northern part of the model domain the core of the northward flowing EACC is subsurface (below 70 m depth) at the beginning of the spawning season (NE monsoon), but it re-establishes in the upper 300 m by May in 2000 and April in 2005 (Supplementary Figures 2, 4). This implied that 2005 larvae migrating down to 50 m are affected longer by the strong northward flow than the 2000 larvae. Three-dimensional passive larvae tend to stay near the surface and are therefore less likely to be carried away from suitable habitat by the strong northward flowing EACC core transitioning from deep to shallow waters during the second half of the spawning season.

virtual larvae with OVM for 2000 (A) and 2005 (B). Reefs were grouped into 15 regions identified by two letters in Figure 1. Color and size of the circles are proportional to the percentage of successful connections from source (origin) to sink (destination) reefs according to the colorbar.

### Acanthurus OVM Region to Region Connectivity Matrices

When grouped at the regional level the Acanthurus OVM numerical experiments showed that in 2000 (**Figure 5A**) the strongest connection was between central Tanzania (cT) and north Tanzania (nT). The north Tanzania (nT) region received virtual larvae from all southward reefs. The south and north Kenya regions (sK, nK) and the south Somalia (sS) region receive recruitments from all other regions. Southern Tanzania (sT), east and west Mafia (eM, wM) and the Dar es Salaam Peninsula (DP) regions provide larvae to most other regions except the offshore reef (oR), but their probabilities of connecting to the Pemba regions are very low. The main sinks for larvae coming from the offshore reef (oR) in 2000 are the distant Kenya (sK, nK) and Somalia (sS) regions. Minimal north to south connections occur with larvae originating at east and west Mafia (eM, wM) and the Dar es Salam Peninsula regions (DP) in Tanzania, the south and north Kenya (sK, nK) regions and south Somalia (sS), connecting to southward regions. Across shore connections are observed mainly from west Zanzibar (wZ) to north Tanzania (nT) and from east to west Mafia (eM to wM).

In 2005 (**Figure 5B**), the offshore Dar es Salaam reef (oR) has strong connections with both Zanzibar (eZ, wZ) and north Tanzania (nT) regions as well as distant Kenya and Somalia regions. The strongest connection of 2005 occurred between the offshore reef (oR) and the south Kenya (sK) region. Most regions successfully connect to northward regions, except to the three Pemba Island reef regions, which get few recruits in both years modeled. Small proportions of the larvae spawned at the Dar es Salaam Peninsula (DP) and north Tanzania (nT) regions connect southward to the west Mafia and west Zanzibar regions, respectively. Across shore connections are weaker.

Interannual variability in the general patterns of reef connectivity for Acanthurus is enhanced when the ontogenetic vertical migration behavior is included, especially regarding the magnitude of the connections. Weaker and fewer connections are observed in 2005 in comparison to 2000 (**Figure 5**). As in the passive scenario, a strong interannual difference is observed in the number and location of south to north connections, with stronger north to south connectivity in the southern and northern most regions in 2000, and uniformly weak north to south connections in 2005. Overall, spatial connectivity of OVM Acanthurus in each of 2000 and 2005 are remarkably similar to the patterns observed for 3D passive Acanthurus, although the overall connectivity is lower with OVM than the passive, particularly in 2005.

### Sensitivity Analysis

### Sensitivity to Perception Distance

The analysis with increased (reduced) perception distance for Acropora (Acanthurus) is presented to provide insight on one of the processes responsible for the large difference in settlement success between the modeled species groups, and to illustrate the variability that might be expected among coral reef species with different life-history strategies. The percentage of settlement

success increased with greater perception distance for both the Acanthurus surgeonfish and the Acropora coral simulations (**Figure 6**). However, the increase in settlement success for the short PLD coral was always much higher than that of the surgeonfish for the same increase in perception distance, with the coral reaching 95% settlement success with a 4 km perception distance. The difference in settlement success between the two genera was significant for all perception distance scenarios (**Figure 6**), indicating that with the same perception distance short PLD virtual larvae will always be more successful. Perception distance scenarios alternative to the reference run experiments are not appropriate for the specific genera used here, but might be appropriate for other coral reef organisms with different life-history traits. Acropora coral larvae perceive reefs through sound (Visram et al., 2010) and chemical cues (Heyward and Negri, 1999; Dixson et al., 2014), but their perception capabilities are unlikely to exceed 100 m. Laboratory experiments have shown that coral larvae are able to detect reef sounds 0– 1 m from the source and move toward them (Visram et al., 2010). If planulae are capable of detecting particle motions anticipated perception distances are on the 10–100 m range (Visram et al., 2010). Despite their sensing abilities, the swimming ability of coral larvae is very limited and usually negligible in comparison to ocean currents (Kingsford et al., 2002; Baird et al., 2014). To the contrary, Acanthurus late larvae are one of the strongest swimmers among coral reef fish larvae, with reported in situ swimming speeds ranging from 8.7 to 65.3 cm s−<sup>1</sup> (Leis and Carson-Ewart, 1999; Leis and Fisher, 2006). They have been observed to navigate in situ disregarding current direction, perhaps guided by a sun compass (Leis and Carson-Ewart, 2003). Navigational capabilities exceeding 1 km are therefore expected for Acanthurus.

#### Diffusion Effect

The inclusion of vertical diffusion greatly increased the vertical spread of the virtual larvae and distributed them throughout the water column over the shelf. This, in turn, increased the horizontal spread of virtual larvae. The main connectivity patterns of the Acanthurus advective only experiments were also represented in the experiments with diffusion, including the interannual differences (not shown). The strength of the connections on the Acanthurus diffusive scenario was, however, an order of magnitude smaller than in the advective only scenario, indicating that the vertical spread of particles released at the same location leads to the majority of them dispersing away from suitable habitat. The extent to which the inclusion of vertical diffusion generated new connections, not represented in the advective only scenario was modest (**Figure 7**). From the 100% represented by the total number of connections found only in one of the two scenarios, 12.4% came from the scenario that included vertical diffusion, whereas 87.6% came from the advective only scenario. Thus, it is clear that including diffusion to the advection scenario produces relatively few new connections to the matrix, and that, for this particular case, the inclusion of a vertical random walk component may not be essential to providing a representative connectivity matrix.

## DISCUSSION

The dominant pattern of connectivity for both Acanthurus and Acropora in the KT region is southern reefs providing virtual larvae to northern reefs. The spatial scale of connectivity is much smaller for the short PLD coral group; successful connections are restricted to a 1◦ radius (∼100 km) around source reefs. 8.2% of Acropora larvae that successfully settle, recruited to their source reef (self-), an important proportion compared to only 1–2% for Acanthurus. Some Acropora were capable of long distance dispersal, particularly larvae spawned at the reef offshore of Dar es Salaam peninsula. This indicates that they can take advantage of the strong offshore EACC to reach distant northern reefs, and that even for short PLD, latitudinal isolation may be minimal, especially at longer (i.e., evolutionary) timescales.

In contrast to the generally short dispersal distances of Acropora, long distance connections from the southern to the northern most reefs (∼950 km) are common for virtual Acanthurus. Their longer pelagic durations lead to greater transport distances and reduced local retention. Overall settlement success was significantly greater in Acanthurus (24%) than in Acropora (<0.5%). This is due to several factors that enhance Acanthurus successful settlement probabilities: longer competency period, greater reef perception distance and swimming ability.

While south to north connections predominate in the connectivity matrices, some north to south connections occur, mostly in inshore regions that experience substantial eddy flows and topographically steered flow reversals. Examples of these are (1) the northern region that is seasonally influenced by the southward flowing Somali current (SC) (**Figure 3**), and (2) the northern entrance of the Zanzibar Channel and the region south of the Dar es Salaam peninsula where nearshore flow reversal is promoted by strong northward offshore currents (Mayorga-Adame et al., 2016). Therefore, there is strong interannual variability in the amount and location of north to south connections depending on the strength of the offshore mesoscale currents. When the Somali Current is strong (e.g., in 2000), short distance north to south connections are common at most latitudes, but are most prevalent near the northern and southern edges of the study region. When northward offshore flow is strong and the SC disappears early in the year (e.g., 2005), north to south connections are restricted to reefs in the wider shelf region between Pemba and Mafia Islands (due to enhanced small scale flow reversals) and the region north of 3◦ S where the Somali Current has a direct effect.

Interannual variability is also evident in the strength of the connections among reefs and the proportion of local retention. Thirteen reef regions (all but oR, eP) experience local retention in 2000, however in 2005 five regions (sT, oR, eP, nP, wP) had no or minimal local retention. In several cases the strong connections among regions are not consistent between 2000 and 2005; analysis of simulations for other years is needed to assess the persistence of connectivity patterns. Multi-year simulations [e.g., James et al. (2002), 20 years' model of reef fish connectivity in a section of the (GBR); Dorman et al. (2015), 46 years' model of Acropora millepora connectivity in the South China Sea] would give further insight on the variability and robustness of the connectivity patterns and help to identify connections that are vital to maintaining regional metapopulations of different species groups.

The different connectivity patterns and scales of dispersal for the two genera characterized in these modeling experiments show that it is important to consider interspecies life-history variability when implementing conservation strategies to ecosystems as diverse as coral reefs, since ideal spatial management strategies would enhance settlement success for a wide suite of species with different perception and dispersal capabilities. Our results indicate, for example, that Acanthurus virtual larvae settling to coral reefs around Pemba Island come from relatively few source reefs, which highlights the need for strong local protection since the resilience, (e.g., potential recolonization of Pemba's Acanthurus populations from more distant reefs), is minimal, despite their relatively lengthy larval pelagic phase. Pemba Island Acropora coral populations are less vulnerable since they show stronger and more variable connections. This seems counter intuitive given the smaller scale of connectivity and higher local retention rates of Acropora, however the local oceanographic regime around Pemba Island, including a strong return flow on the western side of the island, promotes retention at short time scales, favoring Acropora connections, while the much longer PLD of Acanthurus favors transport away from Pemba's suitable habitat.

The level of connectivity of a reef is a component of its resilience and the extent of its ecological impact in the region. For example, strong sink reefs, those receiving settlers from many different source reefs, are more resilient to local and global stresses, since having multiple sources increases the probability of receiving recruits in any given year. The diversity of sources providing potential recruits would enhance resilience to short term local detrimental phenomena such as bleaching events and overfishing. On the other hand, important source reefs, those with potential of providing settlers to many other reefs, could have a disproportionately large ecological impact for many other reefs. Reefs that provide larvae to many other sites are important to protect from a larger ecosystem conservation perspective, since an increase of the local spawning population would likely impact recruitment to a large number of reefs elsewhere, therefore increasing the impacts of spatially limited conservation measures (e.g., MPA) beyond their boundaries (Bode et al., 2006; Figueira, 2009). "Source and sink" maps are useful for identifying ecologically important areas based on the number and type of connections present. Source and sink maps for Acanthurus are shown in **Figures 8A,C**, and for Acropora virtual larvae in **Figures 8B,D**. The passive and OVM scenarios (not shown) for Acanthurus yielded similar source and sink maps. In general reefs south of Mafia Island (8◦ S) provide larvae of both species groups to the greatest number of reefs. In the case of Acanthurus larvae (**Figure 8A**) these reefs connect to more than 350 different reefs, and for Acropora (**Figure 8B**) to more than 70 reefs. Reefs in the northern half of Tanzania are good sources of Acropora larvae, connecting to more than 50 reefs, while Kenyan reefs connect to ∼30 different reefs. Local conservation efforts in these areas are likely to have an important ecological impact beyond their local ecosystem, since they can help maintain and replenish multiple other metapopulations at various destination reefs. Somali reefs to the contrary provide Acanthurus virtual larvae to <50 reefs and Acropora virtual larvae to <10 different reefs. While this may be an artifact of these reefs being near the northern border outflow, the role of Somali reefs in providing recruits of reef species further north is minimal as there are few coral reefs within the immediate north region. Kenyan and Somali reefs are however the most common sink reefs, receiving larvae from many reefs to their south (**Figure 8D**). These northern reefs may be more resilient to local threats. The source and sink patterns reflect the strong, mostly unidirectional south to north flow along the coast. For Acropora larvae, the source and sink maps are much more patchy (**Figures 8B,D**, respectively), reflecting the effects of the smaller dispersal scale of Acropora larvae.

A recent genetic study of Acropora tenuis connectivity in the KT region, reports high but variable connectivity between sample sites, which cluster in 3 different groups: (1) Kenya and northern-Tanzania, (2) southern Tanzania, and (3) sample sites located in the Zanzibar and Pemba channels (van der Ven et al., 2016). No clear genetic break on samples collected along 900 km of coral reefs was observed. Also, no genetic differentiation with increasing geographical separation was found, in contrast to similar studies in the (GBR) and Japan. They associate the genetic uniformity in the KT region with uniform oceanographic conditions promoted by the continuous south to north linear flow of the EACC. The highest differentiation observed in group 3 is associated with local oceanographic conditions causing larval retention. The connectivity patterns of our modeling study agree with their findings, despite the different time scales assessed. The north to south connectivity we report is expected to minimize genetic differences along the KT coast. Our model also corroborates the isolation they infer for their highly differentiated Pemba and Zanzibar Channel sites. Our model results indicate that west Pemba (wP) and west Zanzibar regions, receive the majority of their Acropora virtual larvae through within region recruitment. The circulation patterns depicted by our ROMS model included flow reversals at the northern entrance of the channels and eddy blockage in the southern entrance of the Zanzibar Channel (Mayorga-Adame et al., 2016); these might provide sufficient isolation to upstream sources to produce genetically different Acropora populations in the channel sites.

Genetic connectivity patterns for Pocillopora damicornis (a brooding coral species) based on contemporary gene flow (Souter et al., 2009) can be compared with our modeling results for the longer PLD, broadcast spawner Acropora corals. Souter et al. (2009) identified first generation migrants of P. damicornis at 29 reefs sites in the Kenya-Tanzania region, and therefore determined the degree of isolation of the different reefs sampled. They found patchiness in the degree of isolation at very small scales, with marked differences even between lagoon and fringing reefs within the Malindi Marine National Park and Reserve in south Kenya. The patchiness observed in our Acropora source and sink maps is consistent with their results, indicating strong small-scale spatial variability in the number of connections (degree of isolation) among nearby reefs. Souter et al. (2009) identified isolated reefs, highly dependent on local retention for population renewal, in south Kenya, west Pemba, and south Mafia. In the Acropora simulations these regions receive virtual larvae from <10 different source reefs (**Figure 8D**). The regional Acropora connectivity matrices (**Figures 3B,D**) show that local retention is important for these regions. In our regional connectivity results, however, only west Pemba, east Mafia and south Tanzania show relative isolation, receiving Acropora larvae from only three and two other regions respectively; south Kenya in contrast receives settlers from many regions further south. This discrepancy between our model results and Souter et al.'s (2009) genetic study may reflect the different spatial scales considered, since our regional grouping aggregates connections for several reefs that might have different degrees of isolation. Souter et al. (2009) identify Mnemba Conservation Area (in the east Zanzibar region) as a strong source for other sampled sites. This site shows the highest genetic diversity and is similar only to one site in the Dar es Salaam Peninsula and one site in southeast Mafia Island. In the simulation Acropora larvae that settle in the east Zanzibar region, which includes Mnemba Island, come from few origin reefs (mainly Dar es Salaam Peninsula and east Mafia regions; **Figures 3B,D**). The number of regions that receive Acropora larvae from east Zanzibar ranges between 3 and 5 in the 2000 and 2005 simulations. The source map for Acropora (**Figure 8B**) shows that most reefs around Mnemba (east Zanzibar) provide larvae to ∼30 to 60 different reefs. Our model results identify specific reefs in the west Mafia and southern Tanzania regions as the main providers of Acropora larvae while the genetic results of Souter et al. (2009) do not identify their south Mafia and Mtwara (south of our model domain) sites as important sources. This could be due to the high reef to reef patchiness on the level of isolation identified by both their observational and our modeling study, the uncertainty of which specific reefs were actually sampled for the genetic study, and the shorter PLD of Pocillopora damicornis. To the extent allowed by the comparison of this model with the genetic sampling of specific reefs results of Souter et al. (2009), the main connectivity patterns elucidated by their genetic study for an ecologically similar coral species are well represented in the connectivity results provided by the coupled biophysical model for Acropora. This comparison is limited to the regional level, since the exact location of the reefs sampled by Souter et al. (2009) is not reported.

Only at the beginning of the spawning season did the ontogenetic vertical migration "in silico" experiments of Acanthurus virtual larvae generate more successful settlers than the 3D passive scenario (**Figures 2A**, **5**). This is inconsistent with prior reports in the literature for various larvae in the Caribbean (Paris et al., 2007) and the California Current System (Drake et al., 2013), where OVM consistently increased settlement success. Differences in shear and stratification of the water column of each region may be responsible for this marked difference among oceanographically distinct regions. The shelf circulation of Kenya and Tanzania is dominated by strong alongshore flows with an increased magnitude offshore, a shallow (i.e., <50–100 m) wind driven mixed layer is not common. Northward flow velocities dominate the coastal

virtual larvae from, in both simulated years, to identify the best sink reefs for *Acanthurus* (C) and Acropora (D).

circulation off Kenya and Tanzania down to 300 m depth during most of the year. Therefore, a vertical migration down to 50 m depth would have little effect on transport pathways. During the SE monsoon (Dec-Mar) the Somali Current flows southward in the upper 100 m north of 3◦ S. During this period, which encompasses part of the spawning period, staying near the surface, instead of migrating to deeper waters, would facilitate north to south connections and retention if the duration of the pelagic phase includes the seasonal reversal to northward flow. Only during the transition between NE to SE monsoon conditions would a shallow migration result in significantly shorter horizontal displacements for Acanthurus larvae. Intraseasonal and interannual variability increased when the simple ontogenetic vertical migration behavior was implemented because the evolution of the vertical structure of alongshore velocities was markedly different in the two modeled years (Supplementary Figures 2, 4). The ontogenetic vertical migration pattern modeled here is based on the increased depth of the Acanthurus larvae during ontogeny observed by Irisson et al. (2010). The depth of the migration is not well defined and could be site dependent. For example, Irisson et al. (2010) reported post-flexion Acanthurus larvae in the 25–60 m depth range near reefs in French Polynesia, while Oxenford et al. (2008) found aggregations of late Acanthurus larvae to be more abundant at 120 m in the eastern Caribbean Sea. No observations for the East-African coast exist. Observations of vertical distribution and abundance of pelagic larvae concurrent with hydrographic conditions are needed to design more realistic vertical migration experiments, and to assess larval fish responses to temperature, light, or velocity. The implementation of vertical migration in these numerical experiments was highly idealized, shifting all particles to 50 m depth 20 days after release, ignoring their vertical position at that time. This meant that some larvae that had passively advected deeper than the 50 m fixed migration depth were actually displaced upward with this vertical migrating behavior. The number of particles that advected below 50 m depth was not an important fraction of the successful larvae since most larvae stayed in the upper 5 m when passively advected; a small proportion, however, reached depths below 100 m. Migrating only shallow particles downward would be a more realistic scenario as well as distributing the particles within a broader depth range rather than fixing them to a single specific depth. Many other, perhaps more realistic scenarios are possible next steps. However, in-situ data of larvae depth distributions would be required to properly parameterize more realistic scenarios. The aim of the simple scenario modeled here was to illustrate the potential effects on connectivity of an ontogenetic vertical migration to 50 m (with depth keeping) in a rapidly evolving water column with deep stratification and strong shear.

The numerical experiments presented here are deterministic and represent a population where all larvae develop and behave identically, without actively responding to its environment. Real larvae are complex organisms, with strong inter-specific and potentially intra-individual variability in physiology and behavior, constantly reacting to their environment. Complex models with behavior cueing on the environmental conditions experienced by the virtual larvae have been developed (e.g., Armsworth, 2001; Staaterman et al., 2012; Wolanski and Kingsford, 2014). Assuming that larvae are well adapted to the pelagic phase, larval behavior, particularly sensing, orientation and swimming abilities would enhance their probability of finding suitable settlement habitat, which might reduce interannual variability in settlement success. However, when challenged by increased environmental variability due to climate change effects, their strategies may not be guaranteed to work. The numerical experiments presented here, although idealized, serve as an initial effort to develop hypotheses that might be examined using more complex models and empirical studies. Monitoring recruitment of coral reef organisms is basic to assessing the effects of environmental variability on settlement success. Having long term time series of recruitment of coral reef dependent species in the Kenya-Tanzania region would be valuable for "tuning" models, as has been done for other coral reef regions (i.e., Sponaugle et al., 2012).

The fraction of released larvae that settle on suitable habitat is highly sensitive to the individual's habitat perception and swimming abilities; further knowledge regarding the capabilities of coral reef larvae to perceive, navigate and settle on suitable habitat is a very important and a challenging piece of information to obtain. Both in-situ and laboratory observations of larval development and behavior are needed to further increase the realism of modeling experiments. The dependence of PLD on temperature is well established for aquatic organisms (O'Connor et al., 2007) but observations for the studied genera are insufficient to adequately parameterize the functional response between temperature and PLD. The inclusion of temperature dependent PLD in bio-physical models is essential for examining climate change effects on connectivity and settlement success of marine larvae (Lett et al., 2010; Figueiredo et al., 2014). Changes in ocean circulation will alter connectivity patterns, but physiological effects due to the increased temperature will also have an important effect (Munday et al., 2009; Lett et al., 2010; Kendall et al., 2016). Reduced pelagic larval durations are expected under faster developmental rates, which could lead to a reduction in dispersal distances and the spatial scale of connectivity (Munday et al., 2009; Lett et al., 2010). Bio-physical modeling connectivity studies including temperature dependent PLD report increased local retention (Figueiredo et al., 2014; Andrello et al., 2015) and significant changes in Marine Protected Area network interconnectivity (Andrello et al., 2015) under climate change scenarios. Well-informed idealized experiments that include temperature dependent PLD of virtual larvae are a future direction for assessing the effects of climate change scenarios on connectivity and recruitment of coral reef organisms in the East-African coast.

Larvae in the ocean are subject to mixing at scales smaller than those represented in the ocean circulation model. In particle tracking models these unresolved motions are often implemented as a random walk scaled by the model diffusivity. Simulations that implement a random walk to mimic diffusion are considered more realistic but computationally expensive. We conducted a few sensitivity experiments that included (3D) variable vertical diffusion. Simulations that included vertical diffusion (not shown) reproduced the main connectivity patterns produced by the 3D advective only experiments, but with smaller connectivities—mostly due to greater vertical dispersion that subjected larvae to greater horizontal flow variation. These results are probably more realistic for early or weakly swimming larvae (e.g., coral species) that are unable to maintain their vertical position in the water column in the presence of vigorous vertical mixing.

While reef-to-reef connectivity is important in metapopulation ecology, regional connectivity is expected to be more robust to the uncertainty introduced by the oceanographic and biological assumptions made in these models. Region to region connectivity matrices synthesize the information of reef to reef connectivity matrices, making it more manageable and easier to interpret. The regional summary could assist managers, policy makers and the general public to understand the interconnections among coral reef regions due to pelagic larval dispersion of their local populations. Previous bio-physical connectivity studies highlight the importance of considering larval connectivity at regional levels when trying to prioritize the implementation of management strategies for both conservation and fisheries enhancement goals. One of the insights of examining connectivity at a regional scale is that the importance of international connections becomes obvious, as has been shown by Kough et al. (2013) for the Mesoamerican reefs and by Rossi et al. (2014) for the Mediterranean Sea. In all numerical experiments Tanzanian reefs were an important source of settlers to Kenyan reefs; this provides insight and guidance on the spatial scale at which management strategies are required and points to the need for regional international collaborations in order to provide enduring conservation measures and protection to the east African coral reef ecosystem.

This modeling study is a first approach to understanding the connectivity among coral reef populations in a data poor region. The information provided, even though preliminary, presents a general pattern of the potential regional connectivity and identifies particularly resilient and vulnerable areas as well as the hydrodynamic features driving the connections. Spatial scales of connectivity and settlement success rates are within the ranges reported by other bio-physical modeling studies for similar genera in other coral reef regions (Paris et al., 2007; Dorman et al., 2015). However, the robustness of the connectivity patterns presented needs to be further evaluated by performing experiments for more years and longer spawning seasons, and carrying out more extensive sensitivity analysis to the model assumptions. After gaining more confidence in the modeled connectivity patterns, the information provided by this modeling study could be carefully and critically evaluated, in order to be applied to optimize the effectiveness of marine protected area management and other marine protection efforts. Further modeling experiments similar to those presented here, but better informed by empirical data, and including the capability of larvae to respond to the ocean conditions will provide greater detail on the complex biophysical interactions that occur in the sea, and will provide a more realistic, and less uncertain, representation of connectivity patterns. These results will aid in understanding how a range of species specific individual responses influence

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### AUTHOR CONTRIBUTIONS

CGMA, HB, and YS designed the experiments, analysis and paper. CGMA Carried out the numerical modeling experiments and analysis and wrote initial draft of the paper. HB and YS revised and improved the initial manuscript.

### FUNDING

CGMA was partially funded by CONACYT Mexico.

### ACKNOWLEDGMENTS

Thanks to Dr. Ted Strub for access to computing resources. To CEOAS-OSU technicians Eric Beals and Tom Leach for technical support. To CONACYT Mexico for scholarship funding for CGMA, and to the UK National Oceanography Centre (NOC) for allowing her time to finalize and review this paper. HB thanks the North Pacific Marine Science Organization (PICES) for allowing time for him to contribute to this paper, and for payment of the article processing fee.

### SUPPLEMENTARY MATERIAL

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**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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