Edited by: Aristides (Aris) Moustakas, Universiti Brunei Darussalam, Brunei
Reviewed by: Slawomir Antoni Lux, inSilico-IPM, Poland; Antonios D. Mazaris, Aristotle University of Thessaloniki, Greece
*Correspondence: Emma Samson
This article was submitted to Environmental Informatics, a section of the journal Frontiers in Ecology and Evolution
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Individual-based models (IBMs) incorporating realistic representations of key range-front processes such as dispersal can be used as tools to investigate the dynamics of invasive species. Managers can apply insights from these models to take effective action to prevent further spread and prioritize measures preventing establishment of invasive species. We highlight here how early-stage IBMs (constructed under constraints of time and data availability) can also play an important role in defining key research priorities for providing key information on the biology of an invasive species in order that subsequent models can provide robust insight into potential management interventions. The round goby,
Invasive species are one of the driving forces behind biodiversity loss, and their persistence in non-native areas can result in substantial environmental and economic costs (Pimentel et al.,
There is a continual need for the development and improvement of both new and existing conservation management strategies either to control the spread, reduce biomass or, if possible, to eradicate an invasive species from its non-native environment (Ojaveer et al.,
The accuracy and utility of process-based models for ecological forecasting has vastly improved over the past few years (Cuddington et al.,
Often stakeholders encounter a model only at the stage where it has been tightly parameterized and validated by ecological researchers. Traditional thinking tends to be that a model needs to be well-parameterized and validated before it can be useful in an applied context. Indeed, an often encountered view is that it can be dangerous for a modeler to demonstrate an “immature” model to stakeholders due to risks of losing credibility or of providing unsound advice. However, developing a well-tested model can be a time consuming process, and this is problematic especially when early intervention is often critical for successful management outcomes. It has been repeatedly highlighted that early involvement of stakeholders into ecological management efforts increases chances for success (Bayliss et al.,
As a case study, we use our experience of developing an early-stage model for the round goby's spread through the Baltic Sea in order to facilitate stakeholder engagement. The round goby (
Here, we highlight how a spatially explicit ecological simulation platform, RangeShifter (Bocedi et al.,
The work described in this paper has been designed to be consistent with the adaptive modeling approach for ecological forecasting outlined in Urban et al. (
A schematic representation of the modeling process, from initial literature search to the proposed next steps. Model refinement and evaluation is iterative, reflecting the alterations that are constantly made to the model during the calibration process. Once refined, this model should then be reintroduced to stakeholders for further co-development.
A symposium centered around the spread and impact of the round goby in the Baltic Sea was held in Kalmar, Sweden in June 2016. The organization of the symposium was headed by the Swedish Agency for Marine and Freshwater Management
At the end of the presentation a specific call for input was issued: a slide stating “What we hope to get from you…” followed by six suggested inputs: Specific parameters (e.g., demographic and dispersal), The estimated introduction sites (and when), Patterns for comparing model outputs with spatial and temporal patterns of density and sediment type and habitat, Proposed management techniques. Following the presentation there was an open discussion with a call for feedback and input. In transdisciplinary projects it is important that both scientists and non-academic partners contribute on an equal footing (Hadorn et al.,
The interaction with stakeholders identified essential knowledge gaps, which would have gone unnoticed by us as scientists alone. Crucially the interactions also provided a clear focus in terms of what a useful model would need to include and would need to be able to predict in order that it was most useful to the stakeholders. Also, personal communications with multiple researchers and stakeholders present at the meeting provided an insight into the current understanding of the round goby's spatial presence in the Baltic Sea that was not obvious from searching the literature, including information on new studies that will yield high quality data. Three essential qualitative outcomes of the symposium that were derived from the interactions between modeling team and stakeholders provided strong focus for future work. These related to model building such that key processes driving the spread dynamic are properly represented and parameterized and to developing the model to ensure its relevance for informing key management decisions:
First: A knowledge gap regarding the depth of goby dispersal was highlighted as potentially crucial. Prototype model results shown at the workshop included one suggesting that the invasion dynamic is likely to be very sensitive to the depth range over which gobies can disperse. At the workshop attendees noted that adult gobies are sometime caught in deeper water. However, it was suggested that this occurs during winter months and may reflect some adults exhibiting seasonal migration to deeper waters. It became obvious that whether gobies disperse through deep water or disperse solely in shallow areas is currently unknown. Understanding the depth range of goby dispersal may be of great importance to those involved with the round goby invasion for a number of reasons. Depth acting as a barrier to dispersal may be utilized in numerous management protocols to impede or inhibit goby spread into undesirable areas. Furthermore, understanding goby dispersal depth helps to predict future areas that may be under threat of round goby invasion, even without a human-mediated element to the dispersal. Identifying the potential importance of the depth sensitivity of dispersal for patterns of goby spread was a novel outcome of the workshop that will motivate new empirical work.
Second: Threats of the round goby's invasion of the freshwater systems that connect to the Baltic Sea, particularly with regards to Salmonids were identified, as the round goby may devastate their populations through egg consumption (Chotkowski and Ellen Marsden,
Third; The threat that the round goby poses to the long-tailed duck (
We used a spatially explicit, individual-based model (IBM), RangeShifter (Bocedi et al.,
To represent the Baltic Sea, a gridded seascape was created in ArcGIS 10.3.1 using raster data extracted from the EMODnet Bathymetry portal
At model initiation, individuals were assigned to cells within species introduction points at half carrying capacity. In each year, the overall dynamics consists of reproduction, death of adults, and offspring dispersal. Reproduction by each individual is determined by a stochastic draw from a Poisson distribution having a mean set by the maximum growth rate at low density and subject to density-dependent reduction following Maynard-Smith and Slatkin (
Once reproduction has taken place, individuals could emigrate away from their natal cell, an action dependent on the local density within the cell. If an individual left the cell, its trajectory was modeled using the Stochastic Movement Simulator (SMS; Palmer et al.,
A key issue that emerged from the stakeholder workshop was a lack of knowledge relating to the depths of water through which gobies can disperse. This issue was, in part, highlighted by some of the runs of the prototype model, demonstrated at the workshop, in which it was clear that including a depth threshold resulted in very different spread patterns than omitting one. Accordingly, cell cost was set in relation to a threshold depth for movement: the cost of traversing a cell of the depth threshold and deeper was set to a very high value, and the cost of traversing a cell above the depth threshold was set to a very low value. In doing so, individuals were much less likely to travel into deeper water than that set by the threshold. For all depths, each step an individual took had an associated spatially and temporally constant mortality risk.
Upon reaching a new cell, an individual had the opportunity to settle or continue movement to a different cell. The decision to settle was density-dependent. If the population density was too high in a cell, then the individual would not settle but continue to disperse to a neighboring cell (Bocedi et al.,
The majority of the parameters required for the model were not widely available in the literature or through online resources. Consequently, in order to calibrate the model parameters, the Gulf of Gdansk was chosen, as detailed spatial information regarding the goby's spread through the area was available. This spatial information was primarily obtained from the NOBANIS fact sheet, produced by Sapota (
Parameter values were calibrated using a pattern-oriented modeling approach (POM) (Grimm et al.,
RangeShifter settings and parameter values for Gulf of Gdansk and Baltic Sea models.
Cell-based landscape, cell size | 2,500 m | 2,500 m | |
Rows × Columns | 48 × 43 | 625 × 717 | |
Habitat codes (representing depth classes) | 1–12 | 1–12 | |
Female-only model, no stage structure | |||
Carrying capacity (per ha) (all habitats) | 10.0 | 10.0 | |
Mean growth rate at low density | 1.2, 1.4, 1.6 | 1.2, 1.4, 1.6 | |
Competition coefficient | 1.0 | 1.0 | |
Density-independent emigration rate | 0.7 | 0.7 | |
Transfer model–SMS | |||
Cost for depth layers above threshold | 1 | 1 | |
Cost for depth layers below threshold | 100,000 | 100,000 | |
Perceptual range (cells) | 1 | 1 | |
Perceptual range method | 1 | 1 | |
Directional persistence | 1.0 | 1.0 | |
Per-step mortality risk | 0.1, 0.2, 0.3, 0.4 | 0.1, 0.2, 0.3, 0.4 | |
Density-dependent settlement: | |||
Maximum probability | 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 | 0.4, 0.5, 0.6, 0.7, 0.8 | |
Slope | −10.0 | −10.0 | |
Inflection point | 1.1 | 1.1 |
To assess the accuracy of the model for each parameter combination, four metrics were used, in addition to visually inspecting the model output. Model
In order to calculate the sensitivity, specificity, AUC and κ for each parameter combination, each combination was repeated over 100 simulations. These metrics were calculated using the PresenceAbsence package in RStudio 3.3.1 (Freeman and Moisen,
The species introduction points of the Baltic Sea, where populations were initiated, were estimated using information available in the literature (Kotta et al.,
Model accuracy was most strongly influenced by the depth threshold: 76% of the variance in κ was explained by depth, as compared with 11% by the maximum settlement probability, 4.6% by the per-step mortality risk, 3.3% by the maximum growth rate and negligible amounts by interactions. The model was most accurate for a depth threshold between 10 and 25 m, and accuracy increased slightly with decreasing settlement probability and mortality risk and with increasing growth rate (Figure
Fit of the RangeShifter model for the Gulf of Gdansk: marginal mean values of κ (kappa) in relation to
An example of the effect of varying the depth threshold of dispersal on the accuracy of the predicted population distribution, all other parameters being held constant.
0–5 | 0.587 | 0.876 | 0.432 | 0.843 |
5–10 | 0.471 | 0.997 | 0.588 | 0.803 |
10–15 | 0.740 | 0.993 | 0.807 | 0.906 |
25–30 | 0.897 | 0.930 | 0.757 | 0.957 |
30–35 | 0.892 | 0.904 | 0.699 | 0.944 |
35–40 | 0.888 | 0.889 | 0.666 | 0.935 |
40–45 | 0.883 | 0.881 | 0.647 | 0.932 |
45–50 | 0.883 | 0.871 | 0.628 | 0.924 |
Below 50 | 0.901 | 0.689 | 0.379 | 0.836 |
Example model outputs from four different parameter combinations in the Gulf of Gdansk. X and Y cell numbers represent the cell number, or coordinates, on the gridded landscape created for the modeling exercise. Green cells represent a cell that was colonized by populations in each of the 100 repetitions (i.e., 1.0 refers to 100% of repetitions). Model
An example of the plots used to assess the accuracy of parameter combinations, using kappa, specificity, and sensitivity measures. The accuracy measures vary from zero to one, in which a value of one represents a perfect accuracy measure and zero a poor one. The cutoff threshold represents the number of repeat simulations a cell was required to have been colonized, in order to be characterized as a presence in the final model evaluation, with 1.0 being 100% and 0.0 being 0% of repeats.
Despite obtaining a range of accurate parameter combinations for the Gulf of Gdansk, when they were applied to the entire Baltic, the overall model output was poor when compared to the extensive observed distribution spanning a substantial proportion of the Baltic coastline as reported in the literature (Figure
Comparison between
In this study, we rapidly developed a prototype model of round goby spatial dynamics that was used to facilitate early engagement with stakeholders. We subsequently combined data available in the literature and stakeholder input in order to calibrate the IBM such that it simulated the round goby's spread throughout the Gulf of Gdansk to a high level of accuracy. We then used the calibrated model to simulate its spread through the Baltic Sea, despite the limitation of imprecise and potentially inaccurate presence data. Our experience demonstrates the value of involving stakeholders early in the modeling process. Prototype model results had indicated that predicted spread was highly sensitive to the inclusion of a depth threshold for dispersal, and the subsequent stakeholder communication highlighted how little is currently understood about goby dispersal at various depths. Consequently, various depth thresholds were incorporated into the modeling, in order to assess the impact of depth on model accuracy and therefore goby dispersal. We demonstrated how, by using known spread patterns, it can be possible to use the model to infer details of the dispersal process, in this case related to the depth threshold of goby dispersal. In detail, we could show that that the limit to dispersal depth of the round goby lies between 10 and 25 m. Empirical data are now required on the depth sensitivity of dispersal such that a robustly parameterized model can be used by the stakeholder/modeler grouping in further steps toward identifying management options. The involvement of stakeholders as early as possible in the process and their regular inclusion throughout as co-developers of the modeling will facilitate a cooperation between scientists and stakeholders in putting possible management measures into practice.
Research has identified that the long lag time between research and its publication hinders managers of biological invasions to make use of important results such as our models generated (Matzek et al.,
In our study, we put these theoretical predictions into practice and engaged in a modeling process that used stakeholder input as an essential component. Stakeholders provided two essential inputs regarding future model optimization: providing information on where higher quality distribution data would be available in the near future and on the priority of including depth in the model. Stakeholders contributed their knowledge and understanding on an equal footing. In an excellent recent contribution on how to co-develop models with stakeholders effectively to address pressing ecological problems, Parrott (
A potential advantage of the approach we took in this study is that the stakeholders naturally take the role as the species/system experts, and the potential risk whereby stakeholders perceive that the researchers assume the role of experts and tell them how their system works is reduced. One potential disadvantage of such an approach is that researchers cannot glean data from stakeholders in the form of quantitative assessments through e.g., specifically designed questionnaires. This disadvantage, however, is compensated by the fact that stakeholders can contribute their knowledge freely through unstructured interactions with researchers. For that, it is clearly critical that the modeling team gain the confidence of the stakeholders, but that need not be by having acquired detailed understanding of the particular study system in advance of a first meeting. Indeed, we suggest that the effective establishment of a model co-development group may be facilitated if this is actually not the case and at the start of the process there is a clear division of expertise between modelers and stakeholders. As the process of co-development of a model proceeds, both researchers and stakeholders can build upon this first interaction on an equal footing albeit with quite different expertise. Our study provides a practical example for future model building efforts on how to rapidly initiate transdisciplinary projects, which is absolutely vital if models are to be successfully used to inform early intervention against invasive species.
Calibrating the model with precise spatial data produced a highly accurate model that simulated the spread of the goby throughout the Gulf of Gdansk over an 11 year period. The model outputs obtained from the calibration process highlighted the key role of the depth threshold to movement. However, when scaled up through space and applied to the whole of Baltic Sea, the model failed to predict a distribution similar to that observed in the literature. The failure to produce a model for the Baltic Sea with a high degree of accuracy has several implications.
One of the main downfalls of the Baltic model seems to occur from uncertainty regarding introduction points. In order to obtain a predicted presence from the model that was similar to that of the observed presence, further introduction points would need to be added, if the parameters obtained from Gdansk were to be used. Although short-distance (~30 km/year) active migration appears to occur in some local areas (Azour et al.,
Furthermore, the presence data used to produce the observed map for model calibration was at a coarse spatial scale. It may be that the goby's presence at various depths in the Baltic was not represented in the observed distribution at a fine enough resolution for accurate model assessment. Given more precise presence data, at a finer resolution, the accuracy of the models predicted goby presence in the Baltic Sea could improve substantially. One of the benefits of such models is the ability to identify on which future data collection efforts should be focused. This is in agreement with the recent call for mandatory catch records and citizen science programs in order to collect data on the round goby (Ojaveer et al.,
In order to replicate the observed goby distribution throughout the Gulf of Gdansk, a dispersal depth limit of ~20 ± 5 m produced the most accurate model. It is nevertheless important to note that this was calibrated using one area of the Baltic Sea. Thus, to obtain more accurate results, presence data spanning various depths over more locations in the Baltic Sea are required. Hitherto there have however not been any studies dedicated to investigating this aspect of the biology of the species. Furthermore, as round goby is not a commercial species, no catch-related depth information is available from the fishery. The sparse information that exists is from a Polish young fish surveys program, showing that, although generally considered a shallow water inhabitant, high catch rates occur at 50–60 m depth during winter months (November and January–March) (Grygiel,
Although not identified by the stakeholders in the present study, parameters besides depth should be evaluated for their potential relevance for dispersal tendency. Charlebois et al. (
Not only the abiotic environment, but also personality-dependent behaviors can be important at the invasion front, where local sub-populations consist mostly of bigger/older asocial individuals (Thorlacius et al.,
Until further information is available, our modeled depth trial results may be used as a preliminary guide to assess management regimes and prioritize management areas for vulnerable species. For example, from an applied perspective, the model results raise the prospect that artificial deep channels may stymie the spread of the species. Telemetry-based data on the spread of invasive crayfish in a Central European large lake has also suggested a spread along the shoreline down toward a certain depth isocline. This might make it plausible to slow the natural spread by barriers (Hirsch et al.,
In a practical application of this transdisciplinary approach, we designed a preliminary modeling experiment as an example of how detailed models developed with stakeholders can inform risk assessment of invasive species and help to identify priority areas for management. A key issue that emerged through the stakeholder interaction is the implication of the goby's invasion of the over-wintering habitat of the western Siberian and northern European wintering populations of the endangered long-tailed duck. The populations of the duck may be threatened by the round goby through exploitative competition for food (Hearn et al.,
In this study, we made use of an IBM to simulate the spread of the invasive species. However, it is important to recognize that alternative approaches exist that could equally well be used in transdisciplinary work where models are co-developed to inform understanding and management of invasive species. Indeed, in future studies one valuable approach will be to utilize more than one of these modeling approaches in concert. For example, there can be considerable benefits of jointly developing a stochastic IBM and a typically deterministic integrodifference model to estimate rates of spread (e.g., Travis et al.,
A key challenge is to move beyond the approach most often taken in what are often termed hybrid species distribution models and to relate the environmental variables directly to the key demographic traits (e.g., reproduction, survival, and dispersal), rather than simply using the environmental niche model to demark suitable and unsuitable environments for a focal species. However, many such relationships have yet to be established in detail (see Zurell et al.,
We calibrated an IBM for the round goby, using spatial presence information from the invasion of the Gulf of Gdansk. Stakeholder involvement with question design provided both a preliminary answer and future research directions. It is important that we encourage a culture of publishing work on the process of co-development of models, such that we can learn from one another's successes and failures. This will require more papers, such as this one, that are published at potentially earlier stages of model development and before models are necessarily ready for use to inform management action. In this instance, while short of being ready to inform management action, the model has helped to emphasize the requirement for investment in gathering greater empirical understanding of the depth at which round goby disperse. In the next part of the co-development modeling spiral (Parrott,
Conceptualization: ES, JT, SP, TB, PH, and JB. Formal analysis: ES and SP. Investigation: ES, SP, JT, TB, PH, and JB. Methodology: ES and SP. Project administration: ES and JT. Resources: JT. Supervision: JT. Validation: ES and SP. Visualization: ES. Writing - original draft: ES, SP, JT, PH, JB. Writing - review and editing: ES, SP, PH, JB, JT, TB.
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 Supplementary Material for this article can be found online at:
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