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Edited by: Célia M. Teixeira, Center for Marine and Environmental Sciences (MARE), Portugal

Reviewed by: Vera Sequeira, Center for Marine and Environmental Sciences (MARE), Portugal; Mohammad Sadegh Alavi-Yeganeh, Tarbiat Modares University, Iran; Md Abu Hanif, Chonnam National University, South Korea

*Correspondence: Antonio Aranis,

This article was submitted to Marine Fisheries, Aquaculture and Living Resources, a section of the journal Frontiers in Marine Science

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) and the copyright owner(s) 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.

Araucanian herring,

The Humboldt Current System (HCS) in the South Pacific Ocean (SPO) is among the most productive in the world (

This system, characterized by its high climatic variability, makes small pelagic populations fluctuating, with alternating inter- and intra-annual preponderance leading to relatively dense shoal formations with a marked daily cycle. Shoalings are highly aggregated during the day and dispersed at night together with less dense surface aggregations (

These small pelagic species have a coastal distribution within 50 nautical miles (nm) from the coast. Biological productivity is generally high due to seasonal upwelling events, mainly from mid-September to March, the austral spring–summer period (

Administratively, extraction has been regulated since 2001 through fishing quotas and biological reproductive and recruitment periods since 1996. Although these measures strongly regulate fishing, they also led to periods of different intensities both in the industrial and artisan sectors (

Total pelagic landings in the zone were sustained for some 15 years by Araucanian herring stock, a resource that spurs fishing operations mixed with anchovy. The average catch from 2010 to 2016 was 479,000 t, mainly by the artisan fleet (78%). A hegemonic presence of the species is evidenced in artisan fishery, partly reflecting the magnitude ratio of biomass and assigned quotas.

Recruitment or entry processes of juvenile Araucanian herring have been detected since 1999 using hydroacoustic methods (

Size structure is a key biological trait of the population. To be contrasted correctly with other structures of different strata, it requires weighing upon capture. Hence, frequency-to-size measurements expand from catch in weight or number, representing the biomass or abundance by size class. This procedure requires the concurrence of the three main sampling components, catch or landing, length, and weight of the specimens. However, the imbalance of catch magnitudes affects the correct representation and entails uncertainty about the correct decision when integrating data that can vary spatially, temporally, and in relation to origin (artisan-industrial). In this context, average weights are not always available, though these data are essential for estimating various indices, functions, and statistics. To solve this problem, it is necessary to establish decision criteria regarding the feasibility of finding or obtaining alternative information and assessing another potential and representative solution that replaces the missing one. Lacking any of these estimates implies that significant volumes of catch or fraction landed cannot be processed, with potentially important consequences for the assessment of population structure, demographic fractions, and state of the fisheries. This has led to the need to define criteria for a different estimate of the length–weight relationship, first allowing to resolve the relevance of integrating data and second to offer the best solution for correct integration and representation. In sum, to set a goal for evaluating the validity of integrating pelagic fish length information from samples obtained from various sources, exploring, designing a statistical procedure that allows integrating different data sources or clusters, and incorporating the meta-analysis approach (

In this section, we introduce the data set and study area where the samples have been collected. Afterward, we present the Bayesian procedure to estimate the probability of catch of each length and describe the meta-analysis method to estimate the length distribution. Finally, we present the meta-regression used to test whether there are significant differences between vessel types for each length.

The maritime space of Chile’s central-south is immersed in the Humboldt System, home to highly diverse pelagic species. Among the species with coastal distribution, Araucanian herring and anchovy stand out. In latitudinal extension, pelagic fishing in the zone is taking place in the area between 32°10

The study area included the maritime area from (lat-long) to (lat-long), 200 nm from the coast. Biological data came from routine samplings of the main central-south pelagic fisheries monitoring program, developed by the Fisheries Development Institute [Instituto de Fomento Pesquero (IFOP)]. The research was carried out with the help of artisan and industrial fleets in the ports of San Antonio (Valparaíso Region), Talcahuano, San Vicente, Lota and Coronel (Biobío), Valdivia (Araucanía), and Corral (Los Ríos), as detailed in

Fishing zones and administrative regions of central-south Chile (31°–49° LS).

Fishing area in the central-south macrozone.

Fishing areas | Latitude (S) |
---|---|

San Antonio | 32° 10 |

Talcahuano | 34° 50 |

Valdivia | 38° 30 |

Chiloé | 41° 00 |

Guaitecas | 43° 30 |

Regional coastal limits for catch analysis and industrial and artisan landings.

Regions | North | South |
---|---|---|

Valparaíso | 32° 10 |
33° 53 |

Libertador General Bernardo O’Higgins | 33° 53 |
34° 41 |

Maule | 34° 41 |
36° 00 |

Ñuble | 36° 00 |
36° 26 |

Biobío | 36° 26 |
38° 28 |

Araucanía | 38° 28 |
39° 23 |

Los Ríos | 39° 23 |
40° 14 |

Los Lagos | 40° 14 |
43° 44 |

General Carlos Ibáñez del Campo Region of Aysén | 43° 44 |
48° 49 |

Catches of Araucanian herring were preferably obtained in a normal fishing environmental period in summer–autumn in coastal and protected areas, favorable to upwelling and greater availability of food, such as the Gulf of Arauco and the Bay of Concepción, frequent areas of fishing for the commercial fleet and special monitoring in which during the summer period concentrations of chlorophyll greater than 1 µg/l are normally found. In areas adjacent to the coast, with higher primary productivity (>1 µg/l) and food, which leads to a higher concentration of zooplankton, such as euphausiids and copepods (

Biological data comprise lengths of sampled individuals that originated mainly from commercial fishing (high-catch vessels) and research fisheries (low-catch vessels) catch between January and July 2018. The nets widely used in this small pelagic fishery are virtually the same in terms of length and mesh size of the 12.7-mm fine bodies, which is the most frequent. We used the meta-analysis technique to estimate the distribution of Araucanian herring catch length with data from 18 vessels, three commercial fishing (high-catch vessels) and 15 research fisheries (low-catch vessels). The data set is presented in

Biological data of commercial fishing (vessels 13, 16, and 17) and research fisheries. For each vessel and length, the number of sample individuals is reported.

Vessels | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Length | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |

8 | 0 | 0 | 14 | 0 | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

8.5 | 0 | 0 | 32 | 0 | 48 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

9 | 0 | 0 | 67 | 14 | 57 | 10 | 8 | 0 | 2 | 0 | 0 | 0 | 0 |

9.5 | 0 | 0 | 42 | 27 | 50 | 12 | 23 | 0 | 16 | 0 | 0 | 0 | 0 |

10 | 3 | 29 | 24 | 58 | 19 | 34 | 40 | 2 | 41 | 0 | 0 | 0 | 0 |

10.5 | 61 | 76 | 10 | 48 | 7 | 38 | 52 | 2 | 41 | 0 | 0 | 4 | 0 |

11 | 84 | 62 | 1 | 34 | 0 | 47 | 30 | 3 | 45 | 0 | 0 | 7 | 0 |

11.5 | 24 | 21 | 0 | 17 | 0 | 26 | 19 | 8 | 38 | 0 | 1 | 11 | 0 |

12 | 2 | 10 | 0 | 2 | 0 | 22 | 9 | 9 | 12 | 16 | 11 | 25 | 0 |

12.5 | 0 | 2 | 0 | 0 | 0 | 10 | 12 | 33 | 6 | 14 | 18 | 13 | 0 |

13 | 0 | 1 | 0 | 0 | 0 | 0 | 3 | 27 | 1 | 19 | 12 | 29 | 2 |

13.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 10 | 1 | 0 | 6 | 8 | 11 |

14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 10 | 0 | 0 | 5 | 5 | 22 |

14.5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 16 | 0 | 0 | 0 | 0 | 41 |

15 | 7 | 0 | 0 | 0 | 0 | 0 | 0 | 31 | 0 | 0 | 0 | 0 | 35 |

15.5 | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 42 | 0 | 0 | 0 | 0 | 16 |

16 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 0 | 0 | 0 | 0 | 4 |

16.5 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 7 | 0 | 0 | 0 | 0 | 1 |

17 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 |

Total | 203 | 201 | 190 | 200 | 203 | 201 | 196 | 232 | 203 | 49 | 53 | 102 | 132 |

Vessels | |||||||||||||

Length | 14 | 15 | 16 | 17 | 18 | ||||||||

8 | 0 | 0 | 0 | 0 | 0 | ||||||||

8.5 | 0 | 0 | 0 | 0 | 0 | ||||||||

9 | 0 | 0 | 0 | 0 | 0 | ||||||||

9.5 | 0 | 0 | 0 | 0 | 0 | ||||||||

10 | 0 | 0 | 1 | 1 | 0 | ||||||||

10.5 | 0 | 0 | 10 | 2 | 0 | ||||||||

11 | 0 | 7 | 25 | 4 | 0 | ||||||||

11.5 | 8 | 10 | 33 | 8 | 0 | ||||||||

12 | 29 | 22 | 47 | 10 | 0 | ||||||||

12.5 | 66 | 62 | 35 | 27 | 2 | ||||||||

13 | 66 | 48 | 25 | 41 | 8 | ||||||||

13.5 | 26 | 27 | 17 | 37 | 24 | ||||||||

14 | 18 | 18 | 10 | 35 | 83 | ||||||||

14.5 | 4 | 10 | 8 | 11 | 38 | ||||||||

15 | 0 | 2 | 1 | 2 | 41 | ||||||||

15.5 | 0 | 0 | 0 | 1 | 13 | ||||||||

16 | 0 | 0 | 0 | 0 | 7 | ||||||||

16.5 | 0 | 0 | 0 | 0 | 1 | ||||||||

17 | 0 | 0 | 0 | 0 | 0 | ||||||||

Total | 217 | 206 | 212 | 179 | 217 |

Usually, the sampling design to estimate the size structure corresponded to two-stage random stratified sampling, where the stratum represented the port or fishing area and the month (

The sampling design associated with landing size structure corresponded to a two-stage design within a study stratum or domain. First-stage units were from trips, and second-stage units were from samples. The size structure of catches sampled onboard corresponded to a three-stage design, in which first-stage units were from trips, second-stage units were from sets, and third-stage units were specimens (

The fishing platforms are operating under similar designs, which are similar for both activities (structural characteristics and fishing power). This made it possible to have comparative information without bias and supported by extensive institutional technical experience.

Before the meta-estimation process, we first modeled the random vector (_{1}, _{2}, … , _{19}) that represented the quantity of Araucanian herring caught per vessel for each of the 19 lengths, 8.5, 9, 9.5, … , 16.5, 17. We assumed that the random vector _{1}, _{2}, … _{19}), that is

with pi ≥0, _{1}, _{2}, …, _{19}) is the vector of capture probabilities for lengths, 8.5, 9, 9.5, … ,16.5, 17 cm and _{i} is _{1}, _{2}, …, _{19}) of the multinomial distribution and their corresponding variances. The Bayesian formulation of the model is represented by:

that is, the _{1}, _{2}, …, _{19)}. Then, the posterior distribution of

We had a closed expression for the posterior distribution of vector

and

When _{1}=_{2}=⋯=_{19}=1, which meant using a non-informative

and

We calculated the variance of each parameter _{i}

After carrying out the Bayesian estimation, we obtained a probability matrix _{ij}
_{ij}
_{ij}
_{ij}
_{ij}
_{ij}

We used the meta-analysis technique proposed by _{ij}
_{ij}
_{i}

The meta-analysis integrated data from 18 vessels to generate a common estimate for each length _{j}
_{j}

Where _{j}
^{2}, and _{j}
_{j}
_{j}
_{j}

To estimate the variance τ^{2} of model (2), there are several methods. One that is relatively easy to implement, since it does not require an iterative process or complex calculations, is the estimator by the moment method proposed by ^{2} as:

The global effect was estimated as weighted average of each vessel’s individual estimators, where weights were calculated as the inverse of the sum of the variance of the individual vessel plus the variance between vessels, that is,

with

To obtain the estimate of

Meta-regression (

with distributional assumptions τ_{j}
^{2}) and independent

All analyses were performed with the R programming language using the MCMCpack and metafor packages. The code is available upon request from the authors.

The data used to estimate Araucanian herring catch for 19 lengths for each of the 18 vessels through meta-estimation are detailed in

After obtaining the Bayesian estimates for each length {8, 8.5, 9, … ,16.5, 17}, the estimates for each of the 18 vessels were combined using the previously described meta-analysis methodology. The process was repeated 19 times for each length. The meta-estimate was first performed by separating the data from the samples obtained by each type of vessel (commercial and research ones). Then, a meta-estimate was performed considering the samples jointly from both types of vessels.

Meta-estimation of the length distribution for research

Research catch vessels showed a higher probability of catching Araucanian herring of lengths ranging from 9 to 13 cm. Commercial catch vessels showed a higher probability of catching Araucanian herring of lengths from 12.5 to 15.5 cm. To verify the existence of statistically significant differences in the probability of capture for the different lengths, a meta-regression was used considering a covariate that indicated the type of vessel.

p-values of the hypothesis test that the probability of catch at each length between research catch and commercial catch vessels is equal (red dot, not significant; light blue dot, significant).

Results show differences in the distribution of Araucanian herring length between fishing with commercial and research catch levels for certain sizes.

The meta-analysis methodology combined with Bayesian methods provides a framework to integrate information on Araucanian herring lengths from commercial and research catch vessels in order to estimate the size distribution structure. Our findings were applied in the reports that are delivered to the undersecretary of fisheries and its scientific committee in order to define the modifications of the biological closures of recruitment. According to the results, there are differences in the distribution of Araucanian herring length between commercial and research catch fishing related to certain sizes.

The correct application of a method that overcomes the feasible integration difficulties of sizes in pelagic fish will allow solving a technical issue. Results will also be applied in practical terms for better data interpretation and management, especially for recruitment processes in which diverse population components coexist, making analysis and result difficult. In sum, these results allow to improve, integrate, or segregate information under an objective statistical criterion. For example, this has been applied to the commercial fishing activity and studies under design and scientific methods; it also allows verifying the correct use of information from different vessels, fleets, and fishing gear.

Particular attention should be paid to data corresponding to oceanographic thermal anomalies that could alter biological conditions, especially average specimen weights. It is important to be careful with successive approximations when data are inserted in studies during a warm event (

The practical application can be useful for similar studies of fishery analysts or of another nature, in which there must be contrasted levels of information that are very dissimilar in terms of the size of the sample or universe that they represent, being relevant

The original contributions presented in the study are included in the article. Further inquiries can be directed to the corresponding author.

Conceived and designed the study: AA, RDLC, and CM. Data curation: AA, MR, LC, AG, and KW. Analyzed the data: RDLC. Interpreted the data and wrote the paper: AA, RDLC, CM, MR, LC, AG, and KW. All authors reviewed the article. All authors contributed to the article and approved the submitted version.

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.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.