Detection of fish movement patterns across management unit boundaries using age-structured Bayesian hierarchical models with tag-recovery data

Rujia Bi; Can Zhou; Yan Jiao

doi:10.1371/journal.pone.0243423

Abstract

Tagging studies have been widely conducted to investigate the movement pattern of wild fish populations. In this study, we present a set of length-based, age-structured Bayesian hierarchical models to explore variabilities and uncertainties in modeling tag-recovery data. These models fully incorporate uncertainties in age classifications of tagged fish based on length and uncertainties in estimated population structure. Results of a tagging experiment conducted by the Ontario Ministry of Natural Resources and Forestry (OMNRF) on yellow perch in Lake Erie was analyzed as a case study. A total of 13,694 yellow perch were tagged with PIT tags from 2009 to 2015; 322 of these were recaptured in the Ontario commercial gillnet fishery and recorded by OMNRF personnel. Different movement configurations modeling the tag-recovery data were compared, and all configurations revealed that yellow perch individuals in the western basin (MU1) exhibited relatively strong site fidelity, and individuals from the central basin (MU2 and MU3) moved within this basin, but their movements to the western basin (MU1) appeared small. Model with random effects of year and age on movement had the best performance, indicating variations in movement of yellow perch across the lake among years and age classes. This kind of model is applicable to other tagging studies to explore temporal and age-class variations while incorporating uncertainties in age classification.

Citation: Bi R, Zhou C, Jiao Y (2020) Detection of fish movement patterns across management unit boundaries using age-structured Bayesian hierarchical models with tag-recovery data. PLoS ONE 15(12): e0243423. https://doi.org/10.1371/journal.pone.0243423

Editor: Judi Hewitt, University of Waikato, NEW ZEALAND

Received: March 20, 2020; Accepted: November 21, 2020; Published: December 7, 2020

Copyright: © 2020 Bi et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: The data underlying the results presented in the study are available from Ontario Commercial Fisheries’ Association (https://www.ocfa.ca) and Ontario Ministry of Natural Resources and Forestry (https://www.ontario.ca).

Funding: This work was supported by a grant #458000 awarded to YJ by Ontario Commercial Fisheries’ Association (https://www.ocfa.ca). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Individual movement can have profound consequences for populations by influencing their distribution and abundance, dynamics and persistence, and ecological community structure [1–3]. A full understanding of individual movement behavior helps assess interactions among animals in different locations and is crucial for defining stock structure and developing effective population management strategies [4–6]. Numerous studies have revealed the risks of reduced stock biomass and high probability of overexploitation owing to ignoring individual movements across local populations in fisheries management [e.g. 7–9]. Although many species exhibit a variety of movement patterns, and stock identification techniques reveal complex spatial stock structure [e.g. 10,11], few studies incorporate spatial structure into stock assessment frameworks initially due to limited data to accurately estimate movement patterns [12]. The other impediment is computing power [12]. Fitting individual movement data into stock assessment would complicate model structure and increase the difficulty in model convergence, probably resulting in worse model performance. Over the past few decades, computational advancements make incorporation of movement data into assessment possible [12,13].

For large mammals, direct observations of individual movement are possible, but for other species like fishes, it is generally difficult to obtain information on individual movement from direct observation, and therefore tagging has been widely used in fishery research and movement study [14]. Tags generally contain specific identification information and can be attached to individuals externally or internally [14]. External tags, such as transbody, dart-style and internal-anchor tags, are inexpensive, easily visible and widle used, but are usually restricted to large fishes and with high tag loss [15]. Internal tags, such as coded wire, passive integrated transponder and visible implant tags, are inserted or injected into the fish and carried internally [15]. Internal tags generally show good retention rates, and are much smaller than external tags, so can be used on small fishes [15]. These external and internal tags have been widely used in tag-recovery and capture-recapture studies [16,17]. Tag-recovery studies are those in which individuals are tagged, released, and subsequently harvested as in a commercial fishery; while capture-recapture studies are those in which individuals are tagged, released, and recaptured on multiple sampling occasions [18]. Tag-recovery and capture-recapture data provide information on when and where individuals were tagged, characteristics of those individuals at the time of tagging, and when and where they were recovered [16]. Telemetry-based approaches, such as acoustic telemetry and archival tags, provide a continuous location track as opposed to discrete start/stop endpoints but are high-cost; therefore, combining telemetry tags with conventional tags is often the optimal approach [19].

Analysis of tagging data to estimate individual movement has received considerable attention in fisheries research [e.g. 16,20,21]. A spatial extension of the traditional Brownie model [22] have been widely used to derive movement probability from tagging data [20,21]. The spatial Brownie models separate parameters for survival and movement rates, and parameterize survival and recovery rates in terms of instantaneous natural morality and fishing mortality rates [20,21,23]. Interactions between individual movement and age class, time, and region make the movement process complex and difficult to understand [24]. These parameters can be included in the process model as random factors, so individual movement can be age-, year-, and region-dependent and modeled by formulating hierarchical structures [20,21].

To incorporate age-dependent variation in movement requires that the ages of tagged individuals be known. Intrusive ageing procedures, e.g., ageing by collecting and reading bony parts of the fish, should be avoided because these procedures would decrease survival of collected individuals and complicate subsequent analyses. Alternatively, nonlethal ageing such as fin-ray analysis is recommended [25]. In addition, total length of tagged individuals can be recorded non-intrusively, and age probabilities are then derived from concurrent age-length frequency data [26], which is a fast ageing approach. Most existing published tagging models assume that ages at tagging determined from length or from direct ageing of hard parts are known without error [e.g. 20,21]. When ages are determined from scales, biases are not expected; however, when ages are determined from length, biases can exist [20]. The sample size used to derive age-length frequency has an influence on the accuracy of the age-length relationship [27,28]; the uncertainty in age structure owing to age-length data needs to be considered.

In the present study, we developed a set of length-based, age-structured hierarchical models from tag-recovery data to quantify the movement patterns of yellow perch (Perca flavescens) in Lake Erie. Yellow perch support one of the most important fisheries in Lake Erie and contribute substantially to local economy and society [29,30]. The yellow perch fishery is managed by an interagency quota system. The Yellow Perch Task Group (YPTG), which is composed of provincial and state biologists, uses scientific approaches to establish a recommended allowable harvest annually. The Lake Erie Committee uses the recommended allowable harvest to determine a total allowable catch within each of four management units (MUs, Fig 1) in order to sustain the yellow perch population at a level that supports a consistent harvest [31]. Boundaries of the MUs were drawn based on a socioeconomic basis, such as political boundaries and at least one major port within each MU. Recent genetic [32] and spatial heterogeneity in fish distribution [33] studies suggested intermixing of yellow perch among MUs in Lake Erie. Only very limited studies have been done to understand inherent spatial structure and movement patterns of yellow perch in Lake Erie, and movement rates between stocks are unknown and have not been incorporated into stock assessment models. Simulation of movement patterns of yellow perch across MUs based on tag-recovery data could be used to improve the current management regime. Variations in movements across time and age classes and uncertainties in age classification were incorporated into these models. Bayesian approaches were used to construct these hierarchical models and provide straightforward estimates of parameters [34].

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Fig 1. Spatial units of Lake Erie.

Tag release locations in MU1 are marked by dark green dots, tag release locations in MU2 are marked by dark red dots, recapture locations where recovered fish were tagged and released from MU1 are marked by green triangles, and recapture locations where recovered fish were tagged and released from MU2 are marked by red diamonds. Note that tag release locations are exact location accurate to the nearest 0.01°, while recapture location is only accurate to the nearest 1 min grid.

https://doi.org/10.1371/journal.pone.0243423.g001

Methods

Case study: Yellow perch tagging experiment in Lake Erie

In 2009, the Ontario Ministry of Natural Resources and Forestry (OMNRF) began a yellow perch tagging experiment to understand the spatial exploitation pattern of local populations of tagged fish and to provide independent population estimates with the YPTG stock assessment report. Every year in March and April, spawning or post-spawn yellow perch caught in bottom trawls were collected for the tagging experiment. Passive integrated transponder (PIT) tags were injected into muscle tissue ventrally, anterior to the pelvic fins. A total of 13,694 yellow perch were tagged and released by OMNRF from 2009 to 2015, of which 76% were released from MU1 and 24% were released from MU2 (Table 1). Biological information, such as total length, were recorded for each tagged fish.

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Table 1. Numbers of yellow perch PIT-tagged, recovered and not-recovered in each MU from 2009 to 2015.

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Yellow perch caught by the Ontario commercial fishery were scanned for PIT-tagged fish at ports and in the laboratory by OMNRF and at fish processing plants using racket antennae and readers by the Ontario Commercial Fisheries’ Association (OCFA). Only a sample of the commercial catch was scanned; the proprtions of scanned yellow perch within the total commercial catch (by weight) organized by year and MU is presented in Table 2. Tagged yellow perch were recovered in a four- to five-year period following the tag release. Yellow perch tagged in 2009 and 2010 were not seen after 2013, yellow perch tagged in 2011 were not seen after 2014, and yellow perch tagged after 2011 were recovered until 2015.

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Table 2. Proportions of yellow perch scanned within the commercial catch (by weight) in MUs 1 to 4 from the Ontario commercial fishery from 2009 to 2015.

https://doi.org/10.1371/journal.pone.0243423.t002

Ohio started scanning from 2013 to 2015, and recovered 10 yellow perch that were tagged in Ontario. Due to the limited space and time coverage and scarcity of tags recovered from U.S. waters, the present study only considered yellow perch movement across MUs in Canadian waters, where PIT tag releases were conducted only in MUs 1 and 2, and tagged yellow perch were recovered only from MUs 1, 2 and 3. Although the zero recovery in MU4 was potentially resulted from the low scanning rates in this region (Table 2), benthic ridges (i.e., Long Point–Erie Ridge, Clear Creek Ridge, and Pennsylvania Ridge) between MUs 3 and 4 tend to isolate MU4, as demonstrated by results of spatial heterogeneity analyses of yellow perch distribution [33]. Therefore, in this study, only MUs 1, 2 and 3 were considered.

Age-structured movement model

An age-structured spatial tag-return model was used to describe the dynamics of the tagged fish population among the respective MUs. This type of model has been applied to various fisheries [e.g. 20,21,35]. Symbols used in model equations include variables, estimated parameters and fixed quantities are listed in S1 Table. The probability of an age-a fish tagged in year ty in region k, and harvested and reported in year fy from one of the regions was: (1) where bold symbols represent vectors and matrices, and regular symbols represent scalars, operator × denotes matrix product, operator ∘ denotes Hadamard product or element-wise product, matrix π_a,y is composed of row vectors π_a,y,k denoting movement probability of age-a fish from region k to all regions including region k in year y, exploitation vector u_a,fy is composed of exploitation rates u_a,fy,k of age-a fish in year fy from region k, survival vector S_a,y is composed of survival rates S_a,y,k of age-a fish in year y in region k, and reporting rate vector λ_fy is composed of reporting rates λ_fy,k in year fy from region k. We assumed 100% tag retention rate in terms of the high rention rate of PIT tag [36]. Tag reporting rates were assumed to be equal to the proportions of yellow perch scanned within the commercial catch (Table 2), and treated as fixed quantities in the models.

The exploitation rate of age-a fish in year fy from region k was: (2) where s_a denotes selectivity of commercial gillnet fishery on age-a fish, F_k,fy denotes commercial gillnet fishing mortality in region k in year fy, M denotes instantaneous natural mortality and S_a,fy,k denotes age-specific survival rate in region k in year fy. The age-specific survival rate was modeled as: (3) Fishing mortality varied for each year and each region, and each fishing mortality had a uniform prior over the interval (0, 1). The selectivity was modeled as a double logistic curve that can produce a dome-shaped relationship between selectivity and age, which is appropriate for gears such as gillnets and trap nets. The double logistic curve equation was: (4) where η₁ and η₃ are inflection points for the first (increasing) logistic curve and the second (decreasing) logistic curve, and η₂ and η₄ are the slopes of the two curves. The inflection points η₁ and η₃ were given uniform priors over (1, 6), and slopes η₂ and η₄ were given uniform priors over (0, 10). Commercial gillnet selectivity was standardized to ensure that at least one age class was fully selected as: (5)

The instantaneous natural mortality was assumed to be 0.4 per year in the stock assessment done by YPTG [37]. Because the present study area is an open system—for example, the fishery take of tagged fish from the U.S. side of the lake would be accounted by the natural mortality component in the model—the annual natural mortality rate was expected to be greater than 0.4, but can be much larger due to fisheries other than than the commercial gillnet fishery. The natural mortality was modeled with a uniform prior over the interval (0.2, 2).

Movement configurations

Movement probabilities per region, including the probability staying in the natal region, were estimated through a Dirichlet prior distribution with elemental gamma hyperprior random variables that constrained movement probabilities to be between 0 and 1 and to sum to 1 [38]: (6) (7) where γ is movement parameter. In this way, the Dirichlet priors were weakly informative that had little influence on posterior distributions, so results were mostly derived from data. Prior density was a post-model pre-data distribution associated with movement probabilities based on the Dirichlet priors on the movement parameters, and priors on year or age effects if included. A relatively large movement parameter indicated a preference to move into or stay in a particular region, and a relatively small movement parameter indicated a preference to stay away from that region.

Both temporal and age-specific variations in the movement of yellow perch across MUs were modeled through random effects and fixed effects. The setting of random effects reduced the effective number of parameters while still allowing movement to vary by year and age. An initial-year correction was considered to reduce the bias caused by partial dispersal in the initial year after release.

Constant movement.

A model with constant movement scenario (termed Model C) was developed first, against which different scenarios of temporal and age-specific variations were compared. For the constant movement scenario, the probability of a tagged fish moving from region k to region k’ was modeled as Eqs 6 and 7.

Fixed effects by year.

The pattern of yellow perch movement across MUs might differ across years. In the second scenario (termed Model YF), a separate set of movement parameters was estimated for each year. Effectively, movement parameters were estimated as fixed effects across years. The probability of moving from region k to region k’ in year y was: (8) (9)

Random effects by year.

In the third scenario (termed Model YR), instead of independent uniform priors, the logarithms of movement parameters were modeled as normally distributed with a common variance parameter τ. The movement parameter for a tagged fish moving from region k to k’ in year y was: (10) (11) where ψ_k,k’ was the parameter to estimate. The parameter τ had a uniform prior over the interval (0, 1). Movement probability was computed as shown in Eq 8.

Fixed effects by age.

The movement pattern also might exhibit age-class differences. In the fourth scenario (termed Model AF), a separate set of movement parameters was estimated for each age. The probability of a tagged age-a yellow perch moving from region k to k’ was: (12) (13)

Random effects by age.

In the fifth scenario (termed Model AR), age-class variations in movement were modeled as normal variates with a common variance parameter ω, and the movement parameter for a tagged age-a fish moving from region k to k’ was: (14) (15) where ϕ_k,k’ was the parameter to estimate, and ω had a uniform prior over the interval (0, 1). Movement probability was computed as shown in Eq 12.

Random effects by age and year.

In the sixth scenario (termed Model AY), both temporal and age-class variations were incorporated into the movement model. In this case, the movement pattern of yellow perch was allowed to change both for time and age-class. This model was the most general case among all seven movement models considered. In this model, the probability of a tagged age-a fish moving from region k to k’ in year y was: (16) The movement parameter γ_k,k’,a,y was indexed by both age and year. Age-class variations in movement were modeled as normally distributed with a common variance parameter ν_a, and year-variations in movement were nested in age classes and were modeled as normally distributed with a common variance parameter ν_y: (17) (18) (19) where ν_y and ν_a had a uniform prior over the interval (0, 1).

Random effects by age and year with initial year correction.

During the entire study period, newly tagged yellow perch were released into Lake Erie only in April and May by OMNRF personnel, and the scanning process was continuous from March to December. In the models specified above, there was the assumption that immediately after release, tagged fish fully dispersed according to the movement matrix. This assumption might not hold, because the first year post-release was a partial year compared to subsequent years, and tagged fish might not fully disperse to other regions as in the subsequent years. This would introduce a systematic bias into the model, as we expected to recover more tagged fish in the region of release and fewer tagged fish from other regions during the initial year than predicted. In this scenario (termed Model AYc), we introduced an adjustment factor to the movement matrix to test the assumption of full dispersal during the initial year. The probability of a tagged fish staying in the region of release, for example, in region 1, during the initial year was: (20) with the probability of moving to region 2 and region 3 to be a fraction of the original percentage: (21) (22) where ratio was the adjustment factor to be estimated. To keep the new movement probabilities positive, the adjustment factor ratio was given a uniform prior over the interval (0, 1), where 0 denotes completely small movement during the initial year and 1 denotes full movement during the initial year. Specifically, a 58% (i.e, 7/12) movement during the initial year was hypothesized if movement events are evenly distributed through the remaining seven months of the initial year.

Age classifications

To determine age compositions, age-length relationships were constructed from partnership gillnet surveys conducted by OMNRF in the fall each year. A total of 131,469 yellow perch were aged by otolith readings from 1989 to 2015. Sample sizes varied across length classes and, to include the uncertainty that sample size variation introduced, the age composition of each length-class was modeled as multinomially distributed: (23) where vector n_l denotes the observed age-specific abundance of length-class l, κ_l denotes the state variable of the age composition of length-class l, and N_l denotes sample size for length- class l.

Likelihood

Both recovered and unrecovered tags contributed to the likelihoods of the models. The probability of an individual, originally tagged and released from region tk in year ty from length class l, and recovered from region fk in year fy was: (24) where κ_l,a denotes the state variable of the proportion of age-a individuals in the tagged sample in length-class l, the summation is over all the age classes and P_{a,ty,tk,fy,fk} denotes the age-specific probability of recovering a fish in year fy and region fk, originally tagged at age-a in region tk and year ty.

The probability of a tagged fish being not-yet-recovered was the probability of not observing it in the years subsequent to the tag release. Thus, the probability of a yellow perch, originally tagged and released from region tk and year ty from length-class l not being recovered through 2015 was: (25) where the first summation is over all the age classes, the second summation is over all years after the tag release, and the third summation is over all spatial regions.

Tags recovered in year fy from region fk, originally tagged and released in year ty from region tk belonging to length class l and those unrecovered tags were assumed to be multinomially distributed with negative log likelihood: (26) where NLL is negative log-likelihood, is number of fish tagged and released in year ty from region tk belonging to length class l and recovered in year fy from region fk, is number of unrecovered fish tagged and released in year ty from region tk belonging to length class l.

Model fitting and comparison

Bayesian methods were used because of their convenience for specifying hierarchical models. To simulate Markov Chain Monte Carlo (MCMC) samples from the posterior, we used JAGS 4.0 [39] with R packages rjags [40] and runjags [41] in statistical program R [42]. For each model, five chains with different initial conditions were simulated, and the convergence of different chains was checked by Gelman-Rubin convergence diagnostics [43].

Model performance was compared based on deviance information criterion (DIC) [44], Watanabe-Akaike information criterion (WAIC) [45], and leave-one-out cross-validation (LOO) [46]. The DIC is defined as: where is the posterior mean of the deviance, and p_D is an estimate of the number of parameters in the model.

The WAIC is defined as: where LPPD is the log posterior predictive density.

The LOO is defined as: where y_−i denotes the observations y with the ith component removed. It expresses the posterior probability of observing the value of y_i when the model is fitted to all data except y_i.

The LOO was computed using Pareto smoothed importance sampling, which provides a more accurate and reliable estimate by applying a smoothing procedure to the importance weights [46,47]. The WAIC and LOO were computed with R package loo [48]. The DIC is known to have some problems, like producing a negative estimate of p_D, but the WAIC is more stable because it is fully Bayesian and therefore uses the entire posterior distribution [46]. The LOO is more robust than WAIC in the finite case with weak prior or influential observations [46]. A smaller value of DIC, WAIC or LOO indicates a better model performance. If all of the three criterions showed the same preference for a model, we had more evidence that the preference was correct.

Results

Model comparison

The DIC, WAIC and LOO results for seven models with different yellow perch movement configurations are presented in Table 3. The Gelman-Rubin statistic for all the posterior samples were found to be smaller than 1.1, and thus the convergence of the posterior was validated. Four movement models with random variations in age and/or year (Models AY, AR, YR and AYc) achieved better performance than the model with constant movement (Model C) in terms of having smaller DIC, WAIC and LOO values (Table 3). The model incorporated both temporal and age-class hierarchical variations for the movement parameters (Model AY) performed best with the smallest DIC, WAIC and LOO values. Models with either fixed effects by year or by age on movement matrix (Model YF and AF) produced relatively poor fit to the data, with larger DIC, WAIC and LOO values than other models.

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Table 3. Deviance information criterion (DIC), Watanabe-Akaike information criterion (WAIC) and leave-one-out cross-validation (LOO) of yellow perch models with different movement configurations.

https://doi.org/10.1371/journal.pone.0243423.t003

In terms of DIC, WAIC and LOO values, we recommended Model AY. To further validate Model AY, we compared results on movement probabilities from Models AY, AR and C. The estimates of movement probabilities or the tagging model itself would be integrated into the long-term stock assessement and aid in fishery management. With only 7-year tagging data in hand, contant or age-varied movement scenario (Model C or AR) might be more meaningful for management purposes.An initial-year adjustment factor was added to the movement matrix of model AY to adjust for the possibility of less movement during the initial, partial year, but the adjusted model (Model AYc) did not produce a fit to data superior to the unadjusted model (Table 3). The posterior estimate of the adjustment factor also indicated that the movements during the initial year were largely complete compared to those in subsequent years (S1 Fig). The posterior was concentrated at the higher end of the graph, which indicated complete dispersal. The upper 95% of the posterior density lay above 72%, which was larger than the hypothesized 58% level. These results suggested that yellow perch movement occurs mostly after March and April within a calendar year.

Movement patterns of yellow perch

Age- and year-specific yellow perch movement patterns from the best-supported model (Model AY) are shown in Fig 2. Generally, most yellow perch in MU1 stayed in MU1 (Fig 2A). Yellow perch in MU2 were more likely to move to MU3 or stay in MU2 (Fig 2B). Yellow perch in MU3 were more likely to stay in MU3 or move to MU2 (Fig 2C). Uncertainties on movement probabilities π_2,2, π_2,3, π_3,1, π_3,2 and π_3,3 were larger owing to less fish tagged and released from MU2 and no fish tagged and released from MU3 (Table 1), as well as lower tag reporting rate in MU3 (Table 2). The posterior densities for π_3,1 were little changed compared with the prior density (Fig 2C), due to limited information as stated above.

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Fig 2. Movement probability of a tagged yellow perch from each age class in each year derived from Model AY.

In each panel, solid lines denote posterior densities, dotted line denotes prior density, and shaded areas indicate 95% credible intervals.

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Individuals in MU1 showed stronger site fidelity in 2013 (Fig 3A), individuals in MU2 showed a larger tendency to move to MU3 in 2011 (Fig 3B), and individuals in MU3 showed stronger site fidelity in 2012 and 2014 (Fig 3C). Age-4 individuals were more likely to move outwards–from MU1 to MU2 (Fig 4A), from MU2 to MU3 (Fig 4B), from MU3 to MU2 (Fig 4C), and age-6+ in MUs 2 and 3 were more likely to stay in the natal region (Fig 4B and 4C).

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Fig 3. Year-varied age-average movement probability of a tagged yellow perch.

In each vertical line, solid diamond represents posterior median, solid interval represents interquartile range of posterior, and dash line represents 95% credible interval.

https://doi.org/10.1371/journal.pone.0243423.g003

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Fig 4. Age-varied year-average movement probability of a tagged yellow perch.

In each vertical line, solid diamond represents posterior median, solid interval represents interquartile range of posterior, and dash line represents 95% credible interval.

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Age-specific movement patterns from Model AR are shown in S2 Fig. Age-4 fish were more likely to move outwards, such as moving from MU1 to MU2, from MU2 to MU3, from MU3 to MU2, which was consistent with results from Model AY. Constant movement patterns from Model C are shown in S3 Fig. Models AY, AR and C all revealed that yellow perch individuals in MU1 exhibited relatively strong site fidelity, and individuals from MUs 2 and 3 were likely to move between these units, but movement from MUs 2 and 3 to MU1 appeared limited. Although year and age-variations in movement probabilities derived from Model AY (Figs 3 and 4) were not substantial, there were obvious differences on posterior medians in some years and age classes, for example, posterior median of movement probability π_1,1 in 2013 was 0.90 that was 3–5% greater than π_1,1 in other years; posterior median of movement probability π_2,3 in 2011 was 0.70 that was 3–5% greater than π_2,3 in other years; posterior medians of movement probability π_3,3 in 2012 and 2014 were 0.65 and 0.63 respectively that were 3–9% greater than π_3,3 in other years; posterior median of movement probability π_1,2 at age-4 was 0.13 that was 30–184% greater than π_1,2 at the rest age classes; posterior median of movement probability π_2,3 at age-4 was 0.72 that was 2–10% greater than π_2,3 at the rest age classes; posterior median of movement probability π_3,2 at age-4 was 0.33 that was 29–58% greater than π_3,2 at the rest age classes. Furthermore, Model AY performed best with the smallest DIC, WAIC and LOO values (Table 3), so it was recommended to better understand year-variations in fish movement probabilities, which might be linked to environmental changes. Model AR was recommended when integrating short-term tagging data with long-term fisheries data.

Additional biological and fishery-related parameter estimates

Additional biological and fishery-related parameters were estimated from Model AY. The estimated natural mortality was greater than 0.4 with a posterior median of 1.36 and a 95% credible interval of (1.19, 1.53), as expected, because of the uncounted fishing mortality from the U.S. side of Lake Erie (Fig 5A). The selectivity of the commercial gillnet fishery was greater for age-4, 5 and 6 (Fig 5B). Estimates of fishing mortality in the commercial gillnet fishery varied among MUs and came with large uncertainties (Fig 5C). The fishing mortality in MU1 between 2009 and 2013 was estimated with relatively high precision due to the large number of tagged fish released in MU1. Similar results were derived from Model AR and C (S4 and S5 Figs). Point fishing morality estimates from stock assessment [49] was within the 95% credible intervals derived from Model AY for MU1 from 2010 to 2015, for MU2 in 2014 and 2015, and for MU3 in 2014 and 2015, which had more fish tagged and released. Larger sample size would be required for tagging study to derive more accurate results. The current stock assessment ignored fish movement across MUs [49], which also potentially led to differences in fishing mortality estimates.

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Fig 5. Estimations of additional biological and fishery-related parameters from Model AY.

(a) Posterior density of natural mortality. Blue dotted line indicates posterior median. Ribbon indicates 95% credible interval. (b) Posterior estimates of age-specific selectivity. Solid lines and points indicate posterior median values. Ribbons indicate 95% credible intervals. (c) Posterior estimates of year-specific commercial fishing mortality within each MU. Solid lines and points indicate posterior median values. Ribbons indicate 95% credible intervals. Point estimates from the YPTG stock assessment model for each region were denoted by asterisks.

https://doi.org/10.1371/journal.pone.0243423.g005

Discussion

Although tagging models have been widely used to estimate population parameters such as mortality and movement, the spatially structured tagging model framework is relatively new [20,21,35]. In this study, spatial-structured tag-return models were developed and adapted to the Lake Erie yellow perch population that is managed within discrete MUs, and age and year-dependent variations were addressed. There have been only a few studies of spatially structured tagging models or integrated models applied to real-world data to directly estimate movement rates [e.g. 20,21,50–52]. Our framework using Bayesian analysis provides a robust approach to simultaneously estimate movement, survival and exploitation rates, and to evaluate the uncertainties of parameter estimates.

Model assumptions

The models developed in this study require a series of assumptions that may be not satisfied in practice. Our models assume that fish move between regions at the beginning of each year, and that once they move, the fish immediately takes on the demographic rates of the new stock, which may not be true in the real world. Movements occur seasonally, over a short time-period, or as functions of environmental factors or population density for many populations [53,54]. It is possible to develop models with end-of-year movements or continuous movements throughout each year, if these behaviors are considered more appropriate [e.g. 20,23]. However, complex movement assumptions need more parameters that maybe more than that could be reliably estimated with the current data. Models with end-of-year movements have been found to cause potential biases in movement estimates [55].

Our models assume no tag shedding or tag-induced mortality. Further, our models assume a constant natural mortality for all age classes. The natural mortality rate is estimated with a posterior median of 1.36 and a 95% credible interval of (1.19, 1.53), which is much larger than the 0.4 used by the YPTG. This could have been caused by many factors, including fishing activities other than the Ontario commercial gillnet fishery, bycatch, migration outside of the study area, tag shedding and tag-induced mortality. Point estimates of commercial trap net and angler fishing mortality rates in the U.S. waters estimated from the YPTG stock assessment model [49] are plotted in S6 Fig. The sum of these two fishing mortality rates is large in MU2 in 2014 and 2015 (> 0.4). If a large proportion of the estimated natural mortality is actually fishing mortality from U.S. waters, our models is overestimating the natural mortality of young (pre-selected) fish. Additional information could be collected to account for other factors; for example, double-tagging experiments have been widely used to quantify tag-shedding [54,56–58].

In addition to the above assumptions, our models make the usual assumptions for tag-recovery models: the tagged fish mix with untagged populations completely; the tagged fish are a representative sample of the fish in a particular region; the fate of each fish is independent of that of other fish; fish in a given age-class, region and year have the same survival, movement and capture probabilities [22,59].

Although yellow perch, both in Lake Erie and in most reported freshwater systems, usually show sex-specific growth, maturity and likely also migration [60], our models assume no difference in movement across MUs between sexes because of the high differences in sample size between males and females and the large proportion of individuals of unknown sex. The current sample size for females is much lower than that of males both in tagging and capture across MUs (5,873 tagged males, 268 tagged females), and more than 50% of the tagged fishes (7,547) have unknown sex. Because of the imbalance in fish of known sex and the number of sex-undocumented individuals at more than 50%, any sex-specific difference in movement that is detected in these data may not reflect the underlying reality.

Unlike most published tagging models that assume that ages at tagging are known without error [e.g. 20,21,54], our models consider the uncertainties in age classification. This approach can reduce biases on parameter estimations, especially when the release ages are determined from length and a given age-length relationship in studies like our case study.

Movement patterns of yellow perch in Lake Erie and management implications

The movement patterns of yellow perch in Lake Erie showed age- and year-dependent variations. There were substantial fish movements between MUs 2 and 3 in all tagging years. Winter (i.e. December–February) mean North Atlantic Oscillation (NAO) index [61], annual average water level, annual maximum ice cover and annual average surface temperature in the lake [62] (Fig 6) are considered to affect year-dependent variations in movement patterns.

The high annual average surface temperature and low ice cover associated with high winter NAO index in 2012 indicate a reatively short, warm winter (Fig 6). In 2012, fish in MU1 tended to move to MU2, and fish in MUs 2 and 3 tended to stay in their original regions (Fig 3). Previous research reveals that shorter and warmer winters resulting from higher water temperature might cause lower annual recruitment of yellow perch and increased food scarcity for surviving juveniles [63], and cooler temperatures probably contribute to a favorable habitat in the deeper central basin of Lake Erie.

Movements of yellow perch tend to follow the water circulation pattern of the lake on a large scale [64–66]. High water level might accelerate water movement, helping fish to move across a large scale. Regression analyses revealed that water level displayed a significant positive impact on posterior medians of year-varied age-average movement probability π_2,3 (p-value < 0.05). The relatively high water levels in 2011 and 2015 (Fig 6) may have contributed to the larger tendency of fish moving between MUs 2 and 3 (Fig 3).

Download:

Fig 6. Potential environmental factors.

Winter NAO indices, annual average water level (m), annual maximum ice cover (%) and annual average surface temperature (°C) in Lake Erie from 2009 to 2015.

https://doi.org/10.1371/journal.pone.0243423.g006

The most common movements of MU2 fish are to MU3, and the most common movements of MU3 fish are to MU2. Of the age classes, age-4 fish show the greatest tendency to make these movements. The mechanisms behind the age-dependent variations may be related to age-specific patterns of maturation, reproduction, and predation, etc.

The movement estimates provide useful implications regarding yellow perch in Lake Erie. Stock assessments might be improved by considering the movement between MUs 2 and 3. Stocks with greater outward movement rates and consequent reduction in numbers will generally be more vulnerable to overharvest.

Overall, the age-structured spatial tag-return models developed in the present study provide an opportunity to explore movement, survival and exploitation processes. The Bayesian methods used here allowed extra flexibility for incorporating random effects (e.g., age, year), which can greatly improve the prediction by better explaining sources of variation. We believe our work established a framework that can facilitate additional studies of animal movement based on tagging-recovery data.

Supporting information

S1 Fig.

(a) Age compositions for each length class. TL = total length (mm). Solid lines and points indicate posterior median values. Ribbons and dotted lines indicate 95% credible intervals. (b) Posterior density (black solid line) and prior density (black dotted line) of the initial year correction factor from the Model AYc. Ribbon indicates the upper 95% percentile of the posterior distribution. Blue dotted line indicates posterior median value.

https://doi.org/10.1371/journal.pone.0243423.s001

(DOCX)

S2 Fig. Movement probability of a tagged yellow perch from each age class derived from Model AR.

In each panel, solid lines denote posterior densities, dotted line denotes prior density, and shaded areas indicate 95% credible intervals.

https://doi.org/10.1371/journal.pone.0243423.s002

(DOCX)

S3 Fig. Movement probability of a tagged yellow perch from Model C.

In each panel, solid lines denote posterior densities, dotted line denotes prior density, and shaded areas indicate 95% credible intervals.

https://doi.org/10.1371/journal.pone.0243423.s003

(DOCX)

S4 Fig. Estimations of additional biological and fishery-related parameters from Model AR.

(a) Posterior density of natural mortality. The blue dotted line indicates posterior median. The ribbon indicates 95% credible interval. (b) Posterior estimates of age-specific selectivity. The solid lines and points indicate posterior median values. The ribbons indicate 95% credible intervals. (c) Posterior estimates of year-specific commercial fishing mortality within each MU. The solid lines and points indicate posterior median values. The ribbons indicate 95% credible intervals. Point estimates from the YPTG stock assessment model for each region were denoted by asterisks.

https://doi.org/10.1371/journal.pone.0243423.s004

(DOCX)

S5 Fig. Estimations of additional biological and fishery-related parameters from Model C.

(a) Posterior density of natural mortality. The blue dotted line indicates posterior median. The ribbon indicates 95% credible interval. (b) Posterior estimates of age-specific selectivity. The solid lines and points indicate posterior median values. The ribbons indicate 95% credible intervals. (c) Posterior estimates of year-specific commercial fishing mortality within each MU. The solid lines and points indicate posterior median values. The ribbons indicate 95% credible intervals. Point estimates from the YPTG stock assessment model for each region were denoted by asterisks.

https://doi.org/10.1371/journal.pone.0243423.s005

(DOCX)

S6 Fig. Point estimates of commercial trap net and angler fishing mortality rates in the U.S. waters estimated from the YPTG stock assessment model.

https://doi.org/10.1371/journal.pone.0243423.s006

(DOCX)

S1 Table. Symbols used in the model equations.

Bold symbols represent vectors and matrices, and regular symbols represent scalars.

https://doi.org/10.1371/journal.pone.0243423.s007

(DOCX)

Acknowledgments

We thank Kevin Reid from the OCFA, Andy Cook from the Ontario Ministry of Natural Resources and Forestry (OMNRF) and Carey Knight from the Ohio Department of Natural Resources (ODNR) for sharing data and providing comments on the study framework. We also thank Eric Hallerman from the Department of Fish and Wildlife Conservation at Virginia Tech and Joan A. Browder from the National Oceanic and Atmospheric Administration (NOAA) National Marine Fisheries Service Southeast Fisheries Science Center (SEFSC) for providing comments to strengthen the manuscript.

References

1. Harrison S. Meta-populations and conservation. In: Edwards PJ, May RM, Webb N, editors. Large Scale Ecology and Conservation Biology. London: Wiley-Blackwell; 1994. pp. 111–128.
2. Dieckmann U, O'Hara B, Weisser W. The evolutionary ecology of dispersal. Trends Ecol Evol. 1999; 14: 88–90.
- View Article
- Google Scholar
3. Lowe WH, Allendorf FW. What can genetics tell us about population connectivity? Mol Ecol. 2010; 19: 3038–3051. pmid:20618697
- View Article
- PubMed/NCBI
- Google Scholar
4. Berkes F, Pocock D. Quota management and “people problems”: a case history of Canadian Lake Erie fisheries. Trans Am Fish Soc. 1987; 116: 494–502.
- View Article
- Google Scholar
5. Kendall WL. One size does not fit all: adapting mark-recapture and occupancy models for state uncertainty. In: Thomson DL, Cooch EG, Conroy MJ, editors. Modeling Demographic Processes in Marked Populations. Boston: Springer; 2009. pp. 765–780.
6. Block BA, Jonsen ID, Jorgensen SJ, Winship AJ, Shaffer SA, Bograd SJ, et al. Tracking apex marine predator movements in a dynamic ocean. Nature. 2011; 475: 86–90. pmid:21697831
- View Article
- PubMed/NCBI
- Google Scholar
7. Frank KT, Brickman D. Allee effects and compensatory population dynamics within a stock complex. Can J Fish Aquat Sci. 2000; 57: 513–517.
- View Article
- Google Scholar
8. Ying Y, Chen Y, Lin L, Gao T. Risks of ignoring fish population spatial structure in fisheries management. Can J Fish Aquat Sci. 2011; 68: 2101–2120.
- View Article
- Google Scholar
9. Goethel DR, Berger AM. Accounting for spatial complexities in the calculation of biological reference points: effects of misdiagnosing population structure for stock status indicators. Can J Fish Aquat Sci. 2017; 74: 1878–1894.
- View Article
- Google Scholar
10. Hampton J, Fournier DA. A spatially disaggregated, length-based, age-structured population model of yellowfin tuna (Thunnus albacares) in the western and central Pacific Ocean. Mar Freshw Res. 2001; 52: 937–963.
- View Article
- Google Scholar
11. Palkovacs EP, Hasselman DJ, Argo EE, Gephard SR, Limburg KE, Post DM, et al. Combining genetic and demographic information to prioritize conservation efforts for anadromous alewife and blueback herring. Evol Appl. 2014; 7: 212–226. pmid:24567743
- View Article
- PubMed/NCBI
- Google Scholar
12. Goethel DR, Quinn TJ, Cadrin SX. Incorporating spatial structure in stock assessment: movement modeling in marine fish population dynamics. Rev Fish. 2011;19:119–36.
- View Article
- Google Scholar
13. Maunder MN. Integration of tagging and population dynamics models in fisheries stock assessment. Ph.D. dissertation, The University of Washington. 1998. Available from: https://www.researchgate.net/publication/305280946
14. Thorsteinsson V. Tagging methods for stock assessment and research in fisheries. Report of Concerted Action FAIR CT.96.1394 (CATAG). Reykjavík, Iceland: Marine Research Institute. 2002.
15. Gillanders BM. Tools for studying biological marine ecosystem interactions—natural and artificial tags. In: Nagelkerken I, editors. Ecological Connectivity among Tropical Coastal Ecosystems. Dordrecht: Springer; 2009. pp. 457–492.
16. Hilborn R. Determination of fish movement patterns from tag recoveries using maximum likelihood estimators. Can J Fish Aquat Sci. 1990; 47: 635–643.
- View Article
- Google Scholar
17. Pine WE, Hightower JE, Coggins LG, Lauretta MV, Pollock KH. Design and analysis of tagging studies. In: Zale AV, Parrish DL, Sutton TM, editors. Fisheries Techniques. 3rd ed. Bethesda, MD: American Fisheries Society; 2012. pp. 521–572.
18. Latour RJ. Tagging methods and associated data analysis. FAO Fisheries Technical Paper. 2005; 474: 45.
- View Article
- Google Scholar
19. Hightower JE, Pollock KH. Tagging methods for estimating population size and mortality rates of inland striped bass populations. Am Fish Soc Symp. 2013; 80: 249–262.
- View Article
- Google Scholar
20. Eveson JP, Laslett GM, Polacheck T. A spatial model for estimating mortality rates, abundance and movement probabilities from fishery tag-recovery data. In: Thomson DL, Cooch EG, Conroy MJ, editors. Modeling Demographic Processes in Marked Populations. Boston: Springer; 2009. pp. 987–1010.
21. Vandergoot CS, Brenden TO. Spatially varying population demographics and fishery characteristics of Lake Erie walleyes inferred from a long-term tag recovery study. Trans Am Fish Soc. 2014; 143: 188–204.
- View Article
- Google Scholar
22. Brownie C, Anderson DR, Burnham KP, Robson DS. Statistical Inference from Band Recovery Data: A Handbook. Resource Publication 156. 2nd ed. Washington, DC: US Fish and Wildlife Service; 1985.
23. Joe M, Pollock KH. Separation of survival and movement rates in multi-state tag-return and capture-recapture models. J Appl Stat. 2002; 29: 373–384.
- View Article
- Google Scholar
24. Patterson TA, Thomas L, Wilcox C, Ovaskainen O, Matthiopoulos J. State–space models of individual animal movement. Trends Ecol Evol. 2008; 23: 87–94. pmid:18191283
- View Article
- PubMed/NCBI
- Google Scholar
25. Tzadik OE, Goddard EA, Hollander DJ, Koenig CC, Stallings CD. Non-lethal approach identifies variability of δ¹⁵N values in the fin rays of Atlantic Goliath Grouper, Epinephelus itajara. PeerJ. 2015; 3: e1010. pmid:26082864
- View Article
- PubMed/NCBI
- Google Scholar
26. Fridriksson A. On the calculation of age-distribution within a stock of cod by means of relatively few age-determinations as a key to measurements on a large scale. Rapports et Procès-Verbaux des Réunions, Conseil Permanent International pour l’Exploration de la Mer. 1934; 86: 1–14.
- View Article
- Google Scholar
27. Coggins LG Jr, Gwinn DC, Allen MS. Evaluation of age–length key sample sizes required to estimate fish total mortality and growth. Trans Am Fish Soc. 2013; 142: 832–840.
- View Article
- Google Scholar
28. Hulson PJF, Hanselman DH, Shotwell SK. Investigations into the distribution of sample sizes for determining age composition of multiple species. Fish Bull. 2017; 115: 326–342.
- View Article
- Google Scholar
29. Baldwin NS, Saalfeld RW, Dochoda MR, Buettner HJ, Eshenroder RL. Commercial Fish Production in the Great Lakes 1867–2006. 2009. Available from: http://www.glfc.org/databases/commercial/commerc.php
- View Article
- Google Scholar
30. Regier HA, Hartman WL. Lake Erie’s fish community: 150 years of cultural stresses. Science. 1973; 180: 1248–1255. pmid:17759111
- View Article
- PubMed/NCBI
- Google Scholar
31. Ryan PA, Knight R, MacGregor R, Towns G, Hoopes R, Culligan W. Fish-community goals and objectives for Lake Erie. Special Publications 03–02. 2003. Available from: http://www.glfc.org/pubs/SpecialPubs/Sp03_2.pdf
32. Sepulveda-Villet OJ, Stepien CA. Fine-scale population genetic structure of the yellow perch Perca flavescens in Lake Erie. Can J Fish Aquat.Sci. 2011; 68: 1435–1453.
- View Article
- Google Scholar
33. Bi R, Jiao Y, Zhou C, Hallerman EM. A Bayesian spatiotemporal approach to inform management unit appropriateness. Can J Fish Aquat Sci. 2018; 76: 217–237.
- View Article
- Google Scholar
34. Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. Bayesian Data Analysis. Boca Raton: CRC Press; 2014.
35. Li Y. Innovative stock assessment methods and management solutions for spatially structured fish populations. Ph.D. dissertation, Michigan State University. 2018. Available from: https://www.canr.msu.edu/qfc/publications/pdf-theses-dissertations/2018-td/YangLi_Dissertation_2018.pdf
36. Kaemingk MA, Weber MJ, McKenna PR, Brown ML. Effect of passive integrated transponder tag implantation site on tag retention, growth, and survival of two sizes of juvenile Bluegills and Yellow Perch. N Am J Fish Manag. 2011; 31: 726–732.
- View Article
- Google Scholar
37. YPTG. Report of the Lake Erie yellow perch task group. Wheatley, Ontario: Yellow Perch Task Group. 2015. Available from: http://www.glfc.org/pubs/lake_committees/erie/YPTG_docs/annual_reports/YPTG_report_2015.pdf
38. Royle JA, Dorazio RM. Hierarchical Modeling and Inference in Ecology. San Diego: Academic Press-Elsevier; 2008.
39. Plummer M. JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Hornik K, Leisch F, Zeileis A, editors. Proceedings of the 3rd International Workshop on Distributed Statistical Computing. Vienna, Austria: Technische Universität Wien; 2003. Available from: https://www.R-project.org/conferences/DSC-2003/Proceedings/Plummer.pdf
40. Plummer M. rjags: Bayesian Graphical Models Using MCMC. R package version 4–6. 2016. Available from: https://CRAN.R-project.org/package=rjags
- View Article
- Google Scholar
41. Denwood MJ. runjags: An R package providing interface utilities, model templates, parallel computing methods and additional distributions for MCMC models in JAGS. J Stat Softw. 2016; 71: 1–25.
- View Article
- Google Scholar
42. R Core Team. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. 2019. Available from: https://www.R-project.org/
43. Gelman A, Rubin DB. A single sequence from the Gibbs sampler gives a false sense of security. In Bernardo JM, Berger JO, Dawid AP, Smith AFM, editors. Bayesian Statistics 4. New York: Oxford University Press; 1992. pp. 625–631.
44. Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A. Bayesian measures of model complexity and fit. J R Stat Soc Ser B Stat Methodol. 2002; 64: 583–639.
- View Article
- Google Scholar
45. Watanabe S. Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J Mach Learn Res. 2010; 11: 3571–3594.
- View Article
- Google Scholar
46. Vehtari A, Gelman A, Gabry J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput. 2017; 27: 1413–1432.
- View Article
- Google Scholar
47. Vehtari A, Gelman A. Pareto smoothed importance sampling. 2015; arXiv:1507.02646.
- View Article
- Google Scholar
48. Vehtari A, Gelman A, Gabry J. loo: Efficient leave-one-out cross-validation and WAIC for Bayesian models. R package version 0.1.6. 2016. Available from: https://github.com/stan-dev/loo
- View Article
- Google Scholar
49. YPTG. Report of the Lake Erie yellow perch task group. Wheatley, Ontario: Yellow Perch Task Group. 2016. Available from: http://www.glfc.org/pubs/lake_committees/erie/YPTG_docs/annual_reports/YPTG_report_2016.pdf
50. Punt AE, Pribac F, Walker TI, Taylor BL, Prince JD. 2000. Stock assessment of school shark, Galeorhinus galeus, based on a spatially explicit population dynamics model. Mar Fresh Res. 2000; 51: 205–220.
- View Article
- Google Scholar
51. Taylor NG, McAllister MK, Lawson GL, Carruthers T, Block BA. Atlantic bluefin tuna: a novel multistock spatial model for assessing population biomass. PLoS ONE. 2011; 6: e27693. pmid:22174745
- View Article
- PubMed/NCBI
- Google Scholar
52. Goethel DR, Legault CM, Cadrin SX. Demonstration of a spatially explicit, tag-integrated stock assessment model with application to three interconnected stocks of yellowtail flounder off of New England. ICES J Mar Sci. 2015; 72: 164–177.
- View Article
- Google Scholar
53. MacCall AD. Dynamic Geography of Marine Fish Populations. Seattle, Washington: University of Washington Press; 1990.
54. Polacheck T, Eveson JP, Laslett GM, Pollock KH, Hearn WS. Integrating catch-at-age and multiyear tagging data: a combined Brownie and Petersen estimation approach in a fishery context. Can J Fish Aquat Sci. 2006; 63: 534–548.
- View Article
- Google Scholar
55. Hestbeck JB. Bias in transition-specific survival and movement probabilities estimated using capture-recapture data. J Appl Stat. 1995; 22: 737–750.
- View Article
- Google Scholar
56. Beverton RJH, Holt SJ. On the dynamics of exploited fish populations. Fishery Investigations, Series 2, 19. London: Ministry of Agriculture, Fisheries and Food; 1957.
57. Kirkwood GP, Walker MH. A new method for estimating tag shedding rates with application to data for Australian Salmon, Arripes trutta esper Whitley. Aust J Mar Freshw Res. 1984; 35: 601–606.
- View Article
- Google Scholar
58. Barrowman NJ, Myers RA. Estimating tag-shedding rates for experiments with multiple tag types. Biometrics. 1996; 52: 1410–1416.
- View Article
- Google Scholar
59. Pollock KH, Hoenig JM, Jones CM. Estimation of fishing and natural mortality when a tagging study is combined with a creel survey or port sampling. Am. Fish. Soc. Symp. 1991; 12: 423–434.
- View Article
- Google Scholar
60. Wilberg MJ, Bence JR, Eggold BT, Makauskas D, Clapp DF. Yellow perch dynamics in southwestern Lake Michigan during 1986–2002. N Am J Fish. Manag. 2005; 25:1130–1152.
- View Article
- Google Scholar
61. NCAR (National Center for Atmospheric Research). 2019. The Climate Data Guide: Hurrell North Atlantic Oscillation (NAO) Index (PC-based). Retrieved: 2019 Mar 1. Available from: https://climatedataguide.ucar.edu/climate-data/hurrell-north-atlantic-oscillation-nao-index-pc-based
62. GLERL (Great Lakes Environmental Research Laboratory). Data of water level, ice cover and surface temperature in Lake Erie. Retrieved: 2020 Jan 31. Available from: https://www.glerl.noaa.gov/data/
63. Farmer TM, Marschall EA, Dabrowski K, Ludsin SA. Short winters threaten temperate fish populations. Nat Commun. 2015; 6: 7724. pmid:26173734
- View Article
- PubMed/NCBI
- Google Scholar
64. Whiteside MC, Swindoll CM, Doolittle WL. Factors affecting the early life history of yellow perch, Perca flavescens. Environ Biol Fishes. 1985; 12: 47–56.
- View Article
- Google Scholar
65. Imbrock F, Appenzeller A, Eckmann R. Diel and seasonal distribution of perch in Lake Constance: a hydroacoustic study and in situ observations. J Fish Biol. 1996; 49: 1–13.
- View Article
- Google Scholar
66. Yu H, Jiao Y, Winter A. Catch-rate standardization for yellow perch in Lake Erie: a comparison of the spatial generalized linear model and the generalized additive model. Trans Am Fish Soc. 2011; 140: 905–918.
- View Article
- Google Scholar

[ref1] 1. Harrison S. Meta-populations and conservation. In: Edwards PJ, May RM, Webb N, editors. Large Scale Ecology and Conservation Biology. London: Wiley-Blackwell; 1994. pp. 111–128.

[ref2] 2. Dieckmann U, O'Hara B, Weisser W. The evolutionary ecology of dispersal. Trends Ecol Evol. 1999; 14: 88–90.
View Article
Google Scholar

[3] View Article

[4] Google Scholar

[ref3] 3. Lowe WH, Allendorf FW. What can genetics tell us about population connectivity? Mol Ecol. 2010; 19: 3038–3051. pmid:20618697
View Article
PubMed/NCBI
Google Scholar

[6] View Article

[7] PubMed/NCBI

[8] Google Scholar

[ref4] 4. Berkes F, Pocock D. Quota management and “people problems”: a case history of Canadian Lake Erie fisheries. Trans Am Fish Soc. 1987; 116: 494–502.
View Article
Google Scholar

[10] View Article

[11] Google Scholar

[ref5] 5. Kendall WL. One size does not fit all: adapting mark-recapture and occupancy models for state uncertainty. In: Thomson DL, Cooch EG, Conroy MJ, editors. Modeling Demographic Processes in Marked Populations. Boston: Springer; 2009. pp. 765–780.

[ref6] 6. Block BA, Jonsen ID, Jorgensen SJ, Winship AJ, Shaffer SA, Bograd SJ, et al. Tracking apex marine predator movements in a dynamic ocean. Nature. 2011; 475: 86–90. pmid:21697831
View Article
PubMed/NCBI
Google Scholar

[14] View Article

[15] PubMed/NCBI

[16] Google Scholar

[ref7] 7. Frank KT, Brickman D. Allee effects and compensatory population dynamics within a stock complex. Can J Fish Aquat Sci. 2000; 57: 513–517.
View Article
Google Scholar

[18] View Article

[19] Google Scholar

[ref8] 8. Ying Y, Chen Y, Lin L, Gao T. Risks of ignoring fish population spatial structure in fisheries management. Can J Fish Aquat Sci. 2011; 68: 2101–2120.
View Article
Google Scholar

[21] View Article

[22] Google Scholar

[ref9] 9. Goethel DR, Berger AM. Accounting for spatial complexities in the calculation of biological reference points: effects of misdiagnosing population structure for stock status indicators. Can J Fish Aquat Sci. 2017; 74: 1878–1894.
View Article
Google Scholar

[24] View Article

[25] Google Scholar

[ref10] 10. Hampton J, Fournier DA. A spatially disaggregated, length-based, age-structured population model of yellowfin tuna (Thunnus albacares) in the western and central Pacific Ocean. Mar Freshw Res. 2001; 52: 937–963.
View Article
Google Scholar

[27] View Article

[28] Google Scholar

[ref11] 11. Palkovacs EP, Hasselman DJ, Argo EE, Gephard SR, Limburg KE, Post DM, et al. Combining genetic and demographic information to prioritize conservation efforts for anadromous alewife and blueback herring. Evol Appl. 2014; 7: 212–226. pmid:24567743
View Article
PubMed/NCBI
Google Scholar

[30] View Article

[31] PubMed/NCBI

[32] Google Scholar

[ref12] 12. Goethel DR, Quinn TJ, Cadrin SX. Incorporating spatial structure in stock assessment: movement modeling in marine fish population dynamics. Rev Fish. 2011;19:119–36.
View Article
Google Scholar

[34] View Article

[35] Google Scholar

[ref13] 13. Maunder MN. Integration of tagging and population dynamics models in fisheries stock assessment. Ph.D. dissertation, The University of Washington. 1998. Available from: https://www.researchgate.net/publication/305280946

[ref14] 14. Thorsteinsson V. Tagging methods for stock assessment and research in fisheries. Report of Concerted Action FAIR CT.96.1394 (CATAG). Reykjavík, Iceland: Marine Research Institute. 2002.

[ref15] 15. Gillanders BM. Tools for studying biological marine ecosystem interactions—natural and artificial tags. In: Nagelkerken I, editors. Ecological Connectivity among Tropical Coastal Ecosystems. Dordrecht: Springer; 2009. pp. 457–492.

[ref16] 16. Hilborn R. Determination of fish movement patterns from tag recoveries using maximum likelihood estimators. Can J Fish Aquat Sci. 1990; 47: 635–643.
View Article
Google Scholar

[40] View Article

[41] Google Scholar

[ref17] 17. Pine WE, Hightower JE, Coggins LG, Lauretta MV, Pollock KH. Design and analysis of tagging studies. In: Zale AV, Parrish DL, Sutton TM, editors. Fisheries Techniques. 3rd ed. Bethesda, MD: American Fisheries Society; 2012. pp. 521–572.

[ref18] 18. Latour RJ. Tagging methods and associated data analysis. FAO Fisheries Technical Paper. 2005; 474: 45.
View Article
Google Scholar

[44] View Article

[45] Google Scholar

[ref19] 19. Hightower JE, Pollock KH. Tagging methods for estimating population size and mortality rates of inland striped bass populations. Am Fish Soc Symp. 2013; 80: 249–262.
View Article
Google Scholar

[47] View Article

[48] Google Scholar

[ref20] 20. Eveson JP, Laslett GM, Polacheck T. A spatial model for estimating mortality rates, abundance and movement probabilities from fishery tag-recovery data. In: Thomson DL, Cooch EG, Conroy MJ, editors. Modeling Demographic Processes in Marked Populations. Boston: Springer; 2009. pp. 987–1010.

[ref21] 21. Vandergoot CS, Brenden TO. Spatially varying population demographics and fishery characteristics of Lake Erie walleyes inferred from a long-term tag recovery study. Trans Am Fish Soc. 2014; 143: 188–204.
View Article
Google Scholar

[51] View Article

[52] Google Scholar

[ref22] 22. Brownie C, Anderson DR, Burnham KP, Robson DS. Statistical Inference from Band Recovery Data: A Handbook. Resource Publication 156. 2nd ed. Washington, DC: US Fish and Wildlife Service; 1985.

[ref23] 23. Joe M, Pollock KH. Separation of survival and movement rates in multi-state tag-return and capture-recapture models. J Appl Stat. 2002; 29: 373–384.
View Article
Google Scholar

[55] View Article

[56] Google Scholar

[ref24] 24. Patterson TA, Thomas L, Wilcox C, Ovaskainen O, Matthiopoulos J. State–space models of individual animal movement. Trends Ecol Evol. 2008; 23: 87–94. pmid:18191283
View Article
PubMed/NCBI
Google Scholar

[58] View Article

[59] PubMed/NCBI

[60] Google Scholar

[ref25] 25. Tzadik OE, Goddard EA, Hollander DJ, Koenig CC, Stallings CD. Non-lethal approach identifies variability of δ¹⁵N values in the fin rays of Atlantic Goliath Grouper, Epinephelus itajara. PeerJ. 2015; 3: e1010. pmid:26082864
View Article
PubMed/NCBI
Google Scholar

[62] View Article

[63] PubMed/NCBI

[64] Google Scholar

[ref26] 26. Fridriksson A. On the calculation of age-distribution within a stock of cod by means of relatively few age-determinations as a key to measurements on a large scale. Rapports et Procès-Verbaux des Réunions, Conseil Permanent International pour l’Exploration de la Mer. 1934; 86: 1–14.
View Article
Google Scholar

[66] View Article

[67] Google Scholar

[ref27] 27. Coggins LG Jr, Gwinn DC, Allen MS. Evaluation of age–length key sample sizes required to estimate fish total mortality and growth. Trans Am Fish Soc. 2013; 142: 832–840.
View Article
Google Scholar

[69] View Article

[70] Google Scholar

[ref28] 28. Hulson PJF, Hanselman DH, Shotwell SK. Investigations into the distribution of sample sizes for determining age composition of multiple species. Fish Bull. 2017; 115: 326–342.
View Article
Google Scholar

[72] View Article

[73] Google Scholar

[ref29] 29. Baldwin NS, Saalfeld RW, Dochoda MR, Buettner HJ, Eshenroder RL. Commercial Fish Production in the Great Lakes 1867–2006. 2009. Available from: http://www.glfc.org/databases/commercial/commerc.php
View Article
Google Scholar

[75] View Article

[76] Google Scholar

[ref30] 30. Regier HA, Hartman WL. Lake Erie’s fish community: 150 years of cultural stresses. Science. 1973; 180: 1248–1255. pmid:17759111
View Article
PubMed/NCBI
Google Scholar

[78] View Article

[79] PubMed/NCBI

[80] Google Scholar

[ref31] 31. Ryan PA, Knight R, MacGregor R, Towns G, Hoopes R, Culligan W. Fish-community goals and objectives for Lake Erie. Special Publications 03–02. 2003. Available from: http://www.glfc.org/pubs/SpecialPubs/Sp03_2.pdf

[ref32] 32. Sepulveda-Villet OJ, Stepien CA. Fine-scale population genetic structure of the yellow perch Perca flavescens in Lake Erie. Can J Fish Aquat.Sci. 2011; 68: 1435–1453.
View Article
Google Scholar

[83] View Article

[84] Google Scholar

[ref33] 33. Bi R, Jiao Y, Zhou C, Hallerman EM. A Bayesian spatiotemporal approach to inform management unit appropriateness. Can J Fish Aquat Sci. 2018; 76: 217–237.
View Article
Google Scholar

[86] View Article

[87] Google Scholar

[ref34] 34. Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. Bayesian Data Analysis. Boca Raton: CRC Press; 2014.

[ref35] 35. Li Y. Innovative stock assessment methods and management solutions for spatially structured fish populations. Ph.D. dissertation, Michigan State University. 2018. Available from: https://www.canr.msu.edu/qfc/publications/pdf-theses-dissertations/2018-td/YangLi_Dissertation_2018.pdf

[ref36] 36. Kaemingk MA, Weber MJ, McKenna PR, Brown ML. Effect of passive integrated transponder tag implantation site on tag retention, growth, and survival of two sizes of juvenile Bluegills and Yellow Perch. N Am J Fish Manag. 2011; 31: 726–732.
View Article
Google Scholar

[91] View Article

[92] Google Scholar

[ref37] 37. YPTG. Report of the Lake Erie yellow perch task group. Wheatley, Ontario: Yellow Perch Task Group. 2015. Available from: http://www.glfc.org/pubs/lake_committees/erie/YPTG_docs/annual_reports/YPTG_report_2015.pdf

[ref38] 38. Royle JA, Dorazio RM. Hierarchical Modeling and Inference in Ecology. San Diego: Academic Press-Elsevier; 2008.

[ref39] 39. Plummer M. JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Hornik K, Leisch F, Zeileis A, editors. Proceedings of the 3rd International Workshop on Distributed Statistical Computing. Vienna, Austria: Technische Universität Wien; 2003. Available from: https://www.R-project.org/conferences/DSC-2003/Proceedings/Plummer.pdf

[ref40] 40. Plummer M. rjags: Bayesian Graphical Models Using MCMC. R package version 4–6. 2016. Available from: https://CRAN.R-project.org/package=rjags
View Article
Google Scholar

[97] View Article

[98] Google Scholar

[ref41] 41. Denwood MJ. runjags: An R package providing interface utilities, model templates, parallel computing methods and additional distributions for MCMC models in JAGS. J Stat Softw. 2016; 71: 1–25.
View Article
Google Scholar

[100] View Article

[101] Google Scholar

[ref42] 42. R Core Team. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. 2019. Available from: https://www.R-project.org/

[ref43] 43. Gelman A, Rubin DB. A single sequence from the Gibbs sampler gives a false sense of security. In Bernardo JM, Berger JO, Dawid AP, Smith AFM, editors. Bayesian Statistics 4. New York: Oxford University Press; 1992. pp. 625–631.

[ref44] 44. Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A. Bayesian measures of model complexity and fit. J R Stat Soc Ser B Stat Methodol. 2002; 64: 583–639.
View Article
Google Scholar

[105] View Article

[106] Google Scholar

[ref45] 45. Watanabe S. Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J Mach Learn Res. 2010; 11: 3571–3594.
View Article
Google Scholar

[108] View Article

[109] Google Scholar

[ref46] 46. Vehtari A, Gelman A, Gabry J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput. 2017; 27: 1413–1432.
View Article
Google Scholar

[111] View Article

[112] Google Scholar

[ref47] 47. Vehtari A, Gelman A. Pareto smoothed importance sampling. 2015; arXiv:1507.02646.
View Article
Google Scholar

[114] View Article

[115] Google Scholar

[ref48] 48. Vehtari A, Gelman A, Gabry J. loo: Efficient leave-one-out cross-validation and WAIC for Bayesian models. R package version 0.1.6. 2016. Available from: https://github.com/stan-dev/loo
View Article
Google Scholar

[117] View Article

[118] Google Scholar

[ref49] 49. YPTG. Report of the Lake Erie yellow perch task group. Wheatley, Ontario: Yellow Perch Task Group. 2016. Available from: http://www.glfc.org/pubs/lake_committees/erie/YPTG_docs/annual_reports/YPTG_report_2016.pdf

[ref50] 50. Punt AE, Pribac F, Walker TI, Taylor BL, Prince JD. 2000. Stock assessment of school shark, Galeorhinus galeus, based on a spatially explicit population dynamics model. Mar Fresh Res. 2000; 51: 205–220.
View Article
Google Scholar

[121] View Article

[122] Google Scholar

[ref51] 51. Taylor NG, McAllister MK, Lawson GL, Carruthers T, Block BA. Atlantic bluefin tuna: a novel multistock spatial model for assessing population biomass. PLoS ONE. 2011; 6: e27693. pmid:22174745
View Article
PubMed/NCBI
Google Scholar

[124] View Article

[125] PubMed/NCBI

[126] Google Scholar

[ref52] 52. Goethel DR, Legault CM, Cadrin SX. Demonstration of a spatially explicit, tag-integrated stock assessment model with application to three interconnected stocks of yellowtail flounder off of New England. ICES J Mar Sci. 2015; 72: 164–177.
View Article
Google Scholar

[128] View Article

[129] Google Scholar

[ref53] 53. MacCall AD. Dynamic Geography of Marine Fish Populations. Seattle, Washington: University of Washington Press; 1990.

[ref54] 54. Polacheck T, Eveson JP, Laslett GM, Pollock KH, Hearn WS. Integrating catch-at-age and multiyear tagging data: a combined Brownie and Petersen estimation approach in a fishery context. Can J Fish Aquat Sci. 2006; 63: 534–548.
View Article
Google Scholar

[132] View Article

[133] Google Scholar

[ref55] 55. Hestbeck JB. Bias in transition-specific survival and movement probabilities estimated using capture-recapture data. J Appl Stat. 1995; 22: 737–750.
View Article
Google Scholar

[135] View Article

[136] Google Scholar

[ref56] 56. Beverton RJH, Holt SJ. On the dynamics of exploited fish populations. Fishery Investigations, Series 2, 19. London: Ministry of Agriculture, Fisheries and Food; 1957.

[ref57] 57. Kirkwood GP, Walker MH. A new method for estimating tag shedding rates with application to data for Australian Salmon, Arripes trutta esper Whitley. Aust J Mar Freshw Res. 1984; 35: 601–606.
View Article
Google Scholar

[139] View Article

[140] Google Scholar

[ref58] 58. Barrowman NJ, Myers RA. Estimating tag-shedding rates for experiments with multiple tag types. Biometrics. 1996; 52: 1410–1416.
View Article
Google Scholar

[142] View Article

[143] Google Scholar

[ref59] 59. Pollock KH, Hoenig JM, Jones CM. Estimation of fishing and natural mortality when a tagging study is combined with a creel survey or port sampling. Am. Fish. Soc. Symp. 1991; 12: 423–434.
View Article
Google Scholar

[145] View Article

[146] Google Scholar

[ref60] 60. Wilberg MJ, Bence JR, Eggold BT, Makauskas D, Clapp DF. Yellow perch dynamics in southwestern Lake Michigan during 1986–2002. N Am J Fish. Manag. 2005; 25:1130–1152.
View Article
Google Scholar

[148] View Article

[149] Google Scholar

[ref61] 61. NCAR (National Center for Atmospheric Research). 2019. The Climate Data Guide: Hurrell North Atlantic Oscillation (NAO) Index (PC-based). Retrieved: 2019 Mar 1. Available from: https://climatedataguide.ucar.edu/climate-data/hurrell-north-atlantic-oscillation-nao-index-pc-based

[ref62] 62. GLERL (Great Lakes Environmental Research Laboratory). Data of water level, ice cover and surface temperature in Lake Erie. Retrieved: 2020 Jan 31. Available from: https://www.glerl.noaa.gov/data/

[ref63] 63. Farmer TM, Marschall EA, Dabrowski K, Ludsin SA. Short winters threaten temperate fish populations. Nat Commun. 2015; 6: 7724. pmid:26173734
View Article
PubMed/NCBI
Google Scholar

[153] View Article

[154] PubMed/NCBI

[155] Google Scholar

[ref64] 64. Whiteside MC, Swindoll CM, Doolittle WL. Factors affecting the early life history of yellow perch, Perca flavescens. Environ Biol Fishes. 1985; 12: 47–56.
View Article
Google Scholar

[157] View Article

[158] Google Scholar

[ref65] 65. Imbrock F, Appenzeller A, Eckmann R. Diel and seasonal distribution of perch in Lake Constance: a hydroacoustic study and in situ observations. J Fish Biol. 1996; 49: 1–13.
View Article
Google Scholar

[160] View Article

[161] Google Scholar

[ref66] 66. Yu H, Jiao Y, Winter A. Catch-rate standardization for yellow perch in Lake Erie: a comparison of the spatial generalized linear model and the generalized additive model. Trans Am Fish Soc. 2011; 140: 905–918.
View Article
Google Scholar

[163] View Article

[164] Google Scholar

Figures

Abstract

Introduction

Methods

Case study: Yellow perch tagging experiment in Lake Erie

Age-structured movement model

Movement configurations

Constant movement.

Fixed effects by year.

Random effects by year.

Fixed effects by age.

Random effects by age.

Random effects by age and year.

Random effects by age and year with initial year correction.

Age classifications

Likelihood

Model fitting and comparison

Results

Model comparison

Movement patterns of yellow perch

Additional biological and fishery-related parameter estimates

Discussion

Model assumptions

Movement patterns of yellow perch in Lake Erie and management implications

Supporting information

S1 Fig.

S2 Fig. Movement probability of a tagged yellow perch from each age class derived from Model AR.

S3 Fig. Movement probability of a tagged yellow perch from Model C.

S4 Fig. Estimations of additional biological and fishery-related parameters from Model AR.

S5 Fig. Estimations of additional biological and fishery-related parameters from Model C.

S6 Fig. Point estimates of commercial trap net and angler fishing mortality rates in the U.S. waters estimated from the YPTG stock assessment model.

S1 Table. Symbols used in the model equations.

Acknowledgments

References