Integrated Stock Assessment Research Articles

Empirical validation of integrated stock assessment models to ensuring risk equivalence: A pathway to resilient fisheries management.

The Precautionary Approach to Fisheries Management requires an assessment of the impact of uncertainty on the risk of achieving management objectives. However, the main quantities, such as spawning stock biomass (SSB) and fish mortality (F), used in management metrics cannot be directly observed. This requires the use of models to provide guidance, for which there are three paradigms: the best assessment, model ensemble, and Management Strategy Evaluation (MSE). It is important to validate the models used to provide advice. In this study, we demonstrate how stock assessment models can be validated using a diagnostic toolbox, with a specific focus on prediction skill. Prediction skill measures the precision of a predicted value, which is unknown to the model, in relation to its observed value. By evaluating the accuracy of model predictions against observed data, prediction skill establishes an objective framework for accepting or rejecting model hypotheses, as well as for assigning weights to models within an ensemble. Our analysis uncovers the limitations of traditional stock assessment methods. Through the quantification of uncertainties and the integration of multiple models, our objective is to improve the reliability of management advice considering the complex interplay of factors that influence the dynamics of fish stocks.

Analyzing fishery data and exploring the resource status of Antarctic krill based on its environmental dependence

AbstractAntarctic krill Euphausia superba is a key species in the Southern Ocean ecosystem and has important ecological value. It is also one of the main fishery resources in the Southern Ocean with high economic value. In recent years, with the development of krill fishery and rapid climate change, the conservation and management of krill resources have faced unprecedented challenges. The krill resource is different from the general fishery resources. Due to the krill schooling characteristics, fishery data has some advantages over scientific survey data. Reviewing and analyzing the krill fishery data is necessary. Therefore, in this study, four fishery resource indices (FRIs) were calculated based on Antarctic krill fishery data, and based on the environmental dependence of Antarctic krill, the FRI with the strongest environmental dependence was screened by using the Gradient Forest Model, and the step changes of the FRI with strongest environmental dependence was examined by using the sequential t‐test analyses of regime shifts (STARS). The generalized additive model (GAM) to analyze the correlation between the FRI with the strongest environmental dependence and the main environmental factors, and then explore the resource status of Antarctic krill in the study area. The model results showed that the “FRI_hual” had the strongest environmental dependence and was a better indicator of the status of the Antarctic krill in the study area than the others. In the 2009–2010 year, “FRI_hual” had an obvious regime shift. The interaction of environmental factors “ice_area_2” and “SSH_1” has a great impact on “FRI_hual”. Methods used and results obtained in the study can provide new ideas and a scientific reference for future work, including integrated stock assessment of krill and krill resource monitoring, conservation, and management based on the ecosystem.

Estimating catch within integrated stock assessments: Distinguishing truth from error in sparse-spike data

Collecting accurate information on catch levels from marine recreational fishing can be challenging and often results in highly uncertain estimates of landings and discards. Sparse spikes are a common characteristic of these data, with isolated values much higher (e.g., 2–4 times) the surrounding values in a time series of annual estimates. In many cases, it is unclear whether these spikes represent observation error or true, even if anomalous, values. Utilizing multiple data sources simultaneously, integrated stock assessment models may be able to distinguish truth from error in sparse-spike catch estimates, however this supposition has not been well tested. Here, we developed a simulation study to elucidate conditions under which an integrated stock assessment model might perform well (or poorly) when confronted with sparse-spike catch estimates. We found that unconstrained estimation could distinguish truth from error in anomalous values, but only under specific conditions of supporting data. If the anomaly is known to be biased high, estimated catches can get closer to the true value. If the error mechanism is unknown, our results suggest that the true underlying value of a sparse spike is only recoverable when other input data are highly accurate, primarily a reliable index of abundance, but also age composition data in the same year.

Good Practices for estimating and using length-at-age in integrated stock assessments

Estimating growth (increase in size with age) is an integral component of fish population assessment. The use of integrated assessment models combined with the influence of misfitting size composition data on results have led to renewed interest in how growth is modeled in the assessment process. The types of data available to describe the growth process control how the length-at-age relationship will be estimated. Many factors contribute to the complexity of estimating length-at-age, including multiple sources of biological variability and difficulties in getting representative samples. The growth process in the population dynamics model is linked to all other processes and data but most directly influences the assessment model through 1) converting numbers into weight and vice versa, 2) productivity, and 3) modifying fits of size composition data. In some cases, an assessment may be insensitive to moderate levels of misspecification of the growth process, and therefore, relatively simple treatments may be adequate. However, in many cases, especially those where the fit of size composition is influential in estimating scale, a more thorough treatment of the growth process is needed. A complete treatment of growth will estimate the most important forms of biological variability, including individual, sex-specific, temporal, and spatial variability. Several types of sampling bias, including selectivity, length-stratified sampling, and spatial and measurement error, will likely also need to be addressed. When sufficient data are available, assessment authors should consider estimating the growth process as part of the integrated assessment model or consider empirical approaches for situations with high biological variability and sampling bias.

Stock assessment of Larimus breviceps, a bycatch species exploited by artisanal beach seining in Northeast Brazil

AbstractMotorized trawling was banned off part of the Brazilian coast in 1990 due to environmental impacts, thus artisanal fishermen adopted large beach seines as an alternative. No impact assessments have been conducted on any species; therefore, we examined the life history and stock status of shorthead drum, Larimus breviceps, a primary bycatch in tropical shrimp fisheries. Between 2016 and 2017, 969 shorthead drum were collected and analyzed using ELEFAN‐based models. Females were larger, more abundant, and older than males. Capture rates of juvenile were high, and no mega‐spawners were found. Integrated stock assessment indicated slight overexploitation and growth overfishing. Increased yield per recruit was indicated by high length at first capture. Shorthead drum segregate ontogenetically by size. Growth, mortality, and longevity may be temperature‐influenced. We found that beach seine fisheries may impact shorthead drum by population depletion and potential disruptions to reproductive capacity and recommend further studies and management to improve sustainability.

Data weighting: An iterative process linking surveys, data synthesis, and population models to evaluate mis-specification

Integrated stock assessments specify a distribution for multiple data types, and these distributions control the relative leverage assigned to each datum. A decade of research has demonstrated that (1) proper data weighting is necessary to avoid bias resulting from overweighting noisy age- and length-composition data; (2) sampling data can be pre-processed to estimate the likely sampling variance for composition data; and (3) using random effects to estimate time-varying parameters can improve the fit to data while also changing statistical leverage, and thereby serve a similar role to reweighting data. However, there are also unresolved questions including: (A) Is it more appropriate to model age and length data as proportions-at-age and as an index for the total, or as a series of indices-at-age? (B) Are correlated residuals appropriately addressed via data weighting or do they require additional model changes (i.e., time-varying parameters)? (C) How to efficiently communicate information about sampling imprecision and model errors between sampling and stock-assessment teams? (D) How does model-based expansion of sampling data affect data weighting? and (E) How to address alternative hypotheses about factors driving poor fit to data? Here, we argue that stock assessment errors can be classified using four categories: sampling bias (e.g., changes in survey coverage), sampling imprecision (e.g., finite sample sizes), assessment model bias (e.g., incorrect demographic assumptions) and assessment model imprecision (e.g., random effects). This categorization has several implications with resulting practical recommendations. For example, we define Percent Excess Variance (PEV) from the ratio of input sample size (the measured variance of sampling imprecision) and effective sample sizes (the variance of assessment-model residuals). We propose calculating PEV as standardized diagnostic measuring the net effect of survey bias and assessment model bias and imprecision. We demonstrate PEV in a simulation experiment fitted using the Woods Hole Assessment Model (WHAM) conditioned upon Gulf of Alaska walleye pollock, where unacknowledged variation in fishery selectivity results in a PEV of 77 % and this is eliminated when correctly specifying a time-varying estimation model. We also argue that model-based expansion of data inputs using auxiliary information can mitigate sampling bias, while also measuring sampling imprecision for spatially unrepresentative surveys. Similarly, including random effects can mitigate model bias while increasing model imprecision when the demographic model has little explanatory power. Finally, we observe that down-weighting compositional data for a given fleet fails to propagate information about model residuals when interpreting abundance indices or reference points for that same fleet. When PEV is large for important fleets, we therefore encourage focused research to explain the sources of these errors rather than simply downweighting without propagating information about residuals. However, we acknowledge a continuing role for automated data weighting for less important fleets, although we recommend explicit hypotheses about potential sources of errors in those cases.

Prevalence of effective fisheries management in a developed nation and its link to stock sustainability

Effective fisheries management is instrumental in reducing fishing pressure and facilitating the sustainable harvest of stocks. However, few administrations assess the quality of management in place for stocks when determining performance. Here, Australia was used as a case study to detail the quality of fisheries management in place for a developed nation. As it is difficult to assess management effectiveness, management intensity was used as a proxy across three attributes: stock assessment, harvest strategies, and catch/effort restrictions. Information for each of these three attributes was scored ranging from one for simple attributes (e.g. catch-only stock assessment) to four for robust attributes (e.g. integrated stock assessment) for 601 stocks across eight jurisdictions in 2018. Although the majority of Australia’s stocks are considered sustainable, most stocks are not intensively managed across the three attributes explored. Further, no clear link was apparent between stock status and management intensity which was largely focused towards high value target species and those stocks considered overfished to avoid further depletion. This highlights the need to assess both stock status and management when determining performance. With the prevalence of overfished stocks increasing globally, implementation of improved management should be a key priority for fisheries administrations. However, this analysis reveals that even in a developed nation such as Australia, management at the stock level remains limited. This comprehensive, national level assessment of stock management highlights the benefits of incorporating a management axis into future stock status reports.

Investigating trends in process error as a diagnostic for integrated fisheries stock assessments

Integrated stock assessments consist of fitting several sources of catch, abundance, and auxiliary biological information to estimate parameters of equations that describe the population dynamics of fish stocks. Stock assessments are subject to uncertainty, and it is a common practice to characterize uncertainty using alternative hypotheses and assumptions within an ensemble of models to develop scientific advice for fisheries management. In this context, there is the need to assign levels of plausibility to each of the combinations of factors that ultimately reflect the uncertainty on different biological and fishery processes. In this study, we describe and apply a model diagnostic to identify trends in process error in recruitment deviation estimates within ensembles of integrated assessment models of tropical tunas. We demonstrate that assessment model ensembles for tropical tunas contain distinct scenarios with significant trends in process error that are overlooked, with the associated implications for fisheries management. Using the Indian Ocean yellowfin as a case study, we found that trends in recruitment deviates are linked to extreme productivity scenarios which strongly diverged in scale from deterministic models fitted without recruitment deviates. This indicates that when recruitment deviates show an increasing trend, these can compensate for the loss of biomass in periods of high catch beyond the surplus production. In these cases, variation in recruitment is not a random process, but rather takes the function of a compensatory, systematic driver in productivity. Significant trends in recruitment were positively correlated with increased standard deviations and auto-correlation coefficient, non-random residual pattern in fits to abundance indices, and particularly poor performance of the Age-Structured Production Model (ASPM) diagnostic. We suggest that trends in recruitment deviates can be caused by misspecification of the biological parameters used as fixed values in integrated assessment models. The process error diagnostic described here can provide a statistical criterion in support for hypotheses and assumptions when using ensembles of models to develop fisheries management advice.

Focusing on the front end: A framework for incorporating uncertainty in biological parameters in model ensembles of integrated stock assessments

Uncertainty in population status estimates from stock assessments is important for providing a comprehensive picture of current knowledge of a stock. The use of model ensembles to encapsulate model uncertainty has become increasingly prevalent. The uncertainty of biological parameters that are often fixed in stock assessment models can be quantified for presentation of management advice through model ensembles. An ensemble can be created by randomly drawing values from the likely parameter space using a Monte-Carlo/bootstrap (MCB ensemble) or fixed at either a high, medium, or low value that encapsulates the variability in the parameter and applied in a full factorial grid across the fixed parameters (factorial ensemble). We calculated the management advice from MCB ensembles of various sizes and a 243 model factorial ensemble for Southwest Pacific swordfish (Xiphias gladius) and compared reference points which included model uncertainty only, model and estimation uncertainty, or both uncertainties weighted by sampling importance resampling. Median reference points were significantly different between the two ensemble types with the factorial ensemble having a significantly larger estimate of model uncertainty than the MCB ensemble. Stock assessments with fixed biological parameters can characterize uncertainty in these parameters more efficiently using a MCB ensemble approach. A factorial ensemble approach is appropriate for comparing different model structure assumptions and functional forms of relationships and can be used in combination with a MCB ensemble approach. Incorporation of both model and estimation uncertainty in estimates of reference points is important when providing management advice because including only model uncertainty can lead to biased estimates of the precision of reference points. Further work is needed regarding appropriate weighting of ensembles which incorporate different data sources or have different likelihood weightings.

Northwest Atlantic redfish science priorities for managing an enigmatic species complex

Redfish ( Sebastes spp.) in the Northwest Atlantic (NWA) extend from Baffin Island in the north to the Gulf of Maine in the south. The two most abundant species are Sebastes mentella and Sebastes fasciatus, which are morphometrically similar and difficult to visually distinguish. Redfish are long-lived, slow-growing, late-maturing, tend to produce large year classes episodically, and have complex population structure. Intraspecific genetic groups are abundant in the NWA. They are often semipelagic and patchily distributed, which makes them difficult to survey. These are all characteristics that cause difficulties for stock assessment and for sustainable fisheries management. This was the focus of The Ocean Frontier Institute Northwest Atlantic Redfish Symposium in 2018. In this paper, we synthesize the information known about NWA redfish. To improve the scientific basis for sustainable harvest strategies, key research recommendations involve (1) improved biological sampling including species and ecotype; (2) developing integrated stock assessment models; (3) developing harvest strategies with management reference points that are appropriate for redfish; (4) improving fishing technology and practices to avoid capture of small nonmarketable redfish and other species.

Towards best practice for specifying selectivity in age-structured integrated stock assessments

Specification of how selectivity (the combination of availability and vulnerability) is modelled in integrated stock assessments is key to avoiding bias in estimates of quantities of management interest. Many “rules of thumb” are common in the community but these have yet to be rigorously tested. This paper uses simulation to compare 12 approaches for specifying selectivity in an age-structured integrated stock assessment, including parametric and non-parametric approaches. The operating model represents a two-fishery case where selectivity for one or both fisheries can be dome-shaped and/or time-varying. The results suggest that using AIC to select among selectivity forms is not robust, including when model misspecification is absent, even though the use of model selection criteria such as AIC is common when conducting stock assessments. The use of double normal selectivity was found to be most robust to uncertainty in the true form of selectivity. Estimation of time-variation in selectivity did not lead to appreciable improvements in performance when the true time-variation was random. The double normal form performed poorly if M was estimated along with the other model parameters. Similarly, use of flexible parametric methods, such as splines, performed adequately with informative data, but poorly when the catch series exhibited low contrast and age-composition data were not available from the start of the fishery. This suggests that the best practices for selectivity will depend on knowledge of the likely information content of the data.

Catch and Length Models in the Stock Synthesis Framework: Expanded Application to Data-Moderate Stocks

Many fisheries in the world are data-moderate, with data types (e.g., total removals, abundance indices, and biological composition data) of varied quality (e.g., limited time series or representative samples) or available data. Integrated stock assessments are useful tools for data-moderate fisheries as they can include all available information, can be updated due to the availability of more information over time, and can directly test the inclusion and exclusion of specific data types. This study uses the simulation testing and systematic data reduction from the US West Coast benchmark assessments to examine the performance of Stock Synthesis with catch and length (SS-CL) compositions only. The simulation testing of various life histories, recruitment variabilities, and data availability scenarios found that the correctly specified SS-CL can estimate unbiased key population quantities such as stock status with as little as 1 year of length data although 5 years or more may be more reliable. The error in key population quantities is decreased with an increase in years and the sample size of length data. The removal of the length compositions from benchmark assessments often caused large model deviations in the outputs compared to the removal of other data sources, indicating the importance of length data in integrated models. Models with catch and length data, excluding abundance indices and age composition, generally provided informative estimates of the stock status relative to the reference model, with most data scenarios falling within the CIs of the reference model. The results of simulation analysis and systematic data reduction indicated that SS-CL is potentially viable for data-moderate assessments in the USA, thus reducing precautionary buffers on catch limits for many stocks previously assessed in a lower tier using catch-only models. SS-CL could also be applied to many stocks around the world, maximizing the use of data available via the well tested, multifeature benefits of SS.

Are tag-based integrated stock assessments robust to IUU fishing?

Integrated stock assessments depend on reliable catch and observational data to produce unbiased estimates of fish stock biomass and productivity. However, biases in catch data due to unreported catch are common among many of the world’s fisheries, especially those that are high value and therefore more vulnerable to illegal fishing. Some of these fisheries rely on tag-recapture data to support the estimation of biomass in integrated assessments and set precautionary catch limits intended to safeguard the fish stocks from overexploitation. Tag-recapture data is generally considered to be a more powerful indicator of stock abundance than survey data if the underlying assumptions are met. The effect of unreported catches that include tagged fish on biomass estimates in tag-based integrated assessments is unclear. We used a simulation analysis to determine the impact of under-reported catch on a hypothetical Patagonian toothfish (Dissostichus eleginoides) stock. Several catch scenarios are presented that cover different magnitudes and trend types of under-reported catch. We used the CASAL model (commonly employed to assess toothfish stocks) as both the operating model and the estimation model to evaluate how the various scenarios affected estimation performance of biomass depletion. Biomass depletion was increasingly underestimated as the magnitude of under-reporting increased, regardless of trend in catch. When unreported catch exceeds twice the amount reported combined with unreported tag returns, the estimation model will fail to detect biomass has been depleted below a target reference point of 50 % within 20 years of fishing. The lack of detection will falsely indicate current catch limits are sustainable when in reality they are not. Importantly, these estimates remained largely unchanged among different trends in under-reported catch. For assessments reliant on tag-recapture data, this suggests that it is more critical to estimate the overall quantity of unreported catch and the number of unreported tagged fish than the trend.

A cookbook for using model diagnostics in integrated stock assessments

Integrated analysis has increasingly been the preferred approach for conducting stock assessments and providing the basis for management advice for fish and invertebrate stocks around the world. Many decisions are required when developing integrated stock assessments. For example, the analyst needs to decide whether the model fits the data, if the optimization was successful, if estimates are consistent retrospectively, and if the model is suitable to predict future stock responses to fishing. This study provides practical guidelines for implementing selected diagnostic tools that can assist analysts in identifying problems with model specifications and alternatives that can be explored to minimize or eliminate such problems. Emphasis is placed on reviewing the implementation and interpretation of contemporary model diagnostic tools. We first describe each diagnostic approach and its utility. We then proceed by providing a “cookbook recipe” on how to implement each of the diagnostics, together with an interpretation of the results, using two worked examples of integrated stock assessments with Stock Synthesis. Further, we provide a conceptual flow chart that lays out a generic process of model development and selection using the presented model diagnostics. Based on this, we propose the following four properties as objective criteria for evaluating the plausibility of a model: (1) model convergence, (2) fit to the data, (3) model consistency, and (4) prediction skill. It would greatly benefit the stock assessment community if the next generation of stock assessment models could include the diagnostic tests presented in this study as a set of open source tools.

Good practices for including environmental data to inform spawner-recruit dynamics in integrated stock assessments: Small pelagic species case study

When assessing the status of a fish population for advising management, the spawner-recruit (S-R) relationship, which represents stock productivity, is an important biological process to consider, including the extent to which environmental drivers should be explicitly accounted for in recruitment estimation. Fishery managers are increasingly making requests for analysts to investigate the utility of including environmental data in stock assessment applications. Consequently, research is needed that addresses both specific environmental processes that may influence stock parameters and robust methods for including such data in the assessment. Two methods for incorporating environmental information in an integrated assessment model were evaluated in this study, based on: 1) including an environmental covariate as an additional component of the S-R function; or 2) using the covariate outside the S-R relationship as a survey index of recruitment. The methods were implemented in a broadly employed stock assessment software package (Stock Synthesis) using population/fishery processes generally applicable to an exploited small pelagic fish species (Pacific sardine). Simulation analysis was used to examine how environment-recruitment considerations in the assessment influenced model performance. The quality (bias and precision) of estimates of abundance and derived quantities generated from the models were examined statistically. Findings indicated that both methods for including an environmental index in the model resulted in relatively high quality estimates for a diverse group of output variables, depending on assumptions regarding bias correction and penalties associated with the recruitment deviation estimates. Several estimated quantities were found to be generally unbiased and relatively precise (e.g., stock biomass and average recruitment), regardless of the method implemented in the model; whereas, the choice of the method did impact the quality of results associated with more sensitive quantities (e.g., virgin recruitment and depletion). Recommendations for approaches based on both methods, as well as practical considerations associated with the methods are discussed.

How does growth misspecification affect management advice derived from an integrated fisheries stock assessment model?

Analysts must make many decisions regarding model specification when fitting integrated fishery stock assessment models. While variation in vital rates (i.e., recruitment, somatic growth, and natural mortality) is common, capturing this variation in models fit to available data is often infeasible or impractical. Failing to account for this variation can result in underestimates of uncertainty and even biased estimates of stock status used for management advice. Here, we seek to determine how growth misspecification affects management advice derived from integrated stock assessment models that use the Stock Synthesis platform. We conduct a simulation-based case study on California Current petrale sole (Eopsetta jordani) to test whether and how the inclusion or omission of somatic-growth variation introduces bias into management reference points when estimation models misspecify growth. Scenarios we explored included inter-annual and regime-like changes in two key parameters (k, the initial slope of the growth curve, and L2, the asymptotic maximum length) used to model somatic growth in Stock Synthesis. We find misspecification of growth can overestimate management quantities, particularly the estimate of current biomass relative to the unfished biomass (stock depletion). This results in an overly optimistic view of stock status. This bias may be mitigated or eliminated if the assessment model includes growth variation. Including growth variation in the estimation model can also reduce the uncertainty in estimated management quantities by correctly attributing process error to somatic growth. However, the magnitude of detected biases is exceeded by the uncertainty when data are limited, suggesting that estimating growth variation is helpful only in relatively data-rich stock assessment models. We suggest authors of data-rich assessments consider incorporating time-varying growth parameters into assessment models or decision tables more frequently to account for potential biases and reduce uncertainty caused by temporal growth variation.

Abundance trends of highly migratory species in the Atlantic Ocean: accounting for water temperature profiles

Abstract Relative abundance trends of highly migratory species (HMS) have played a central role in debates over the health of global fisheries. However, such trends have mostly been inferred from fishery catch rates, which can provide misleading signals of relative abundance. While many biases are accounted for through traditional catch rate standardization, pelagic habitat fished is rarely directly considered. Using a method that explicitly accounts for temperature regimes, we analysed data from the US pelagic longline fishery to estimate relative abundance trends for 34 HMS in the Atlantic Ocean from 1987 through 2013. This represents one of the largest studies of HMS abundance trends. Model selection emphasized the importance of accounting for pelagic habitat fished with water column temperature being included in nearly every species’ model, and in extreme cases, a temperature variable explained 50–60% of the total deviance. Our estimated trends represent observations from one fishery only, and a more integrated stock assessment should form the basis for conclusions about stock status overall. Nonetheless, our trends serve as indicators of stock abundance and they suggest that a majority of HMS (71% of analysed species) are either declining in relative abundance or declined initially with no evidence of rebuilding. Conversely, 29% of the species exhibited stable, increasing, or recovering trends; however, these trends were more prevalent among tunas than either billfishes or sharks. By estimating the effects of pelagic habitat on fishery catch rates, our results can be used in combination with ocean temperature trends and forecasts to support bycatch avoidance and other time-area management decisions.

Towards a spatial integrated stock assessment model for European hake northern stock

European hake (Merluccius merluccius) is a key species in the management of several mixed fisheries in the north-east Atlantic where regional spatial management plans are being set up. The wide spatial distribution of hake and the lack of knowledge of some processes involved in its spatial dynamics could hamper the assessment and management of hake.To help understand the processes, we implemented a spatial version of the Stock Synthesis stock assessment model for northern hake, including available data on this stock and the associated fisheries. For the 1978–2012 time series, the model distinguished the Bay of Biscay, the Celtic Sea and a northern area aggregating the West of Scotland and the North Sea. The model considered an age-structured population for each age class and area, a seasonal migration, global recruitment allocated to areas and fishing fleets for each area. Parameters for stock and exploitation spatio-temporal dynamics were estimated by likelihood maximization for each quarter and area.The comparison of spatial and non spatial models goodness of fit showed they were close, although the fit to abundance indices slightly improved with the spatial model.Fishing mortalities, spawning stock biomasses and recruitments were slightly different from the current assessment model estimates, essentially at the beginning and the end of the time series. On average over the time series, fishing mortality estimates relative to the abundance were higher in the Bay of Biscay than elsewhere, spawning stock biomass estimates were higher in the Celtic Sea than elsewhere, and recruitment occurred mainly in the Bay of Biscay. Finally, the final spatial model estimated a strong movement from the northern area to the Celtic Sea. The final spatial model is a step towards a spatial assessment and management of the stock.

Extending integrated stock assessment models to use non-depensatory three-parameter stock-recruitment relationships

Stock assessments based on the integrated paradigm often include an underlying stock-recruitment relationship. This, along with estimates of fishery selectivity and biological parameters, allows the biomass and fishing mortality associated with Maximum Sustainable Yield (BMSY and FMSY respectively) to be calculated. However, the estimates of these quantities may differ from the proxies assumed in the harvest control rules that are used to provide management advice. Moreover, the estimated values for BMSY and FMSY are related functionally in population dynamics models based on 2-parameter stock-recruitment relationships such as the commonly used Beverton-Holt or Ricker relationships. Use of 2-parameter stock-recruitment relationships (SRRs) consequently restricts the ability to fully quantify the uncertainty associated with estimating BMSY and FMSY because 2-parameter SRRs restrict the potential range of values for BMSY/B0. In principle, BMSY/B0 and FMSY can be more independent if the stock-recruitment relationship is more general than these 2-parameter SRRs. This paper outlines eleven potential 3-parameter stock-recruitment relationships and evaluates them in terms of whether they are able to match a wide range of specifications for BMSY (expressed relative to unfished spawning stock biomass, B0) and FMSY (expressed relative to natural mortality, M). Of the eleven 3-parameter stock-recruitment relationships considered, the Ricker-Power stock-recruitment relationship is found to best satisfy the characteristics of (a) being able to mimic a wide range of BMSY/B0 and FMSY/M values, (b) not to lead to negative recruitment for biomasses between 0 and B0, and (c) not to lead to increasing recruitment while approaching the limit of zero population size. Bayesian assessments of three example groundfish species off the US west coast (aurora rockfish, petrale sole, and cabezon) are conducted using Simple Stock Synthesis based on the Beverton-Holt and Ricker-Power stock-recruitment relationships to illustrate some of the impacts of allowing for a 3-parameter stock-recruitment relationship.

Inferring absolute recruitment and legal size population numbers of southern rock lobster (Jasus edwardsii) in South Australia's Southern Zone fishery using extended forms of depletion modelling

An extended depletion model (EDM) is presented that estimates both a time-series of the number of animals recruiting to legal size as well as start-year exploitable population size. EDM requires total catch in numbers for all months, but fits only to monthly catch rates of legal size lobsters over a restricted period during each year, aggregating catch and recruitment over the remaining months. Applied to a South Australian southern rock lobster (Jasus edwardsii) fishery over 1994–2014, catch rates for January, February, and March were fit under assumptions of no recruitment and equal catchability during these months of high catches. No assumptions are made about catchability during April–December. A hybrid model, EDM-CSA, combines EDM and catch-survey analysis (CSA), by additionally fitting to a recruitment index. Comparisons were made with estimates from a length-based integrated stock assessment model (LenMod). All parameter estimation was by maximum likelihood. Mean estimates of recruitment from the models differed by no more than 3% and of population size by no more than 12%. Trends in recruitment and population size were similar among models. A likelihood ratio test using EDM detected a significant increase in catchability from 2011 to 2012, which was sustained during 2012–2014, and that was corroborated by fisheries-independent survey data. Hyperstability in fishery catch-rates was also supported.