Bayesian Stock Assessment Research Articles

Management strategy evaluation of harvest control rules for Pacific Herring in Prince William Sound, Alaska

Abstract Management strategy evaluation (MSE) provides a mechanism to test the relative performance of alternative management strategies on a fishery. For Pacific herring in Prince William Sound, Alaska, no directed fisheries have occurred in over 30 years, providing an opportunity to evaluate potential management strategies before a fishery is opened. Here we evaluate and compare 10 harvest control rules (HCRs) ranging from simple threshold rules to rules accounting for population age structure, biomass trends, and weight distribution using an MSE integrated with a fully Bayesian stock assessment estimation model. We developed a utility function that shows simple threshold HCRs outperform the more complex rules, especially for catch stability. According to this utility function, the best rule had a lower limit threshold than the current default rule, while the worst rule had a higher limit threshold. Our simulations demonstrate that sufficient computing power exists for MSEs based on Bayesian estimation methods, thus opening a pathway for MSEs to simulation test probabilistic control rules, which provide a buffer against scientific uncertainty and should reduce the risk of overfishing.

A Bayesian stock assessment of the eastern Pacific gray whale using abundance and harvest data from 1967-1996

Abundance and harvest data since 1966/67 were used to assess the eastern Pacific stock of gray whales. A Bayesian statistical method was used to estimate probability distributions for the parameters of both a simple and an age and sex structured population dynamics model, as well as output quantities of interest. Model comparisons using the Bayes Factor provided conclusive evidence that an additional parameter should be used to account for unexplained variation in the abundance time series. Incorporating the additional variance parameter decreased the precision of the estimates of the other parameters. Point estimates of carrying capacity ranged from 24,640-31,840 for the different models, but the posterior distributions from the selected models were very broad and excluded few values. The current depletion level (population size as a fraction of carrying capacity) was estimated to be about 0.75, with a lower 2.5th percentile of 0.36. The probability that the population was still below one-half of its carrying capacity was estimated to be 0.21, with a corresponding probability of 0.28 that the population was still below its maximum sustainable yield level. Quantities from which catch limits could potentially be calculated were estimated, including current replacement yield, maximum sustainable yield and the quantity Q1 (described in Wade and Givens, 1997).

An examination of certain of the assumptions made in the Bayesian approach used to assess the eastern North Pacific stock of gray whales (Eschrichtius robustus)

An assessment of the eastern North Pacific stock of gray whales (Eschrichtius robustus) is conducted using a variant of the Bayesian stock assessment method of Wade (2002). This variant is based on the BALEEN II population dynamics model and uses parameters whose values are more familiar to members of the International Whaling Commission’s Scientific Committee. The sensitivity of the results to changes to some of the specifications used in the assessment is examined. The results are shown to be relatively insensitive to the first year considered in the analysis and the year for which a prior on absolute abundance is specified. An alternative Bayesian assessment method which involves projecting the population forward from pre-exploitation equilibrium in 1600 is also considered. As expected from previous assessments, results from this method are unable to mimic the recent trends in absolute abundance obtained from shore counts and are inconsistent with the fact that the fishery was commercially extinct by the end of the 19th Century. Allowing for underestimation of historical commercial and aboriginal catches provides improved consistency with recent trends in abundance but does not resolve these problems completely. The impact of process error (in the form of temporally correlated fluctuations in calf survival) on the dynamics of the population is found to be largely inconsequential in terms of resolving the inconsistency between historical catches and recent estimates of abundance.

Applying Bayesian model selection to determine ecological covariates for recruitment and natural mortality in stock assessment

Abstract Incorporating ecological covariates into fishery stock assessments may improve estimates, but most covariates are estimated with error. Model selection criteria are often used to identify support for covariates, have some limitations and rely on assumptions that are often violated. For a more rigorous evaluation of ecological covariates, we used four popular selection criteria to identify covariates influencing natural mortality or recruitment in a Bayesian stock assessment of Pacific herring (Clupea pallasii) in Prince William Sound, Alaska. Within this framework, covariates were incorporated either as fixed effects or as latent variables (i.e. covariates have associated error). We found most support for pink salmon increasing natural mortality, which was selected by three of four criteria. There was ambiguous support for other fixed effects on natural mortality (walleye pollock and the North Pacific Gyre Oscillation) and recruitment (hatchery-released juvenile pink salmon and a 1989 regime shift). Generally, similar criteria values among covariates suggest no clear evidence for a consistent effect of any covariate. Models with covariates as latent variables were sensitive to prior specification and may provide potentially very different results. We recommend using multiple criteria and exploring different statistical assumptions about covariates for their use in stock assessment.

A Bayesian approach to assess the status of Southern Hemipshere humpback whales (Megaptera novaeangliae) with an application to Breeding Stock G

The Bayesian stock assessment methodology presently being applied in the Comprehensive Assessment of the Southern Hemisphere humpbackwhales, which uses a sex- and age-aggregated population model, is detailed. This methodology is applied to Breeding Stock G, which winters offthe west coast of South America. This application takes into account the recently updated historic catch series, as well as the most recent estimatesof absolute abundance and population trend information.

A framework for assessing which sampling programmes provide the best trade-off between accuracy and cost of data in stock assessments

Abstract Fisheries surveys are required to assess the status of fish populations but are rarely evaluated to determine which data provide most information for least cost. We develop such a method focused on Pacific herring (Clupea pallasii) in Prince William Sound, Alaska. This population collapsed in 1992–93 and an intensive monitoring programme has been developed to assess why herring have not yet recovered, including the development of a Bayesian stock assessment model. We conducted a Monte-Carlo simulation study that calculated the deterioration in assessment performance when each survey was excluded, which allowed us to assess the trade-off between cost and improvement in model performance from including each survey data. For $10,000 a year the disease survey reduces bias and imprecision in current biomass by 34% on average, increases model reliability by 22%, and decreases by 31% the probability of a false management conclusion related to regulating the fishery. For $350,000 a year the diver survey reduces bias and imprecision by 12%, increases model reliability by 6%, and decreases the probability of a false management conclusion by 23%. The framework presented here can be used in other fisheries to weigh the costs and benefits of alternative sampling programmes in estimating current biomass.

Bayesian stock assessment of Pacific herring in Prince William Sound, Alaska.

The Pacific herring (Clupea pallasii) population in Prince William Sound, Alaska crashed in 1993 and has yet to recover, affecting food web dynamics in the Sound and impacting Alaskan communities. To help researchers design and implement the most effective monitoring, management, and recovery programs, a Bayesian assessment of Prince William Sound herring was developed by reformulating the current model used by the Alaska Department of Fish and Game. The Bayesian model estimated pre-fishery spawning biomass of herring age-3 and older in 2013 to be a median of 19,410 mt (95% credibility interval 12,150–31,740 mt), with a 54% probability that biomass in 2013 was below the management limit used to regulate fisheries in Prince William Sound. The main advantages of the Bayesian model are that it can more objectively weight different datasets and provide estimates of uncertainty for model parameters and outputs, unlike the weighted sum-of-squares used in the original model. In addition, the revised model could be used to manage herring stocks with a decision rule that considers both stock status and the uncertainty in stock status.

General state-space population dynamics model for Bayesian stock assessment

AbstractThis study presents a state-space modelling framework for the purposes of stock assessment. The stochastic population dynamics build on the notion of correlated survival and capture events among individuals. The correlation is thought to arise as a combination of schooling behaviour, a spatially patchy environment, and common but unobserved environmental factors affecting all the individuals. The population dynamics model isolates the key biological processes, so that they are not condensed into one parameter but are kept separate. This approach is chosen to aid the inclusion of biological knowledge from sources other than the assessment data at hand. The model can be tailored to each case by choosing appropriate models for the biological processes. Uncertainty about the model parameters and about the appropriate model structures is then described using prior distributions. Different combinations of, for example, age, size, phenotype, life stage, species, and spatial location can be used to structure the population. To update the prior knowledge, the model can be fitted to data by defining appropriate observation models. Much like the biological parameters, the observation models must also be tailored to fit each individual case.

Stock assessment and projections incorporating discard estimates in some years: an application to the hake stock in ICES Divisions VIIIc and IXa

Abstract Fernández, C., Cerviño, S., Pérez, N., and Jardim, E. 2010. Stock assessment and projections incorporating discard estimates in some years: an application to the hake stock in ICES Divisions VIIIc and IXa. – ICES Journal of Marine Science, 67: 1185–1197. A Bayesian age-structured stock assessment model is developed to take into account available information on discards and to handle gaps in the time-series of discard estimates. The model incorporates mortality attributable to discarding, and appropriate assumptions about how this mortality may change over time are made. The result is a stock assessment that accounts for information on discards while, at the same time, producing a complete time-series of discard estimates. The method is applied to the hake stock in ICES Divisions VIIIc and IXa, for which the available data indicate that some 60% of the individuals caught are discarded. The stock is fished by Spain and Portugal, and for each country, there are discard estimates for recent years only. Moreover, the years for which Portuguese estimates are available are only a subset of those with Spanish estimates. Two runs of the model are performed; one assuming zero discards and another incorporating discards. When discards are incorporated, estimated recruitment and fishing mortality for young (discarded) ages increase, resulting in lower values of the biological reference points Fmax and F0.1 and, generally, more optimistic future stock trajectories under F-reduction scenarios.

Impacts of prior mis-specification on Bayesian fisheries stock assessment

One of the key features of a Bayesian stock assessment is that the modeller needs to provide knowledge on model parameters. Priors summarise modellers’ understanding of model parameters and are often defined by a probability distribution function. Priors are often mis-specified with arbitrary and unrealistic accuracy and precision in perceiving the state of nature for the parameters as a result of our limited understanding of fisheries ecosystems. Commonly used probability functions such as normal distribution functions tend to be sensitive to prior mis-specification, resulting in large uncertainty and/or errors in Bayesian stock assessment. Fat-tailed functions such as the Cauchy distribution function have been found to be robust to prior mis-specification. Using the Maine sea urchin fishery as an example, we evaluated the impacts of mis-specification in defining the prior distributions on Bayesian stock assessment. The present study suggests that the quantification of priors with a Cauchy distribution tends to be robust to the prior mis-specification. Given our limited understanding of fisheries a function such as the Cauchy distribution function that is robust to prior mis-specification tends to be more desirable. Future studies should explore the use of other fat-tailed distribution functions for quantifying priors in fisheries stock assessment.

Assessing a stock assessment framework for the green sea urchin Strongylocentrotus drobachiensis fishery in Maine, USA

A Bayesian stock assessment framework with a size-structured population dynamics model used to assess the green sea urchin, Strongylocentrotus drobachiensis, fishery in Maine, USA was evaluated, using a simulation approach, for its performance in describing sea urchin population dynamics under different recruitment dynamics and data quality. This study suggests that the current stock assessment model performs well in estimating key sea urchin fishery parameters such as exploitable stock biomass, total stock biomass, natural mortality, and fishing mortality under different simulation scenarios, and can capture the dynamics of the Maine sea urchin population. The recruitment dynamics of the sea urchin are likely to vary greatly with large changes occurring in its ecosystem. The finding that the current assessment framework is able to capture different patterns of recruitment dynamics implies that the current assessment framework will remain effective in future stock assessments of the Maine sea urchin fishery.

Developing robust frequentist and Bayesian fish stock assessment methods

AbstractErrors in fitting models to data are usually assumed to follow a normal (or log normal) distribution in fisheries. This assumption is usually used in formulating likelihood functions often required in frequentist and Bayesian stock assessment modelling. Fisheries data are commonly subject to atypical errors, resulting in outliers in stock assessment modelling. Because most stock assessment models are nonlinear and contain multiple variables, it is difficult, if not impossible, to identify outliers by plotting fisheries data alone. Commonly used normal distribution‐based frequentist and Bayesian stock assessment methods are sensitive to outliers, resulting in biased estimates of model parameters that are vital in defining the dynamics of fish stocks and evaluating alternative strategies for fisheries management. Because of the high likelihood of having outliers in fisheries data, frequentist or Bayesian methods robust to outliers are more desirable in fisheries stock assessment. This study reviews three approaches that can be used to develop robust frequentist or Bayesian stock assessment methods. Using simulated fisheries as examples, we demonstrate how these approaches can be used to develop the frequentist and Bayesian stock assessment approaches that are robust to outliers in fisheries data and compare the robust approaches with the commonly used normal distribution‐based approach. The proposed robust approaches provide alternative ways to developing frequentist or Bayesian stock assessment methods.

A length-based Bayesian stock assessment model for the New Zealand abalone Haliotis iris

We describe a length-based Bayesian model for stock assessment of the New Zealand abalone Haliotis iris (paua). We fitted the model to five data sets: catch-per-unit-effort (CPUE) and a fishery-independent survey index, proportions-at-length from both commercial catch sampling and population surveys, and tag–recapture data. We estimated a common component of error and used iterative re-weighting of the data sets to balance the residuals, removing the arbitrary data set weightings used in previous assessments. Estimates at the mode of the joint posterior distribution were used to explore sensitivity of the results to model assumptions and input data; the assessment itself was based on marginal posterior distributions estimated from Markov chain–Monte Carlo simulation. Assessments are presented for two stocks in the south of New Zealand. One may be recovering after recent catch reductions; the other is over-exploited and likely to decline further. Assessment for the first stock was robust; assessment for the second stock was sensitive to the CPUE data and may be too optimistic. We discuss future directions and potential problems with this approach.

Development of Bayesian stock assessment methods for Namibian orange roughy Hoplostethus atlanticus

Bayesian methods are useful in fisheries stock assessment because they provide a conceptually elegant and statistically rigorous approach to making decisions under uncertainty. The application of Bayesian stock assessment methods in the management of Namibian orange roughy Hoplosthethus atlanticus within the 200 mile EEZ of Namibia is reviewed. Time-series of relative abundance are short and their reliability in indicating abundance trends is uncertain. The development of informative prior probability density functions (pdfs) for the constants of proportionality ( q ) for hydro-acoustic, commercial trawl swept area, and research trawl swept area indices produced statistically consistent prior estimates of absolute abundance for each of the three grounds where more than one index of abundance was available. The posterior pdfs for stock assessment model parameters were used to account for uncertainty in evaluations of the potential consequences of alternative harvesting policies under a stock reduction model in which catch removals were assumed to account for any declines. It appears that all orange roughy stocks off Namibia have been depleted below the limit reference point (50% of long-term unfished biomass). However, the stock reduction model could not easily account for the large declines in indices on the four fishing grounds over the period from 1995 until 1999 when the informative priors for q were applied. In the 2000 stock assessment, the Bayesian procedure was updated to account formally for uncertainty in model structures that could explain the decline in abundance. The possibility of very low stock abundance could still not be discounted when these uncertainties were accounted for. Although this most recent methodology applies more statistical rigour, its complexity has hindered its acceptance in Namibia. However, if it is worth quantifying risks and uncertainties in future stock assessments for the provision of precautionary management advice, it is proposed that the assessment protocols adopted be probabilistic to account for uncertainty in model parameters, that careful attention be given to subjective judgements about their inputs and the representation of uncertainty within them, and that, where appropriate, alternative hypotheses about stock abundance and mechanisms for catchability and stock decline be taken into account. Keywords: Bayesian, orange roughy, stock assessment, structural uncertainty African Journal of Marine Science 2001, 23: 241–264

Bayesian stock assessment using a state–space implementation of the delay difference model

This paper presents a Bayesian approach to fisheries stock assessment using the delay difference model to describe nonlinear population dynamics. Given a time series of annual catch and effort data, models in the Deriso-Schnute family predict exploitable biomass in the following year from biomass in the current and previous year and from past spawning stock. A state-space model is used, as it allows incorporation of random errors in both the biomass dynamics equations and the observations. Because the biomass dynamics are nonlinear, the common Kalman filter is generally not applicable for parameter estimation. However, it is demonstrated that the Bayesian approach can handle any form of nonlinear relationship in the state and observation equations as well as realistic distributional assumptions. Difficulties with posterior calculations are overcome by the Gibbs sampler in conjunction with the adaptive rejection Metropolis sampling algorithm.

Bayesian stock assessment using a state-space implementation of the delay difference model

Bayesian stock assessment using a state-space implementation of the delay difference model

Bayesian stock assessment: a review and example application using the logistic model

Bayesian statistical methods have recently been combined with conventional methods for fisheries stock assessment (e.g. catch-age analysis) to provide a conceptually elegant approach for providing fishery management advice under uncertainty. Uncertainties in the advice provided can be conveyed using posterior probability distributions (or “posteriors”) for the potential outcomes of each policy option. Posteriors can be estimated using data (e.g. catch-age data and relative abundance indices) for the fish population of interest and prior probability distributions for population model parameters (e.g. stock-recruit function parameters) based on data from similar fish populations. Despite growing interest, Bayesian methods remain accessible to relatively few. To increase the accessibility of these methods, the conceptual basis for Bayesian statistical estimation is reviewed and set in the context of fisheries stock assessment. The use of Bayesian methods is illustrated by fitting a logistic model to relative abundance indices for Namibian hake (Merlucius capensis and M. paradoxus) and presenting a decision analysis of alternative harvest policy options. Some alternative approaches are outlined for constructing prior and posterior probability distributions and some recent applications in fisheries. Some of the problems that can be encountered while implementing Bayesian methods are also discussed.

Bayesian stock assessment using catch-age data and the sampling - importance resampling algorithm

Une approche bayesienne a l'evaluation des stocks de poissons exploites par la peche est souhaitable parce qu'elle donne une densite de probabilite (dp) des parametres du modele de population. Cette dp peut aider les gestionnaires des peches a cerner les consequences d'autres politiques de recolte et vehiculer l'incertitude au sujet des quantites d'interet, comme la biomasse de la population. Toutefois, il existe peu d'analyses des prises par âge qui font appel aux methodes de Bayes. Dans le present article, nous etendons l'algorithme echantillonnage - reechantillonnage d'importance de sorte que l'on puisse estimer une dp des parametres du modele de population en utilisant les donnees sur les prises par âge et les indices d'abondance relative. Nous illustrons la methode en estimant une dp a 54 parametres pour la limande a nageoires jaunes (Limanda aspera) dans l'est de la mer de Bering. L'exemple demontre comment les donnees sur les prises par âge peuvent servir a ameliorer grandement l'estimation bayesienne et, egalement, illustre la possibilite d'introduire des biais significatifs lorsqu'on traite les indices d'abondance obtenus a l'aide de releves par chalutage comme etant des mesures absolues de la taille des stocks.

Bayesian stock assessment using catch - age data and the sampling - importance resampling algorithm

Bayesian stock assessment using catch - age data and the sampling - importance resampling algorithm

Bayesian fishery stock assessment and decision making using adaptive importance sampling

Bayesian fishery stock assessment and decision making using adaptive importance sampling