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The environmental conditions that marine populations experience are being altered because of climate change. In particular, changes in temperature and increased variability can cause shifts in spatial distribution, leading to changes in local physiological rates and recruitment success. Yet, management of fish stocks rarely accounts for variable spatial dynamics or changes in movement rates when estimating management quantities such as stock abundance or maximum sustainable yield. To address this concern, a management strategy evaluation (MSE) was developed to evaluate the robustness of the international management system for Pacific hake, an economically important migratory stock, by incorporating spatio-temporal population dynamics. Alternative hypotheses about climate-induced changes in age-specific movement rates, in combination with three different harvest control rules (HCR), were evaluated using a set of simulations that coupled single-area estimation models with alternative operating models representing spatial stock complexity. Movement rates intensified by climate change caused a median decline in catches, increased annual catch variability, and lower average spawning biomass. Impacts varied by area and HCR, underscoring the importance of spatial management. Incorporating spatial dynamics and climate change effects into management procedures for fish stocks with spatial complexity is warranted to mitigate risk and uncertainty for exploited marine populations.

Integrated population dynamics models use a variety of data types, and all the data used impact modeled processes and estimated dynamics. Paired age-length data treated as conditional age-at-length (CAAL) data are increasingly being used as a data component in stock assessment models. The original intent of the use of CAAL data was to directly estimate the length-at-age process, including the associated variability in length-at-age. However, we show that introduction of CAAL data that are not representative of the age-structure of the population can cause bias and imprecision in estimates of not only growth, but also dynamics and management quantities. Estimation of an appropriate age-based observations-modeled process may improve model performance. We also show that even the use of representative CAAL data in a model with misspecified age-based systems-modeled processes (natural mortality and time-varying growth) can lead to bias and imprecision in growth, dynamics, and management quantities. In these cases, estimation of an age-based observations-modeled process magnified the bias and imprecision. Greater consideration of this type of data is needed.

Selectivity is a key parameter in stock assessments that describes how fisheries interact with different ages and sizes of fish. It is usually confounded with other processes (e.g., natural mortality and recruitment) in stock assessments and the assumption of selectivity can strongly affect stock assessment outcome. Here, we introduce a new semi-parametric selectivity method, which we implement and test in Stock Synthesis. This selectivity method includes a parametric component and an autocorrelated nonparametric component consisting of deviations from the parametric component. We explore the new selectivity method using two simulation experiments, which show that the two autocorrelation parameters for selectivity deviations of data-rich fisheries are estimable using either mixed-effect or simpler sample-based algorithms. When selectivity deviations of a data-rich fishery are highly autocorrelated, using the new method to estimate the two autocorrelation parameters leads to more precise estimations of spawning biomass and fully selected fishing mortality. However, this new method fails to improve model performance in low data quality cases where measurement error in the data overwhelms the pattern caused by the autocorrelated process. Finally, we use a case study involving North Sea herring (Clupea harengus) to show that our new method substantially reduces autocorrelations in the Pearson residuals in fit to age composition data.

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.

Stock assessment analysts are exploring an increasingly diverse and complex range of models while also facing higher expectations for consistency, documentation, and transparency in reports and management advice, all within a tight timeline. Meeting these goals requires increased efficiency at all steps in the assessment process from data processing, through model development and selection, to report writing and review. Here, we describe one widely used tool that has proven successful in increasing the efficiency of the assessment process: the r4ss package, which supports the use of the Stock Synthesis modeling framework. What began 15 years ago as a tool to provide simple model diagnostics, including plots showing data and model results, has grown into a large collection of R functions to support many aspects of the assessment process. We provide an overview of the r4ss features and illustrate its utility with examples from recent applications. Finally, we discuss lessons learned from the ongoing development of r4ss that can be applied to similar efforts associated with the next generation of stock assessment packages.

Spatial patterns due to age-specific movement have been a source of unmodelled process error. Modeling movement in spatially explicit stock assessments is feasible, but hampered by a paucity of data from appropriate tagging studies. This study uses simulation analyses to evaluate alternative model structures that either explicitly or implicitly account for the process of time-varying age-based movement in a population dynamics model. We simulated synthetic populations using a two-area stochastic population dynamics operating model. Simulated data were fit in seven different estimation models. Only the model that includes the correct spatial dynamic results in unbiased and precise estimates of derived and management quantities. In a single-area assessment model, using the fleets-as-area (FAA) approach may be the second best option to estimate both length-based and time-varying age-based selectivity to implicitly account for the contact selectivity and annual availability. An FAA approach adds additional observation error performed nearly as well. Future research could evaluate which stock assessment method is robust to uncertainty in movement and is more appropriate for achieving intended management objectives.

Theoretical considerations and applied examples suggest that stock assessments are highly sensitive to the weighting of different data sources whenever data sources conflict regarding parameter estimates. Previous iterative reweighting approaches to weighting compositional data are generally ad hoc, do not propagate uncertainty about data-weighting when calculating uncertainty intervals, and often are not re-adjusted when conducting sensitivity or retrospective analyses. We therefore incorporate the Dirichlet-multinomial distribution into Stock Synthesis, and propose it as a model-based method for estimating effective sample size. This distribution incorporates one additional parameter per fleet (with the option of mirroring its value among fleets), and we show that this parameter governs the ratio of nominal (“input”) and effective (“output”) sample size. We demonstrate this approach using data for Pacific hake, where the Dirichlet-multinomial distribution and an iterative reweighting approach previously developed by McAllister and Ianelli (1997) give similar results. We also use simulation testing to explore the estimation properties of this new estimator, and show that it provides approximately unbiased estimates of variance inflation when compositional samples capture clusters of individuals with similar ages/lengths. We conclude by recommending further research to develop computationally efficient estimators of effective sample size that are based on alternative, a priori consideration of sampling theory and population biology.

Fishery catch projection models play a central role in fishery management, yet are underrepresented in the literature. A wide range of statistical approaches are employed for the task, including multiple regression models, autoregressive methods, different classes of generalized linear models, mixed model approaches and many others. However, the applicability of these statistical approaches can be limited in specific cases of complex fisheries. We developed a new catch projection model for quota-based fisheries on the West Coast of the U.S. to forecast annual catch and landings for a variety of groundfish species in the Northeast Pacific Ocean. The model projects total and landed catch of each species by individual vessel and for the entire fishing fleet, using a combination of weighted mean vessel attainment rates and historical catch rates, and generates uncertainty intervals. It demonstrated an ability to produce highly accurate predictions at both fleet (R 2 = 0.9847) and vessel levels (R 2 = 0.8447). The model framework contains much built-in versatility, is generalizable enough to serve a variety of quota based applications, and the approach can be tailored to other fisheries around the world. With the proliferation of quota based management of commercial fisheries, tools such as this one are increasingly useful for sustainable management of fishery resources.

Somatic growth in fishes often varies through time. Despite this, most stock assessments either fix or estimate a time-invariant growth relationship because estimating time-varying growth parameters can be data intensive and subject to multiple sources of bias. Additionally, estimates of growth are often confounded with estimates of selectivity, particularly if selectivity is also time varying. Incorporating empirical weight-at-age (EWAA) information into assessments is a little-studied alternative that accounts for time-varying growth, but foregoes fixing or estimating growth and length–weight relationships. However, this method requires annual measures of fish weights at each age, and missing values must therefore be interpolated. We used Stock Synthesis in a simulation-testing framework to compare the effect of estimating a single time-invariant growth curve, time-varying growth curves, and incorporating EWAA information on management quantities and parameter estimates. We ran simulations across two fish life histories (hake-like and rockfish-like) and three data cases (data-rich, data-rich with a late-starting survey, and data-moderate). We found that when growth was time invariant, the EWAA approach was unbiased but had twice the median average relative error compared to a model that estimated growth from age and length data. However, for data-rich cases with time-varying growth, the EWAA method resulted in more accurate estimates of spawning stock biomass compared to the approach that estimated time-invariant and time-varying growth parameters, as evidenced by at least a five-fold reduction in range of median relative errors. The magnitude of this effect was greatest for the long-lived, slow-growing life history. For the relatively fast-growing species, estimates from the EWAA method were particularly sensitive to interpolating missing values.

Analysts conducting stock assessments using integrated, age-structured models must discretize length data into a limited number of bins (data bins). Furthermore, some modeling frameworks also allow users to specify a distinct structure for how lengths of fish are represented in the model (model bins). The effect of choices regarding the number and width of these bins on model output is unclear, and these choices are made inconsistently in assessments across regions and species. Here, we used the stock synthesis modeling framework, and the ss3sim stock assessment simulation package, to explore the effects of choices about length discretization on stock assessment performance for three fish life-history types and four data cases. We found that, with all other aspects of a model fixed, increasing the model bin width tended to increase estimates of spawning biomass, but this effect depended on the shape of length-based processes (e.g., growth, maturity, and selectivity). Thus, we suggest analysts using model bins wider than 1 cm explore the effect of this decision on derived management quantities. In the context of estimation, there generally was a predictable tradeoff between estimation accuracy and model run time, with finer model and data bins always improving estimation accuracy and model convergence, but increasing run time. In some cases, wider data bins reduced run time (by up to 50%) with little sacrifice in model estimation performance, particularly those using conditional age-at-length data. This study identifies key aspects to consider when binning length, and provides pertinent information for stock assessment best practice guidelines.

The explicit incorporation of movement in the modelling of population dynamics can allow improved management of highly mobile species. Large-scale movements are increasingly being reported for sharks and rays. Hence, in this review we summarise the current understanding of long-scale movement patterns of sharks and rays and then present the different methods used in fisheries science for modelling population movement with an emphasis on sharks and rays. The use of movement data for informing population modelling and deriving management advice remains rare for sharks and rays. In the few cases where population movement was modelled explicitly, movement information has been solely derived from conventional tagging. Though shark and ray movement has been increasingly studied through a range of approaches these different sources of information have not been used in population models. Integrating these multiple sources of movement information could advance our understanding of shark and ray dynamics. This, in turn, would allow the use of more adequate models for assessing stocks and advising management and conservation effort.

Integrated assessment models frequently track population abundance at age, and hence account for fishery removals using a function representing fishery selectivity at age. However, fishery selectivity may have an unusual shape that does not match any parametric function. For this reason, previous research has developed flexible ‘non-parametric’ models for selectivity that specify a penalty on changes in selectivity as a function of age. In this study, we describe an alternative ‘semi-parametric’ approach to selectivity, which specifies a penalty on differences between estimated selectivity at age and a pre-specified parametric model whose parameters are freely estimated, while also using cross-validation to select the magnitude of penalty in both semi- and non-parametric models. We then compare parametric, semi-parametric, and non-parametric models using simulated data and evaluate the bias and precision of estimated depletion and fishing intensity. Results show that semi- and non-parametric models result in little decrease in precision relative to the parametric model when the parametric model matches the true data-generating process, but that the semi- and non-parametric models have less bias and greater precision when the parametric function is misspecified. As expected, the semi-parametric model reverts to its pre-specified parametric form when age-composition sample size is low but performs similarly to the non-parametric model when sample size is high. Overall, results indicate few disadvantages to using the non-parametric model given the range of simulation scenarios explored here, and that the semi-parametric model provides a selectivity specification that is intermediate between parametric and non-parametric forms.

The second dorsal spine has historically been used for age determination in the spiny dogfish shark. The dorsal spines are located on the external surface of the body and are subjected to natural wear and breakage. Two methods have been developed to account for the worn portion of the spine and extrapolate the lost annuli. We compared the performance of these methods using a large data collection assembled from multiple sources, and evaluated their utility for stock assessment and management of the spiny dogfish shark Squalus suckleyi in the Northeast Pacific Ocean. Our results showed that the two methods produced very different age estimates for older fish with worn spines. Both methods raised significant questions about some aspects of the age estimates produced, and further exploration of techniques to account for worn spine annuli is needed. It is therefore important to develop alternative methods for shark age determination, including those using stained vertebrae.

100 years after Rosa Lee (1912) showed that higher mortality on faster growing fish can alter length-at-age distributions in fish populations, we present a computationally-efficient and parsimonious method for modeling size-selective mortality within a commonly-used assessment model, Stock Synthesis. Stock Synthesis allows the normal distribution of length-at-age to be partitioned into three or five overlapping platoons with slow, medium, or fast growth trajectories. The platoons are tracked separately in the model, and experience different degrees of size-selective fishing pressure and mortality, but are assumed to be unobservable except through changes in the length distribution. Simulations are used to explore this phenomenon in conjunction with dome-shaped selectivity, an alternative explanation for observing fewer than expected large fish in sampled data, but with very different implications for population productivity. For data simulated both with and without platoons, misspecification of the assumptions about growth are found to bias model results, with selectivity often incorrectly identified as the cause of fewer observations of larger fish. Trends in dome-shaped selectivity were explored as a potential diagnostic of model misspecification.

Many fisheries stock assessment models are implemented specifically for likelihood-based estimation or for Bayesian inference (via full integration of the joint posterior distributions), but not all have appropriate structure for both statistical approaches. Bias correction of recruitment deviations, in particular, must be adjusted to achieve consistency in each case. Fisheries management often uses the two types of results similarly, setting future catch quotas based on expected values or posterior medians depending on which is available given time constraints. Using two recent examples from the U.S. west coast, Pacific hake and sablefish, both implemented in Stock Synthesis, we find that likelihood-based estimates of key management quantities, such as spawning biomass, corresponded well with posterior modes, but tend to be lower (on an absolute scale) than posterior median values and that the asymptotic approximation for uncertainty intervals based on the Hessian matrix tends to overestimate the likelihood of smaller stock sizes and underestimate that of larger stock sizes. This pattern may be caused by a basic asymmetry in most fisheries data-sets: the necessity of a minimum stock size to have generated the observed catch/time-series, but little information regarding the plausibility among much larger stock sizes. Where only one type of inference is available, this asymmetry may be important for management decision-making. Even if management takes explicit account of uncertainty, in some cases adding a precautionary buffer that scales with the relative uncertainty in point estimates, the differences in catch advice may turn out to be important and the relative reductions non-linear.

Understanding the relationship between abundance of spawners and subsequent recruitment is one of the central issues in fisheries stock assessment. We developed a new, pre-recruit survival based stock–recruitment model that enables explicit modeling of survival between embryos and age 0 recruits, and allows the description of a wide range of pre-recruit survival curves. The model is especially useful for low fecundity species that produce relatively few offspring per litter and exhibit a more direct connection between spawning output and recruitment than species generating millions of eggs. The proposed model provides additional flexibility in the stock–recruitment options that may be explored in any fishery stock assessment, and it is now available within the Stock Synthesis assessment platform. In this paper, we describe the mathematical formulation of the new stock–recruitment model, explain how this model can be specified within Stock Synthesis, and use it to model the stock–recruitment relationship of the spiny dogfish shark in the Northeast Pacific Ocean. We compare the results of the application of our new stock–recruitment model, with those from traditional Beverton–Holt relationship, and illustrate why the new approach is more appropriate for this species.

The confounded effects of changes in climate and density on a population’s demography are hard to separate for long-lived species because demographic traits are usually the aggregated result of conditions faced over years. Demographic parameters are compared for spiny dogfish ( Squalus acanthias ) in the Northeast Pacific, the longest lived and latest maturing of all sharks, using samples from the 1940s and 2000s. This 60-year interval has seen ocean temperatures rise by almost 1 °C and dogfish harvests peak above 50 000 tonnes (t)·annum–1 and then drop below 50 t·annum–1. Over this period, the age at 50% maturity for dogfish declined from 43 to 32 years, while the estimated average number of embryos per litter for a 100 cm dogfish increased from 5.9 to 6.7. Growth parameters changed significantly, with faster growth to a smaller size. Leslie matrix analysis showed that these changes could lead to an increase in population growth rate of about 1%. Comparison with published demographic parameters from the 1970s and 1980s indicated that the greatest change in demographic parameters occurred between the 1940s and 1970s, prior to the largest changes in ocean temperatures. The implications for fishing on long-lived populations during times of rapid environmental change are explored.

Correlations among life history parameters have been discussed in the ecological literature for over 50 years, but are often estimated while treating model estimates of demographic rates such as natural mortality (M) or individual growth (k) as "data." This approach fails to propagate uncertainty appropriately because it ignores correlations in estimation errors between parameters within a species and differences in estimation error among species. An improved alternative is multi-species mixed-effects modeling, which we approximate using multivariate likelihood profiles in an approach that synthesizes information from several population dynamics models. Simulation modeling demonstrates that this approach has minimal bias, and that precision improves with increased number of species. As a case study, we demonstrate this approach by estimating M/k for 11 groundfish species off the U.S. West Coast using the data and functional forms on which pre-existing, peer-reviewed, population dynamics models are based. M/k is estimated to be 1.26 for Pacific rockfishes (Sebastes spp.), with a coefficient of variation of 76% for M given k. This represents the first-ever estimate of correlations among life history parameters for marine fishes using several age-structured population dynamics models, and it serves as a standard for future life history correlation studies. This approach can be modified to provide robust estimates of other life history parameters and correlations, and requires few changes to existing population dynamics models and software input files for both marine and terrestrial species. Specific results for Pacific rockfishes can be used as a Bayesian prior for estimating natural mortality in future fisheries management efforts. We therefore recommend that fish population dynamics models be compiled in a global database that can be used to simultaneously analyze observation-level data for many species in life history meta-analyses.

Several life history traits of sharks result in juveniles being particularly vulnerable to exploitation. However, population level impacts of harvests on juvenile sharks have not been well quantified. This paper examines a range of harvest strategies, including those targeting juveniles. Reproductive value and yield per recruit are used to compare the harvests, which are represented by Leslie matrix models with a harvest matrix. Two species are used as examples: the short-lived Rhizoprionodon taylori and the long-lived Squalus acanthias. Harvests that maintain a stationary population size cause reproductive values to change in opposing ways, but they remove equal fractions of the population's reproductive potential. A new theorem gives population growth as a function of the fraction of reproductive potential removed by a harvest, a relationship useful for comparing harvests on juveniles and adults. Stochastic projections indicate that the risk of depletion is associated with the fraction of reproductive potential removed annually, a measure which encompasses the information in both the selectivity and the rate of fishing mortality. These results indicate the value of focusing conservation efforts on preserving reproductive potential.

AnewunderstandingofthestructureofstripedmarlinstocksinthePacificOceanwasthebasisforestimating the population dynamics in the western and central northern Pacific (1975-2010). Dynamics were estimated using large- scale spatial data and a fully integrated length-based and age-structured model. The model used fishery-dependent catch, size composition and catch per unit effort (CPUE) as likelihood components. Time-varying selectivity patterns were used inthemodellingtoaccount forchangesinfishing practices.Estimatesoffishing intensityshowedapatternofexploitation generally exceeding the levels associated with maximum sustainable yield (MSY). Estimates of spawning biomass and recruitment described a population that was relatively stable near biomass levels associated with MSY until the 1990s, when recruitment declined and biomass levels fell below those associated with MSY. The reduction in recruitment could beexplainedbyalossofspawningbiomassandpotentiallychangesinenvironment.Thefutureprospectsofrebuildingthe stock will depend on the relative importance of the roles maternal biomass and environment play in determining recruitment strength. Additional keywords: environmental versus maternal effects, integrated modelling, time-varying selection.