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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.

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.

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.

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.

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.