In statistical integrated age structured population models, there are two common practices used to incorporate somatic growth into the population dynamics. First, a parametric somatic growth model is fit externally to length-at-age data and the estimates are input to the model as fixed parameters. Second, the model simultaneously estimates growth parameters with other population dynamics and fishery processes. When growth is estimated externally to the stock assessment model, the effects of population dynamics and the cumulative effects of fishing on size-at-age on growth estimates are typically not accounted for. In addition, ignoring gear selectivity when estimating growth (internally or externally) is problematic because fisheries tend to select faster-growing fish. Therefore, growth estimated from unrepresentative data may not reflect the true population growth curve, which can lead to biased stock assessment results, biological reference points and management quantities. Furthermore, the quality and quantity of length- and age-composition data can affect the accuracy of parameter estimates and thus management reference points. Growth may be estimated internally when there is length composition data, or tag-recapture data. However, incorporating age-composition data in addition to length-composition data may or may not improve stock assessment estimates. For instance, even if length- and age-composition data are both available, the quality and quantity of this information can affect the accuracy of stock assessment outputs, with larger repercussions on some life-history types than others. Thus, estimation of growth parameters within a stock assessment model is not possible for all life-history types. Therefore, it is important to quantify the importance of different data types and quantity to stock assessment estimates across life-history types. Here we used ss3sim, a simulation framework based on Stock Synthesis, to evaluate the types and quantity of data that are needed to estimate somatic growth within an assessment model and the tradeoffs between estimating growth internally versus externally. The focus of this research is not only on the ability to estimate growth but also on the impact of potential model misspecification related to growth estimation on assessment-derived quantities of interest to management across contrasting life-history types. We used measurements of bias and precision with respect to spawning stock biomass, fishing mortality level, and management reference points to quantify the performance of stock assessment models that internally estimated somatic growth parameters compared with stock assessment models that had somatic growth fixed at externally estimated values.
Age and length composition data provide important information needed to estimate biological growth in integrated stock assessments. There is an extensive literature on estimating effective sample sizes and appropriately weighting compositional likelihoods relative to indices of abundance. However, there are other subjective decisions facing analysts with regard to how to incorporate length composition data in an assessment: the number and spacing of composition bins, whether to compress the tails of the distribution, and whether to add a constant to observed and expected proportions to make the likelihood calculations more robust. There has been little formal investigation of how these decisions impact the ability to estimate growth, leaving analysts to use personal preference. In this study, we investigate the implication of these options on the estimation of growth and management quantities using ss3sim, a simulation framework utilizing Stock Synthesis, a generalized, integrated stock assessment model. We performed simulations across life histories, fishery exploitation patterns, and a wide range of type, quantity, and quality of compositional and index data. We also explored model selection-based approaches to guide these decisions. Results from this study can be used to help guide analysts in the treatment of length composition data to optimize growth estimation and performance of stock assessments for management purposes.
Modeling growth in modern statistical stock assessments typically requires fitting respective models to seasonal- or annual-based time series of growth-related data, often size- and age-composition time series developed from fishery and/or survey samples collected in the field. The underlying time step (quarter, semester, annual, etc.) is an important model dimension, serving as the basis for growth estimation and accurately identifying potential changes in growth over time. The objective of the study is to evaluate the influence of intra-annual variability in composition data on estimating growth parameters and dynamics in the model. In this evaluation, stock assessments are conducted based on alternative time-step dimensions and results are compared using simulation methods. Quantitative comparisons are presented for derived growth parameter estimates (e.g., K, length-at-agemin and -agemax, L∞) and management quantities (e.g., SSBcurrent, depletion, MSY). Other practical considerations related to model development, such as model complexity (total number of estimated parameters) and speed (run time), are qualitatively contrasted. Stock assessments and associated simulations are evaluated in terms of two broad life history strategies: shorter-lived, more productive species (e.g., small pelagic spp.); and longer-lived, less productive species (e.g., groundfish spp.). Finally, inherent sample size consequences associated with finer-scale time step considerations are generally discussed.
Abstract: Fisheries stock assessments typically assume fish grow according to a theoretical growth curve (e.g., von Bertalanffy, Richards, or Gompertz). In some cases, such as Pacific hake (Merluccius productus), growth is empirically incorporated into stock assessments with weight-at-age data from research surveys or fishery observations. Estimating growth and incorporating weight-at-age data into stock assessments may each bias fisheries reference points, provided to decision makers, but these biases have not been well studied. Monte Carlo simulations were used to identify conditions under which using empirical weight-at-age in stock assessments provide more robust estimations of stock status and management reference points than when growth is internally estimated. Results of this research will provide guidance to fisheries scientists regarding under what circumstances (i.e., fishing pattern, life-history type, and data availability) it is most beneficial to estimate growth within a stock assessment rather than empirically incorporate growth data.
Pacific mackerel are a productive small pelagic species inhabiting the Northeast Pacific Ocean, characterized by highly variable and infrequent recruitment success and associated stock abundance in any given year based primarily on oceanographic conditions and less so, on direct fishing pressure. In this context, determination of appropriate selectivity assumptions and estimators to use in formal fish stock assessments is not straightforward and demands further scrutiny, given both outside and inside the model, plausible scenarios exist for using age or length data in concert with age- or length-based selectivity. The current stock assessment model was simplified by omitting/pooling particular data sources and fixing parameters to produce two baseline models that included either age-composition or length-composition data. Each baseline model was evaluated in terms of age and length selectivity parameterization. A parametric bootstrap procedure within the Stock Synthesis modeling platform was used to produce four simulated data sets for examining the quality (precision and bias) of derived management statistics of interest (current spawning biomass, MSY, stock depletion, etc.). The benefits of this approach for conducting future sensitivity analysis and diagnostic examinations surrounding the ongoing stock assessment are discussed in this presentation.
Selectivity is one of the most influential components of integrated stock assessment models. The choice among alternative selectivity types is often subjective and can produce very different assessment results and related impacts on management quantities. Integrated stock assessment models have typically relied on parametric selectivity functions that can be straightforward to implement and interpret, but may lack enough flexibility to fit the age or size composition data. Although non-parametric functional forms, such as cubic splines, allow for more flexibility, they have not been used as extensively. Good practices for using cubic spline selectivity are not available and their tradeoffs compared to other functional forms are little known. Here we use a simulation approach to develop and test a general method to implement cubic spline selectivity using the Stock Synthesis assessment model. The method takes into account the range, number and location of knots, as well as their slopes used to define the cubic splines. The approach is tested on multiple, single species stock assessments to include a wide range of life histories, data availability, and selectivity shapes. The pros and cons of using cubic spline selectivity relative to alternative parametric functional forms are discussed, along with good practices and alternative implementation methods.
Management of marine resources depends on assessment of stock status in relation to established reference points. The efficacy of fishery stock assessments in estimating historical abundance patterns and providing the basis for applying harvest strategies depends on factors such as species-specific life-history traits, characteristics of the fishery, and the quality and quantity of available data. Statistical catch-at-age (or catch-at-length) models have become an established tool for assessing the status of fish stocks worldwide. Stock Synthesis (SS) is a statistical catch-at-age analysis population modeling framework increasingly used in stock assessments. SS can use several data sources for parameter estimation. A simulation-estimation process is used to evaluate the performance (bias and precision) of SS in terms of estimating standard metrics used in fishery management, conditioned upon fishery input data and life-history traits. Three main questions are addressed: 1) How well can management metrics be estimated for different life-history types (e.g., demersal, long-lived pelagic, and short-lived pelagic) when the same information (in terms of quantity and quality of data) are used?, 2) How does the frequency and duration of length- and age- composition data (and conditional age-at-length data) affect the bias or precision of estimates of management quantities for different life-history types?, and 3) How does catch history affect the estimation of management metrics for different life-history patterns?
Natural mortality (M) is typically assumed to be constant across time, sex, and age in fishery stock assessment models. However, M is rarely constant in reality as a result of the combined impacts of predation, environmental factors, and physiological trade-offs. Although one can acknowledge the potential importance of modelling heterogeneity in M, methods to estimate even an age- and time-invariant M within age-structured assessment models rely on informative length- and age-composition data, which are not always available. Misspecification of M can lead to bias in quantities estimated by stock assessment models, potentially resulting in misspecification of fishery reference points and catch limits, with the magnitude of bias likely dependent on life history and fishing history. Monte Carlo simulation is used to evaluate the ability of statistical catch-at-age (SCAA) models to estimate spawning stock biomass, stock status, and fishery reference points when the true M is age-specific or age-invariant, but time-varying. Stock assessment methods included SCAA models with (1) an age-invariant pre-specified M, (2) an age-invariant estimated M, and (3) age-specific estimated M. Simulations were conducted for three hypothetical fish stocks under two historical fishing scenarios. Stock Synthesis was used to generate the data and estimate management quantities. Bias and variance is evaluated for spawning stock biomass, depletion, and estimated parameters and the "minmax" approach is used to identify a "best" way to deal with M when it is thought to vary over time or by age (i.e. identify the stock assessment configuration for the assessment which is least wrong given no information about the true characteristics of M).
Retrospective patterns are systematic changes in estimates of population size, or other assessment model-derived quantities, that occur as additional years of data are added to an assessment. These patterns are an insidious problem in stock assessment, and can lead to severe errors when providing management advice. However, the cause of these patterns is not fully understood. A few studies have shown that retrospective patterns can arise from model miss-specification, particularly when data are non-stationary but this is ignored when assessments are conducted, and that the inclusion of time-varying selectivity can help to eliminate, or at least reduce, their incidence. We use simulations to explore which factors may lead to retrospective patterns in statistical catch-at-age stock assessment models. Specifically, we test how several biological and modeling factors can induce retrospective patterns for various life histories. We explore the potential effects of catch patterns, as well as model misspecification from time-varying biological parameters, time-varying selectivity and catchability, and their interactions. In cases where retrospective patterns were observed, we evaluate the appropriateness of including time-varying selectivity in the assessment as a means to correct them.