State-space Assessment Model Research Articles

Incorporation of observation uncertainty in stock assessment using spatio-temporal modeling of catch-at-length and age-at-length survey data

Abstract Spatio-temporal models are essential tools for estimating abundance indices and quantifying the associated uncertainty. Time series of index uncertainties can be used to objectively determine the influence each index has on the assessment. This can involve reducing the influence of indices in years with limited data. However, incorporating uncertainty in age-length conversion into assessment models has remained a challenge. In this research, we propose an index estimation approach that combines an abundance-at-length model with a model for age-at-length to generate age-specific abundance indices. By jointly modeling abundance-at-length and age-at-length, we address uncertainties in both components of the index-at-age. Using North East Arctic haddock (Melanogrammus aeglefinus) as a case study, we validate the uncertainty of the indices by integrating them into the state space assessment model SAM. The results indicate that the uncertainty estimates are realistic, and we further demonstrate that incorporating uncertainty in age conversion has effects on the assessment results. Our case study demonstrates that incorporating the uncertainty in age-at-length data improves the characterization of uncertainty in stock assessment, and hence better accounts for risk in precautionary management.

Are state-space stock assessment model confidence intervals accurate? Case studies with SAM and Barents Sea stocks

Our main contribution is to examine the reliability of confidence intervals using the SAM state-space fish stock assessment model used for the assessment of many stocks by the International Council for the Exploration of the Seas. We focus on frequentist statistical inferences and more specifically on inference conditioned on specific values of the state-space model random effects drawn from their process distribution. This is somewhat consistent with simulation self-test procedures that are commonly used to examine the reliability of state-space assessment model results. However, recent research has indicated that some estimation bias may be expected in the conditional setting. Hence, we also investigate recently proposed bias corrected confidence intervals appropriate for the conditional inference setting. The SAM simulation coverage probabilities of 95% confidence intervals for SSB and Fbar were usually slightly larger than 95%, but in a small number of years these coverage probabilities could be much smaller than 95%. The bias corrected confidence intervals were more reliable. When averaged over years, the SAM and bias corrected confidence interval coverage probabilities were similar for the Northeast Artic cod and saithe case studies, but the bias corrected confidence intervals performed much better overall for the haddock case study.

Detecting significant retrospective patterns in state space fish stock assessment

Retrospective patterns are commonly investigated to validate fish stock assessment models. A widely applied measure for retrospective bias is Mohn’s ρ and corresponding retrospective plots. However, retrospective patterns can be interpreted differently by experts. To make decisions regarding significant retrospective patterns less subjective, we proposed a post-sample Mohn’s ρ significance test. As case studies, we applied the state space assessment model SAM with data on Northeast Arctic cod and Norwegian coastal cod north of 67°N. We showed that the acceptance regions of Mohn’s ρ depends on both the data available and the assessment model complexity. We also assessed the test power under a range of assumption violations and conclude that Mohn’s ρ is useful for detecting violations associated with bias, but not for violations associated with variances and correlations.

Prediction–variance relation in a state-space fish stock assessment model

AbstractThe state-space assessment model (SAM) is extended by allowing a functional relationship between observation variance and the corresponding prediction. An estimated relationship between observation variance and predicted value for each individual observation allows the model to assign smaller (or larger) variance to predicted larger log-observations. This relation is different from the usual assumption of constant variance of log-observations within age groups. The prediction–variance link is implemented and compared to the usual constant variance assumption for the official assessments of North East Arctic cod and haddock. For both of these stocks, the prediction–variance link is found to give a significant improvement.

Multi-fleet state-space assessment model strengthens confidence in single-fleet SAM and provides fleet-specific forecast options

Abstract The state-space assessment model (SAM) is increasingly used to assess fish stocks in International Council for the Exploration of the Sea. One unique feature of the SAM class is that it allows the fishing selectivity to vary over time, and the degree to which it varies is not subjectively assigned, but estimated within the model. Selection may vary over time due to changes in the spatial pattern of the fish stock or fishing fleet, but a direct cause of selectivity change can be changed in fishing technology or other measures that target specific segments of the fish stocks. If the relative catches from fishing fleets which target different age or size classes of a species are changing over time, then the overall selectivity will also change—even if the selectivity within each fleet is fairly constant. A recent extension of the SAM model allows multiple fleets to be defined. It has been applied to two herring stocks to allow more detailed and fleet-specific management options in forecasts. For both stocks, the assessment from the multi-fleet models was consistent with the results from the single-fleet models, which strengthens confidence in the estimated time-varying selectivity for these and other stocks.

Implementing two-dimensional autocorrelation in either survival or natural mortality improves a state-space assessment model for Southern New England-Mid Atlantic yellowtail flounder

Survival is an important population process in fisheries stock assessment models and is typically treated as deterministic. Recently developed state-space assessment models can estimate stochastic deviations in survival, which represent variability in some ambiguous combination of natural mortality (M), fishing mortality (F), and migration. These survival deviations are generally treated as independent by age and year, despite our understanding that many population processes can be autocorrelated and that not accounting for autocorrelation can result in notable bias. We address these concerns, as well as the strong retrospective pattern found in the last assessment of Southern New England yellowtail flounder (Limanda ferruginea), by incorporating two-dimensional (2D, age and year) first-order autocorrelation in survival and M. We found that deviations were autocorrelated among both years (0.53 ± 0.09, 0.63 ± 0.16) and ages (0.33 ± 0.12, 0.40 ± 0.16) when estimated for survival or M, respectively. Models with 2D autocorrelation on survival or M fit the data better and had reduced retrospective pattern than models without autocorrelation. The best fit model included 2D autocorrelated deviations in survival as well as independent deviations in M and altered estimates of spawning stock biomass by 18 % and F by 21 % in model years. In short-term projections with F = 0, including 2D autocorrelation in survival or M reduced spawning stock biomass by 48 %. We conclude that incorporating 2D autocorrelated variation in survival or M could improve the assessment of Southern New England yellowtail flounder in terms of model fit and consistency of biomass projections.

Implementing two-dimensional autocorrelation in either survival or natural mortality improves a state-space assessment model for Southern New England-Mid Atlantic yellowtail flounder

Implementing two-dimensional autocorrelation in either survival or natural mortality improves a state-space assessment model for Southern New England-Mid Atlantic yellowtail flounder

Simulation testing methods for estimating misreported catch in a state-space stock assessment model

AbstractState-space stock assessment models have become increasingly common in recent years due to their ability to estimate unobserved variables and explicitly model multiple sources of random error. Therefore, they may be able to better estimate unobserved processes such as misreported fishery catch. We examined whether a state-space assessment model was able to estimate misreported catch in a simulated fishery. We tested three formulations of the estimation model, which exhibit increasing complexity: (i) assuming no misreporting, (ii) assuming misreporting is constant over time, and (iii) assuming misreporting follows a random walk. We tested these three estimation models against simulations using each of the three assumptions and an additional fourth assumption of uniform random misreporting over time. Overall, the worst estimation errors occurred when misreporting was ignored while it was in fact occurring, while there was a relatively small cost for estimating misreporting when it was not occurring. Estimates of population scale and fishing mortality rate were particularly sensitive to misreporting assumptions. Furthermore, in the uniform random scenario, the relatively simple model that assumed misreporting was fixed across ages and time was more accurate than the more complicated random walk model, despite the increased flexibility of the latter.

Temporal and environmental variation in growth and maturity and effects on management reference points of Georges Bank Atlantic cod

Temporal variation in demographic rates has been observed in various fish populations and environmental influences are likely to be a key factor. Here we show how it can be important to combine state-space models for environmental covariates and demographic rates when evaluating effects of the former on the latter. In an application to Georges Bank Atlantic cod (Gadus morhua), we show how estimates of the environmental covariate can be aliased with unknown temporal variation in growth rates and that stronger and opposite effects of the environment can incorrectly be found when the autocorrelation in the growth rate is not separately modeled. The perception of effects on maturity also depends on whether an appropriate distribution is considered for the maturity observations. Bottom temperature did not improve prediction of maturity parameters, but temporal variation driven by other sources did. Both bottom temperature and temporal variation improved performance of growth models. Finally, we found growth and maturity estimation to be important contributors to uncertainty of spawning biomass and biological reference points when incorporated into a state-space assessment model.

Comments on incongruous formulations in the SAM (state-space assessment model) model and consequences for fish stock assessment

The stock assessment model SAM (state-space assessment model) is an important tool for analysing fishery data and is used for abundance estimation of several different fish stocks. We demonstrate incongruous formulations in the equations that relate the catch data to fish abundance, and in the fishery and natural mortality rates. We present example results to show how these formulations introduce bias, and compound the uncertainty in model estimates. Finally, we provide corrections to the system equations to remedy the drawback.

Data-moderate assessments of Cape monkfish Lophius vomerinus and west coast sole Austroglossus microlepis in Namibian waters

There is global interest in providing scientific advice on optimal harvesting of all commercially exploited fish stocks. Nevertheless, many commercially important stocks lack analytical assessments. Therefore, we evaluate a data-moderate stock assessment method: the stochastic surplus production model in continuous time (SPiCT). The method was applied to two Namibian stocks: (i) the data-rich Cape monkfish Lophius vomerinus, where results are compared to a new data-rich assessment using a state–space assessment model (SAM); and (ii) the data-moderate west coast sole Austroglossus microlepis, which is an important bycatch species in the Cape monkfish fishery, but currently unassessed. The information available to the data-moderate assessment is total commercial catch, commercial catch per unit effort (CPUE), and survey CPUE. SPiCT and SAM gave largely consistent estimates of relative fishing mortality (F/FMSY) and relative exploitable biomass (B/BMSY) for the Cape monkfish stock, although with some discrepancies. Differences in the biomass estimates between the two assessments suggest that further investigation is required to understand the cause, and that some caution is necessary when considering the biomass of the stock. SPiCT shows that the west coast sole may be overexploited, although the confidence bounds were too wide for a firm conclusion. Similarity in the estimates of F/FMSY for Cape monkfish in recent years, using SPiCT relative to SAM, likewise indicates the suitability of SPiCT for managing west coast sole.

A state-space approach to incorporating environmental effects on recruitment in an age-structured assessment model with an application to southern New England yellowtail flounder

The state-space model framework provides a natural, probabilistic approach to stock assessment by modeling the stochastic nature of population survival and recruitment separately from sampling uncertainty inherent in observations on the population. We propose a state-space assessment model that is expanded to simultaneously treat environmental covariates as stochastic processes and estimate their effects on recruitment. We apply the model to southern New England yellowtail flounder (Limanda ferruginea) using data from the most recent benchmark assessment to evaluate evidence for effects of the mid-Atlantic cold pool and spawning stock biomass on recruitment. Based on Akaike’s information criterion, both the cold pool and spawning stock biomass were important predictors of recruitment and led to annual variation in estimated biomass reference points and associated yield. We also demonstrate the effect of the stochasticity of the mid-Atlantic cold pool on short-term forecasts of the stock size, biomass reference point, and stock status.

Accounting for correlated observations in an age-based state-space stock assessment model

Abstract Fish stock assessment models often rely on size- or age-specific observations that are assumed to be statistically independent of each other. In reality, these observations are not raw observations, but rather they are estimates from a catch-standardization model or similar summary statistics based on observations from many fishing hauls and subsamples of the size and age composition of the data. Although aggregation mitigates the strong intra-haul correlation between sizes/ages that is usually found in haul-by-haul data, violations of the independence assumption can have a large impact on the results and specifically on reported confidence bounds. A state-space assessment model that allows for correlations between age groups within years in the observation model for catches and surveys is presented and applied to data on several North Sea fish stocks using various correlation structures. In all cases the independence assumption is rejected. Less fluctuating estimates of the fishing mortality is obtained due to a reduced process error. The improved model does not suffer from correlated residuals unlike the independent model, and the variance of forecasts is decreased.

A state-space stock assessment model for northern cod, including under-reported catches and variable natural mortality rates

A state-space assessment model for the northern cod (Gadus morhua) stock off southern Labrador and eastern Newfoundland is developed here. The model utilizes information from offshore trawl surveys, inshore acoustic surveys, fishery catch age compositions, partial fishery landings, and tagging. This is done using an approach that avoids the use of subjective data-weighting. Estimates of fishing mortality rates (F) are usually conditional on assumptions about natural mortality rates (M) in stock assessment models. However, by integrating much of the information on northern cod, it is possible to estimate F and M separately. It is also possible to estimate a change in the offshore survey catchability by including inshore acoustic biomass estimates. The proposed model also accounts for biased total catch statistics, which is a common problem in stock assessments. The main goal of the model is to provide realistic projections of the impacts of various levels of future fishery catches on the recovery of this stock. The projections incorporate uncertainty about M and catch. This is vital information for successful future fisheries. The model has been developed for the specific data sources available for northern cod, but it could be adapted to other stocks with similar data sources.

Estimation of time-varying selectivity in stock assessments using state-space models

Time-varying selectivity is one of the main challenges in single species age-based assessment models. In classical deterministic VPA-type models the fishing mortality rates are unfiltered representations of the observed catches. As a consequence the selectivity becomes time-varying, but this representation is too fluctuating, because it includes the observation noise. In parametric statistical catch at age models a common assumption is that the selectivity is constant in all years, although time-varying selectivity can be introduced by splitting the data period in blocks with different selectivities, or by using smoothing splines and penalized time-deviances. However, these methods require subjective choices w.r.t. the degree of time-varying allowed. A simple state-space assessment model is presented as an alternative, which among other benefits offers an objective way of estimating time-varying selectivity pattern. The fishing mortality rates are considered (possibly correlated) stochastic processes, and the corresponding process variances are estimated within the model. The model is applied to North Sea cod and it is verified from simulations that time-varying selectivity can be estimated.

Impact of survey design changes on stock assessment advice: sea scallops

Abstract Smith, S. J., and Hubley, B. 2014. Impact of survey design changes on stock assessment advice: sea scallops. – ICES Journal of Marine Science, 71: 320–327. Annual surveys of marine resources are used to monitor changes in population composition and abundance. Improvements in the performance and coverage of these surveys can readily be evaluated for the surveys themselves but should also be considered in the context of the stock assessment models that use the estimates from these surveys. For those surveys based on a probability design, improvements in the probability design are usually evaluated with respect to the resultant increase in precision of the survey estimates. Survey precision estimates can be included in many stock assessment models as observation error, as long as the process error component of the model is also identified. Advice on catch levels for sea scallop populations (Placopecten magellanicus) around Nova Scotia is developed using a Bayesian state space assessment model in which both observation and process error terms have been defined. Information on survey estimates of precision are included in the observation error component of the assessment model and the impacts of changes in survey precision on the provision of advice can be evaluated in terms of reference points and management advice. The sensitivity of stock assessment advice to changes in the level of precision of survey estimates was evaluated for three scallop fisheries around Nova Scotia. The results indicated that the impact of the changes depended upon the degree of concurrence between the annual changes in biomass as observed from the survey and those predicted by the model.