Stock Synthesis Assessments of Spatially Structured Fish Populations with an Environmental Driver on Recruitment Distribution : A Simulation Study and Discussion Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/fn1072641

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  • Stock assessments use statistical models and empirical data to re-create the population dynamics of a stock in order to provide estimates of biomass and fishing mortality rates to inform fisheries management. Fish stocks are not uniformly distributed across spatial regions, but stock assessments typically ignore stock spatial structure, for the sake of model simplicity. Similarly, although environmental variations are likely to affect a stock's dynamics, assessments rarely consider such direct environmental relationships. This study explores how spatial structure and environmental variability influence the accuracy of assessment results produced by the Stock Synthesis assessment software. An operating model is used to simulate fish population dynamics influenced by spatial and environmental variability and to generate data sets for analysis by Stock Synthesis. The operating model mimics the dynamics of an age-structured population that is divided into two regional subpopulations, with no movement of fish between regions. The population dynamics include random variability in the size of annual recruitment, the spatial distribution of recruitment, and regional fishing mortality. The operating model provides deterministically calculated true values of stock biomass for comparison with estimates from Stock Synthesis and generates random data sets for analysis by Stock Synthesis. Two types of data are provided to Stock Synthesis, fisheries-dependent data (annual catch biomass, age compositions and catch per unit effort) and fisheries-independent data (survey biomass indices, age compositions and environmental indices for the spatial distribution of recruitment). Except for the observations of catch and the environmental indices, these data include simulated observation error. The study uses a full factorial experimental design with two factors that influence the population dynamics and three factors that control how different Stock Synthesis models are configured. The population dynamics factors are (a) three patterns for the regional rates of fishing mortality (the exploitation histories) and (b) three patterns for the environmental forcing of the recruitment distribution. The factors for the Synthesis model configurations are (a) whether or not the data are treated as coming from two regions or from a single region, (b) whether or not data from the survey are available, and (c) whether or not the environmental indices are available in the two-region configuration. Six Stock Synthesis model configurations are applied to each random data set, making this a repeated measures design. Data set replicates include randomness in the population dynamics and observation error. To evaluate the bias and accuracy of Stock Synthesis estimates two variables are examined: the relative errors of spawning biomass for an unfished stock (SSB₀) and the spawning biomass in the 25th year of the simulation (SSB[subscript current]). Linear mixed effects (LME) models, with repeated measures for the Synthesis model configurations, are applied to develop simplified statistical models for the two relative error variables. Within the LME model the fixed effects included the two population dynamics factors and the Synthesis model configurations. The random effects in the model account for the lack of independence between model configurations due to the repeated measures design. Linear hypothesis tests are applied to gauge the relative importance of the experimental factors through contrasts of the LME model coefficients. Estimates of SSB₀ and SSB[subscript current] responded differently to the various experimental factor levels. SSB₀ was generally more precisely estimated. For all combinations of factor levels the estimates of biomass (SSB₀ and SSB[subscript current]) were biased low. As expected, experimental runs that included the exact spatial structure of the true stock and had supporting survey data in a spatial stock assessment usually resulted in a reduction of bias. Incorporating an environmental index for the recruitment distribution reduced bias in the biomass estimates when survey data were available but not otherwise. The regional exploitation histories also had a considerable effect on bias in the estimates of biomass. However, the patterns of environmentally forced recruitment distribution had relatively little influence on the bias and precision of the biomass estimates. Results of the study are discussed in terms of implications for future research and application in real-world stock assessments. Future research should explore additional factors such as a range of life history characteristics and movement between regions to expand the generality of the results. To apply a spatial stock assessment with environmental variables to real data one must consider the following: the scale of the spatial structure, the availability of data, and whether an environmental relationship is persistent and informative. The current study provides a foundation for the exploration and development of reliable spatially structured stock assessments that include environmental drivers.
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