A new semi-parametric method for autocorrelated age- and time-varying selectivity in age-structured assessment models

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.