Modeling time-varying selectivity in size-structured assessment models

Abstract Within fisheries assessments, selectivity refers to the relative probability of a fish of a particular size or age being caught. Selectivity, typically modelled using a parametric function, is informed primarily by age- and size-composition data. This function can vary annually, and not accounting for this variation can result in biased estimates of abundance and mortality. Past simulation studies evaluating time-varying selectivity focused on age-structured models with little focus on size-structured models. In addition, the generating function for the size-composition data often mirrored the likelihood function. Unfortunately, this is not realistic and there is a need to determine which likelihood function is most robust. Therefore, this paper addresses two questions using simulation: (a) which is the best method for modeling time-varying selectivity and (b) which is the most robust likelihood function for size-composition data given time-varying selectivity. Both questions are addressed within the context of size-structured assessment methods. The results reveal that discrete time blocking can adequately capture time-varying selectivity. This could reduce the number of estimated parameters and hence the variance of estimated quantities. As for likelihood functions, the results reveal that the three likelihoods considered, multinomial, Dirichlet-multinomial and the multivariate normal, are all valid options. However, our preferred option is the multinomial because it has better estimates for desirable management quantities more often than the others.