Best Practices for Constructing Size-Structured Population Dynamics Models used for Stock Assessments

Abstract

All models are predicated on assumptions which makes them simplified versions of reality. An important goal of stock assessment scientists is to expand the capability of stock assessment models to improve their ability to estimate the size of fished populations and how they will change over time. Several types of population dynamics models can be used for stock assessment, with age-structured models, which track the population by age, being the most popular. Unfortunately, there are valuable fished species such as crabs and lobsters that are difficult to age. Size-structured models that track the population by size are good alternatives. The objective of this dissertation is to improve the performance of size-structured models used for stock assessments. Three aspects of size-structured models are explored: growth, selectivity, and natural mortality. Size-transition matrices define growth in size-structured models. They are constructed from an underlying growth curve, typically the von Bertalanfy growth curve, defined by three parameters: the growth rate (k), the asymptotic height (L∞), and the variation in the size increment. Most assessments assume individuals follow a single growth curve with process error, which is unrealistic. A new size-transition matrix construction method that allows L∞ and k to vary among individuals through numerical integration was developed and compared with methods that allow individuals to follow (a) a single growth curve with process error, or (b) one of three growth curves, each with process error. The number of size-classes in the size-transition matrix and how the data are generated heavily dictate performance. Not accounting for temporal variation in selectivity can lead to biased estimates of abundance and mortality. Simulations suggest that discrete time blocking of selectivity can adequately capture time-varying selectivity as this could reduce the number of estimated parameters and hence the variance of estimated quantities. As for likelihood functions for size-composition data, the results reveal that multinomial, Dirichlet-multinomial and multivariate normal are all valid options. Natural mortality (M) has a strong influence on stock assessment model outputs including estimates of spawning stock biomass, MSY and fishing mortality. Estimating M is difficult since it is confounded with several factors including catchability, recruitment, and growth. Simulation shows that terminal molt does not affect the ability to estimate M. However, estimating growth simultaneously with M has a negative impact on the ability to estimate M but a positive effect on the quality of the estimates for spawning stock biomass.