Estimating length-transition probabilities as polynomial functions of premoult length

Abstract

In length-based lobster stock-assessment models where the population is subdivided into discrete length classes, growth is represented as a matrix of length-transition probabilities. At specific times during the model year, the length-transition probabilities specify the proportions growing into larger length classes. These probabilities are calculated by integration of gamma or normal distributions over the length intervals of each larger length class. The mean growth from any given length category is commonly modelled by a von Bertalanffy or other continuous growth curve. The coefficients of variation, describing variance among individuals, are modelled by functions constant or linear with length. These approaches have yielded good descriptions of growth for males and juveniles, but the von Bertalanffy curve does not capture the rapid decrease in mean growth rate after maturity for females. We generalized this length-transition model by writing the parameters of the growth distributions as polynomial functions of carapace length. This generalization procedure increases the number of parameters depending on the degree of polynomial employed. In fits to South Australian rock lobster (Jasus edwardsii) tagrecovery data, each increase in polynomial degree yielded a significantly better fit for females and successfully represented the decrease in growth at maturity. For males, the von Bertalanffy description was little improved by higher polynomials.