Estimation of seasonal growth parameters using a stochastic Gompertz model for tagging data

This paper addresses the problem of growth estimation from tagging data that exhibit large heterogeneity in size-increments. Precision in growth estimation is essential for stock assessment, especially for abalone fisheries, because they are managed in part by size limits. However, abalone growth is notoriously variable, changing dramatically between seasons and sites. It is also known that juvenile growth does not fit the commonly used von Bertalanffy model. We present a modified deterministic Gompertz model for tagging data and three stochastic versions in which asymptotic length is a random parameter. The Kullback's informative mean was used to discriminate between models with respect to the fit to data. Every 3 months over an 18-month period, abalone were collected from within an area of approximately 200 m x 200 m at Point Cook reef, in Port Phillip Bay. They were brought to shore, tagged, measured, and returned within 1-2 hours. Previously tagged abalone were found and measured in situ with vernier calipers to minimize disturbance. Thus, the data provide information on the growth of abalone for six consecutive 3-month periods (seasons). Sizes ranged from 15 to 125 mm maximum shell length at release. The distribution of asymptotic length was estimated from all the length increment data for large size classes. The parameter g of the Gompertz model, and distributions of length-increments for various initial sizes, were obtained for each season. The numerical results show that juvenile growth varies more markedly with season than with initial size; whereas, in larger abalone, growth increments vary with initial length and are less dependent on season.