Generalised linear modeling of fecundity at length in southern rock lobsters, Jasus edwardsii

Accurate fecundity estimates are central to population modelling of reproductive status and egg production in a fishery. Southern rock lobster (Jasus edwardsii) fisheries are managed with the consideration of performance measures based on the level of current egg production relative to the unfished stock. Egg production is a function of the size at the onset of maturity, the size structure of the stock, and the fecundity at length of lobsters. Fecundity at length of the Tasmania stock of J. edwardsii has not been reported previously and was estimated from seven sites around Tasmania. Data were analysed by classical linear regression and also generalised linear models (GLM) with gamma and Poisson distributions. GLM with a gamma distribution produced the best fit and did not require a correction factor to generate a model on the linear scale. Individual fecundity ranged from 43,918 to 660,156 and could be predicted from carapace length according to the equation F = −1.707 + 2.969 (log length). The coefficient of length approximated three, implying the fecundity at length relationship is cuboidal. Despite the spatial heterogeneity in reproductive parameters in this fishery, the inclusion of spatial information and egg development stage into the analysis only explained an additional 1% of the variance in fecundity. Thus, it appears valid to apply the relationship across the fishery without spatial separation.