A Gamma/Direchlet model for estimating uncertainty in age-specific abundance of Norwegian spring-spawning herring

An approach to estimating the statistical uncertainty in age-specific abundance of Norwegian spring-spawning herring is presented. The method is applied to data from a survey on the overwintering stock in the Vestfjord system in northern Norway in December 1996. It is based on building separate statistical models for acoustic and biological data. The acoustic data are modelled as a gamma-transformed spatial random field and fitted to echo readings from the survey. The biological data are fitted to a two-stage model using multinomial sampling from Dirichlet-distributed age proportions. Uncertainty in the abundance by age distribution is obtained by bootstrapping. Previous assessments have a priori taken the abundance by age from a skewed distribution, such as gamma or log-normal families. In contrast, this analysis results in an estimated abundance by age that seems symmetric and does not display heavy tails.