Hierarchical models improve abundance estimates: Spawning biomass of hoki in Cook Strait, New Zealand

It is often difficult to estimate abundance for a dynamic population, i.e., one that is moving through the survey area or in which birth or mortality rates are high. One approach is to estimate the proportion of animals present during each survey, using a model that estimates the dynamics of the survey proportion of the population. However, this can increase the uncertainty of the estimates if the dynamics parameters are not well estimated. Here we approached this problem by developing methods using hierarchical model structures, which allow us to share information on the dynamics parameters across years. We applied this modeling approach to the estimation of residence time and spawning biomass for New Zealand hoki (Macruronus novaezelandiae) in Cook Strait spawning grounds. By sharing parameters across years, we obtained better parameter estimates than by the traditional assumption that the dynamics in one year are independent of those of other years. By integrating the estimation of residence time into a dynamic model using simulated maximum likelihood methods, we also were able to calibrate acoustic estimates of spawning biomass for the fact that not all individuals are on the grounds at the time of the acoustic survey. We discuss alternative model formulations for the application of hierarchical methods to stage-structured data and the analysis of data from acoustic surveys of spawning fish.