Investigation of fisheries management issues using an age-structured state-space model, with application to Hauraki Gulf snapper

Abstract

The performance of fisheries stock assessment models was investigated through the application of an age-structured state-space population model to various data sets. Areas investigated include the response of models to systematic and variable under-reporting of total catches, low levels of total catch, different proportions-at-age data sampling regimes, the inclusion of tagging data and the choice of the number of age classes to model. To achieve this a function was created to simulate a fish population with desired characteristics such as recruitment collapse or low levels of catches. This was based on the Hauraki Gulf snapper fishery. An age-structured state-space population model was developed using TMB, where the true number of individuals at each age in each year was considered the unobserved true state. These unobserved states were treated as latent variables. The joint density function was marginalised over the latent variables in TMB using the Laplace approximation. MCMC methods were used on this marginalised joint density to obtain credible intervals about parameters of interest. These credible intervals were found to better reflect the uncertainty introduced by the latent variables compared to Wald based confidence intervals. Alternative models to the state-space model were developed including a non-state-space version of the model and non-state-space models which aimed to incorporate some of the uncertainty present in the state-space model and the real world systems by estimating natural mortality. The non-statespace model was also implemented in CASAL for validation purposes. Model comparison using the DIC showed that the state-space model was preferred over all of the non-state-space models for all data sets used. The investigation of model performance found that the model was generally able to estimate relative abundance when there was under-reporting, low levels of catch, or less data available. However, estimates of absolute abundance, and the precision of these estimates, was affected by these issues in the scenarios investigated.