Modeling population dynamics and nonstationary processes of difficult-to-age fishery species with a hierarchical Bayesian two-stage model

Modeling population dynamics and establishing a comprehensive population assessment for fishery species that are difficult to age have been challenging. Determination of age for such species is still an unresolved issue or is at best uncertain. Catch-survey analysis does not require full age information but can still provide a comprehensive population assessment. It was extended to incorporate multiple surveys and multiple sources of uncertainties within the statistical catch-at-age framework in the applications to crustaceans. Here, we further generalize and extend the multiple survey catch-survey analysis into a hierarchical Bayesian two-stage model by applying the hierarchical Bayesian approach. The hierarchical Bayesian approach can sufficiently incorporate uncertainty and expert opinions in parameter estimation. We developed a series of models with different assumptions for natural mortality and catchability, including nonstationary (i.e., time-varying) assumptions. We evaluated model robustness to these assumptions and compared population dynamics estimates and population status determination. We demonstrated the application of the hierarchical Bayesian two-stage model using the North Carolina blue crab (Callinectes sapidus) example. In this example, estimation of population size and fishing mortality and determination of population status were robust to the natural mortality and catchability assumptions. The North Carolina blue crab population is less likely to have nonstationary catchability or nonstationary natural mortality. Its natural mortality is more likely to vary by stage than by sex or over time.