Modelling non-stationary natural mortality in catch-at-age models

Non-stationarity in the natural mortality of many species has been discussed among research scientists, but no generally applicable models/methods have been developed where a statistical catch-at-age (SCA) model framework is used. Using the Atlantic weakfish (Cynoscion regalis) fishery as an example, several SCA models are developed to assess the population dynamics, then compared. Models used included (i) an SCA with constant natural mortality, (ii) an SCA with unknown natural mortality, but with a hierarchical prior distribution from a mixture of distributions based on life-history information, (iii) an SCA with age-specific unknown natural mortality, (iv) an SCA with time-varying natural mortality, following a random-walk process, and (v) an SCA with age-specific time-varying natural mortality. The last two models imply that the population dynamics are not stationary. A Bayesian approach was used to estimate parameters, and performance of the models was compared through goodness-of-fit and the retrospective patterns of the models. A simulation study was then conducted to test the uncertainty resulting from model selection, the efficiency of using the best model selected based on deviance information criterion, and whether changes in natural mortality could be detected. An SCA with time-varying natural mortality, following a random-walk process, is proposed for the example fishery here. The estimated non-stationary temporal patterns in natural mortality were linked further to climate-ocean oscillation indices, to diagnose possible mechanisms/linkages to these temporal variations in natural mortality.