Modeling Nonstationary Natural Mortality in Catch-At-Age Models

Nonstationary population dynamics are rarely applied in stock assessments, especially when statistical catch-at-age models are used.  Nonstationarity of the natural mortality of several species along the Atlantic coast has been discussed among research scientists, but analyses are generally case specific.  No generally applicable models/methods have been developed to test the possible hypotheses of nonstationarity.  In this study, using the Atlantic weakfish (Cynoscion regalis) fishery as an example, we compared several statistical catch-at-age models to assess the population dynamics.  Models that we used included 1) a statistical catch-at-age model (SCA) with constant natural mortality, 2) a SCA with unknown natural mortality but a hierarchical prior distribution from a mixture of distributions based on life history information, 3) a SCA with age-specific unknown natural mortality, 4) a SCA with time-varied natural mortality following a random walk process, and 5) a SCA with an age-specific time-varied natural mortality following a random walk process.  The last 2 models imply that the population dynamics are not stationary.  A Bayesian approach was used to estimate parameters, and performance of the models was compared by goodness-of-fit and the retrospective patterns of the models.  A SCA with time-varied natural mortality following a random walk process was recommended for the example fishery from this study.  The estimated non-stationary temporal patterns of natural mortality were further linked to climate ocean oscillation indices to diagnose possible mechanisms/linkages to these temporal variations of natural mortality.