Hierarchical statistical framework to combine generalized depletion models and biomass dynamic models in the stock assessment of the Chilean sea urchin (Loxechinus albus) fishery

Generalized depletion models are useful for representing catch dynamics when biological compositional data are lacking but high frequency records of catch and effort are available. A shortcoming of these models is that although they estimate vulnerable abundance they do not provide direct information on the productivity of the stocks. Here we combine generalized depletion models with a biomass dynamic model of the Pella–Tomlinson type. The inference framework is hierarchical, with initial biomass estimates from generalized depletion models being used as input to the biomass dynamic model to estimate its hyper-parameters. Two hierarchical inference approaches are employed: the standard state-space framework and a new hybrid marginal-estimated approximation to the likelihood function, which make different simplifying assumptions. We apply this assessment approach to the first Chilean fishery with a Management Plan, the southern sea urchin fishery. Results from both hierarchical inference methods show a stock fluctuating between high and low biomass levels, for which maximum sustainable yield appears as a risk-prone annual harvest policy. Given this we propose an alternative annual harvest rate corresponding to the average latent productivity over the years of peaks and troughs of biomass fluctuations.