A generalised model for evaluating yield and the long-term status of fish stocks under conditions of uncertainty
This paper presents a general fish stock projection model for assessing the long-term annual yield which satisfies objectives for the maintenance of the spawning stock biomass in accordance with CCAMLR criteria. These specify a bound on the probability that the spawning biomass will become depleted to below some specified level over a specified period and set a further constraint on the long-term status of the stock relative to the pre-exploitation biomass. The model provides a flexible method for assessing the influence of different patterns of growth, natural mortality, spawning and fishing on estimates of yield and yield per recruit. It can also be used to evaluate stochastic stock trajectories under a specified catch regime. The model uses an adaptive Runge-Kutta algorithm to calculate stock trajectories and catch rates over a specified simulation period. The procedure numerically integrates a set of differential equations which incorporate functions that specify growth, mortality, age-dependent selectivity and seasonal patterns in fishing mortality. Results from the model are compared with existing analyses from the krill yield model. The model can include a known catch history and thus allow assessments of yield to be made for existing fisheries. An example is presented for the Patagonian toothfish, Dissostichus eleginoides, around South Georgia Island.