A stochastic approach to stock reduction analysis

Stock reduction analysis (SRA) can complement more detailed assessment methods by using long-term historical catches to estimate recruitment rates needed to have produced those catches, yet still end up with stock sizes near those estimated by the detailed methods. A longer historical perspective can also add information to the estimation of reference points such as unfished biomass (B-0) or target biomass (B-MSY). Deterministic SRA models provide a single stock size trajectory that is vanishingly unlikely to have actually occurred, while stochastic SRA attempts to provide probability distributions for stock size over time under alternative hypotheses about unfished recruitment rates and about variability around assumed stock-recruitment relationships. These distributions can be generated with age-structured population models by doing large numbers of Monte Carlo simulation trials and retaining those sample trials for which the stock would not have been driven to extinction by historical catches. By resampling from these trials using likelihood weights (sampling - importance resampling method), it is possible to move into fully Bayesian, state-space assessment modeling through a series of straightforward steps and to provide understandable visualization of how much the data help to reduce uncertainty about historical fishing impacts and stock status.