Discriminating alternative stock–recruitment models and evaluating uncertainty in model structure

Abstract

Fish stock–recruitment (S–R) assessment is one of the most essential keystones for fisheries management. Yet the analysis involves a variety of uncertainties. Amidst these difficulties, uncertainty in model structure is perhaps the most problematical to investigate because no rigorous statistical techniques can be used to explore the fundamental biological processes in S–R relationships. In this paper, I used computer simulations to investigate: (1) the differences between the estimated parameters of alternative S–R models as a function of stock characteristics: population growth rate, data range, fishing mortality, and process noise; and (2) the probability of selecting a correct model using information criteria. Two popular S–R functions, the Ricker and the Beverton–Holt models, were used as examples. Time series data were generated from a known S–R model and fitted by alternative models. The results show that when the two models fit the data similarly well, significant differences in parameters existed between the alternative models. The Ricker model tended to underestimate the population growth rate (initial slope) and the carrying capacity parameter, whereas the Beverton–Holt model overestimated these parameters. The management quantities (e.g., optimal virgin stock size) produced by one model were more conservative (i.e., larger optimal stock size or lower optimal harvest rate) under some conditions but became less conservative under other conditions. The differences between the alternative models were functions of the population growth rate, long-term fishing mortality, and data range of the stock size. The correct and incorrect models were statistically indistinguishable. For typical fishery data the probability of selecting the correct model based on information criteria was approximately 0.70 for the Ricker model and 0.61 for the Beverton–Holt model.