Incorporating Allee effects in fish stock–recruitment models and applications for determining reference points

Abstract

A new type of stock–recruitment model is examined that incorporates Allee effects, which may occur when fish populations are small. The model is a natural extension of traditional models, which only incorporate the negative effects of increasing density on fecundity and (or) survival. Because the new model is intrinsically nonlinear and because of convergence problems at local optima, we use a maximum likelihood approach with a global genetic search algorithm to estimate model parameters. Parameter uncertainty is obtained from the inverse of the Fisher information matrix. Based on this new model, an extinction probability curve is developed using the parameter defining the Allee effects. This curve can readily be used to calculate the theoretical probability of extinction for a single brood line in one generation for any particular spawner number or biomass. Alternatively, because managers may wish to assign reference points corresponding to particular extinction probabilities, spawner numbers can be determined for these reference points. Two Pacific salmon populations, North Thompson coho (Oncorhynchus kisutch) and Chilko sockeye (O. nerka), are used to demonstrate the approach. It is found that the Allee effect parameter is statistically significant for the Thompson coho, but not for Chilko sockeye.