The effect of adaptive change in the prey on the dynamics of an exploited predator population

Abstract

Mathematical models examine the relationship between harvesting effort and stock size for a predator species when the prey adapts to the risk of predation. In one set of models, the prey can increase its own reproductive rate if it increases its vulnerability to the predator. In the second set of models, each of two prey species has fixed characteristics, but changes in the average characteristics within the prey trophic level occur via shifts in the relative abundance of the two species. In both models, the equilibrium predator population can increase as harvest of that species increases. In the case of two-prey models, the predator's equilibrium population always increases with an increased harvest rate if the two prey coexist and share a single resource. The predator's equilibrium population often decreases from its maximum size to zero over a very small range of harvest rates, once those rates become high enough. Because increased stock size is often used to justify increased harvest rates, this relationship poses a risk that harvest rate will increase to the point where the stock quickly collapses. The results are relevant to understanding changes in the population size of a species experiencing declining environmental conditions.