EVOLUTIONARY INSTABILITY IN PREDATOR-PREY SYSTEMS

The dynamical stability properties of Lotka-Volterra equations have been used frequently to predict the persistence of predator-prey assemblages and trophic webs, yet they do not take into account evolutionary change. The incorporation of genetic variation into a stable food web will make it less stable in many cases. Since populations containing genetic variation do persist in nature, such theoretical results appear paradoxical. In order to attempt to resolve this paradox, we develop a model based on phenotypic change in investment in predatory or anti-predator traits, in coevolving species. The model is akin to previous models of arms-race coevolution using evolutionarily stable strategy (ESS) theory, but we seek to understand the evolutionary dynamics in phenotype space, as well as to identify any evolutionarily stable states that may occur. The relationship between investment and the Lotka-Volterra interaction terms is defined in a very general form, so as to cover a wide range of cases in nature. From the general case and more specific examples based on hypotheses about the factors affecting predator-prey interactions, we derive conditions for the occurrence of coevolutionarily stable states, where both species are playing evolutionarily stable strategies with respect to their interaction with the other species. Coevolutionarily stable states are found to be unusual outcomes of predator-prey coevolution. However, lack of evolutionary stability is not seen to imply ecological impermanence, as natural selection is found to prevent mutual extinction of predator and prey under certain conditions. © 1993 Academic Press. All rights reserved.