Models of Coevolution

Various aspects of genetic models of coevolution are reviewed and discussed. The emphasis is on the assumptions made in coevolutionary models and the questions addressed. In the first part of the review, general results from models of single species or of interacting species are summarized. In a number of cases, there are useful maximization and equilibration principles that can be applied to particular coevolutionary problems. Such principles can sometimes be used without making explicit genetic assumptions. The second part of the review summarizes various models of particular types of ecological interactions: generalized competition, character displacement, predator-prey and host-parasite interactions, and mutualism. When possible, the principles available from the general theory are applied. There is also some discussion of the role of different time scales of genetic and ecological change and of the role of assumptions concerning genetic variability in each species. The current emphasis in theoretical studies is on the equilibrium properties of panmictic species under constant conditions. Even under those restrictive conditions, a wide variety of results can be obtained, but it does not seem that there is a consistent effect of coevolution on community stability.