The Coevolution and Stability of Competing Species

If two species compete for two renewable resources, will they coevolve so as to make continued coexistence more likely? This question is analyzed using the equations of MacArthur (1972) but allowing the constants in those equations to undergo evolutionary change, subject to constraints. Individual selection will cause these variables to take values which are evolutionarily stable, in the sense that if all individuals in a population have those values no mutant can invade it. It is then possible to compare the evolutionarily stable values for each species on its own with the values when they coexist. Two cases are considered: a coarse-grained case in which at any instant a consumer can search for one resource or the other but not for both, and a fine-grained case in which both resources can be sought simultaneously. In both cases, each consumer in the absence of its competitor would evolve as a generalist. In competition, each consumer will coevolve as a specialist on a different resource patch type in the coarse-grained case, or, in the fine-grained environment, each consumer will become more specialized on one resource although not necessarily completely so. In the fine-grained case, it is possible for two generalists to coexist, but co-evolution will lead to character divergence. For the cases considered, the co-evolved divergence of the consumers leads to greater global stability of the consumer community even though it has negligible effect on the local Lyapunov stability. The increased community stability results from natural selection acting on individuals in the separate consumer populations. No group selection at either the population or community level is necessary.