The evolutionary response of systems to a changing environment
To model evolution as an evolutionary game, we have used a fitness generating function to define the fitness of any individual in a community bounded by the same evolutionary constraints. Using a single fitness generating function, we have previously investigated the effect of external inputs on a community at an evolutionarily stable strategy (ESS). Of particular interest are the circumstances under which the external input promotes the coexistence of several strategies in a community that otherwise would have a single-strategy ESS. The external inputs can include physiographic changes, human intervention, or the introduction of a new species not modeled by the single fitness generating function. We consider in detail here the situation of introducing a predator into a hitherto unexploited community of prey. In this case, the prey and predators each have a separate set of evolutionary constraints which produce two different fitness generating functions. Necessary conditions for determining the ESS under two or more fitness generating functions are presented. The coevolution of predator and prey is then examined with the aid of frequency-dependent adaptive landscapes, one for each fitness generating function. As a result of disruptive selection imposed by the predator, it is possible, under different niche breadths of the predator, to obtain ESSs composed of one or more coexisting prey strategies and one or more predator strategies.