Evolution in fine-grained environments I. Environmental runs and the evolution of homeostasis

In this paper we discuss the problem of evolution when individual organisms are subjected to heterogeneous environments within their own lifetimes. We first develop a model of environmental heterogeneity in which there are two discrete environmental states. Transitions between states are governed by a stochastic matrix. Next, we examine how an organism responds to this heterogeneity. We assume that L consecutive time units of the environmental process are sampled during the normal life span of the organism, and that the individual's fitness is determined in part by a component unrelated to this heterogeneity and by other components that describe the fitness response to the heterogeneity. The fitness responses are functions of the environmental state and of how long the organism has been previously exposed to that state; i.e., fitness response is dependent upon the environmental context. We then discuss how this individually experienced heterogeneity is translated to the populational level. Finally, genetic constraints are overlaid so that the tools of population genetics may be used to make evolutionary predictions.