The Effects of Environmental Autocorrelations on the Progress of Selection in a Random Environment

Abstract

A heuristic method for obtaining Markovian approximations to the solutions of non-Markovian stochastic difference equations is described. The technique is based on recent results given in Guess and Gillespie (1977). The approximating Markov processes are either diffusions or else the solutions to ordinary differential equations with parameters representable by diffusions. The appropriate approximating process is determined by the strength of the autocorrelation. By applying this technique to the problem of selection in random environments, certain useful observations are made. In general, heterozygosity decreases with increasing autocorrelation in the environment. For moderately and strongly autocorrelated environments, the effects of increasing the autocorrelation are analogous to the effects of increasing the variance. This is not true, however, for weakly autocorrelated environments. Finally, the analysis of discrete-time models by continuous-time approximations based on the Stratonovich calculus is shown to give misleading results.