AUTOCORRELATED RANDOM ENVIRONMENTS AND THEIR EFFECTS ON GENE FREQUENCY

In the previous paper (Cook and Hartl, 1974) we considered the distribution of gene frequencies in a population evolving in a fluctuating environment when the environmental changes were uncorrelated. In the present article we extend the theory to include autocorrelations in the environment. WVe consider three models. The first (denoted model III in the previous paper) assumes a population reproducing in discrete, nonoverlapping generations accompanied by changes in fitness that occur at regular intervals. The second (called model IVA) assumes a population reproducing continuously in overlapping generations when the random variable on which fitness depends changes at arbitrarily chosen times. And the third (model IVB) assumes a population with overlapping generations in which the environment changes continuously. As before, the transition from model IVA to model IVB is obtained by a limiting procedure. Of the three models, model IVA is the most powerful because it includes the others as special cases and because it is sufficiently general to permit consideration of environments in which the rates of environmental change are themselves changing. One interesting case of model IVA is model IVB. This has recently been analyzed in detail by Gillespie (1972), and here we confirm his results using a markedly different approach.

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