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UNCORRELATED RANDOM ENVIRONMENTS AND THEIR EFFECTS ON GENE FREQUENCY

Two kinds of drift processes in population genetics can be distinguished. The first may be called the classical drift problem: Given a large number of populations of effective size N undergoing a defined system of mating with respect to a locus at which the selection coefficients are known constants, and given the initial status of the populations with regard to the gene frequencies, what is the distribution of gene frequencies among the populations at some future time? In this drift process the differences in gene frequency among the populations are caused by the finiteness of the populations and the sampling error among the gametes of each generation that this entails. Were the populations infinite in size, the deterministic forces of selection would cause each population to evolve in precisely the same way, with no differences in gene frequency arising. Studied first by the pioneers of population genetics, Fisher (1922, 1930) and Wright (1931, 1937, 1938, 1945, 1964), whose principal interest was in the form of the distribution of gene frequencies at equilibrium or at the state of steady decay, the classical drift problem was tackled energetically by Kimura (1955a, 1955b, 1955c, 1957, 1962, historical review 1964), who employed to advantage the Kolmogoroff diffusion equation as an approximation to the drift process. The second kind of drift process does not depend on the finiteness of the populations. Here one assumes large number of populations, each of infinite size, in which