Some Properties of Finite Populations Experiencing Strong Selection and Weak Mutation

Abstract

Some general properties of populations experiencing strong selection (.alpha. = 2NS [N = population size, S = selection intensity] .mchgt. 1) and weak mutation (.THETA. = 4NU [U = mutation rate between any pair of alleles] .mchgt. 1) with k .mchlt. .infin. alleles are described. Under these assumptions a true boundary layer dynamics emerges with rare alleles remaining near 0 for an exponentially distributed length of time; thereafter they enter the interior of the allelic frequency space where natural selection alone operates at a much faster time scale than occurs in the boundary layer. This structure allows a much simpler description of the evolutionary process than by the conventional diffusion analysis. Particular models examined include over-dominant selection and selection in a randomly fluctuating environment. For the latter model it is shown that drift and mutation can have a profound effect on the number of polymorphic alleles as suggested earlier by Nei and Takahata. Apparently a fundamental parameter is the product .alpha..THETA.. If this quantity is very small, evolution effectively stagnates. If .alpha..THETA. is moderate, the above described boundary layer dynamics emerge, whereas if .alpha..THETA. is very large, drift does not effectively inhibit the progress of evolution. In the time scale of the process the rate of evolution is directly proportional to the population size.