An analysis of neutral-alleles and variable-environment diffusion models

Three diffusion models are formulated for the evolution of a diploid population with K alleles at one locus with completely symmetric mutation and random genetic drift, a variable-environment, and all the above mechanisms. For the diallelic case, the transient behavior is studied by solving the corresponding diffusion equations by an asymptotic method valid for short time intervals. The transient behavior of the three models is compared for the case when their stationary distributions are identical. The expected amount of heterozygosity is computed using the asymptotic solution and is compared to an exact result. The asymptotic results are extended to the general case with K alleles at the locus for the symmetric mutation and variable-environment models.Research supported by the National Science Foundation under Grant MCS 79-01718