The rate of allelism of lethal genes in a geographically structured population

The expected rate of allelism, E[I(x)], of lethal genes between two colonies with distance x in a structured population is studied by using one- and two-dimensional stepping-stone models. It is shown that E[I(x)] depends on the magnitude of selection in heterozygous condition (h), the rate of migration among adjacent colonies (m), the number of loci which produce lethal mutations (n) and the effective population size of each colony (N).--E[I(x)] always decreases with distance x. The rate of decrease is affected strongly by the magnitude of m. The rate of decrease is faster when m is small. E[I(x)] also decreases with increasing N and n. The effect of h on E[I(x)] is somewhat complicated. However, E[I(0)] is always smaller when h is small than when it is large.--For large x, the following approximate formulae may be obtained: (see PDF) where q and Var (q) are the mean and the variance of gene frequencies in each colony, t is approximated as t=h, (see PDF), -h for the partially recessive, completely recessive, and overdominant lethals, respectively, and C(0) is a function of m and t. It is clear that E[I(x)] declines exponentially with x in a one-dimensional habitat. The decrease E[I(x)] is faster in a two-dimensional habitat than in a one-dimensional habitat. The present result is applied to some of the existing data and the estimation of population parameters is also discussed.