Variance of genetic distance and correlation of heterozygosity between populations under the pressure of stepwise mutation

Using the stepwise mutation model of Ohta and Kimura (1973), formulas are developed for the correlation of heterozygosity and the variance of genetic distance between two finite populations. Studied in detail is the case where the sizes of the two descendant populations are equal to that of the ancestral population and the mutation rate is the same for all loci. Numerical computations are carried out by using the present formulas and those of Li and Nei (1975Genet. Res.25) for the infinite-allele model. The results are as follows: The correlation of heterozygosity decreases with time faster for the stepwise mutation model than for the infinite-allele model. However, the relationships between the correlation of heterozygosity and the normalized genetic identity for the two models are very similar, if the average heterozygosities of the two populations are around 0.20 or less. On the other hand, the variance of genetic distance for the stepwise mutation model may become considerably smaller than that for the infinite-allele model, if the average heterozygosities of the two populations are larger than 0.05. The ratio of the standard deviation to the mean is, however, very large for the stepwise mutation model as well as the infinite-allele model.