Drift variances of FSTand GST statistics obtained from a finite number of isolated populations

Approximate formulas for the mean and variance of the F_STor G_ST statistic in a finite number of isolated populations are developed under the effect of random genetic drift. Computer simulation has shown that the approximate formulas give a fairly accurate result unless the initial frequency of one of the alleles involved is close to 1 and t/2N is large, where N is the effective size of a subpopulation and t is the number of generations. It is shown that when the number of subpopulations (s) is small, the mean of F_STor G_ST depends on the initial gene frequencies as well as on s. When the initial frequencies of all alleles are nearly equal to each other and the number of subpopulations is large, the distribution of F_ST in the early generations is bell-shaped. In this case Lewontin and Krakauer's k parameter is approximately 2 or less. However, if one of the initial allele frequencies is close to 1, the distribution is skewed and leptokurtic, and the k parameter often becomes larger than 2 in later generations. Thus, even under pure random genetic drift, Lewontin and Krakauer's test of selective neutrality of polymorphic genes in terms of F_ST is not always valid. It is also shown that Jacquard's approximate formula for k generally gives an overestimate.