Gene identity and genetic differentiation of populations in the finite island model.

A formula for the variance of gene identity (homozygosity) was derived for the case of neutral mutations using diffusion approximations for the changes of gene frequencies in a subdivided population. It is shown that when gene flow is extremely small, the variance of gene identity for the entire population at equilibrium is smaller than that of the panmictic population with the same mean gene identity. On the other hand, although a large amount of gene flow makes a subdivided population equivalent to a panmictic population, there is an intermediate range of gene flow in which population subdivision can increase the variance. This increase results from the increased variance between colonies. In such a case, each colony has a predominant allele, but the predominant type may differ from colony to colony. The formula for obtaining the variance allows us to study such statistics as the coefficient of gene differentiation and the correlation of heterozygosity. Computer simulations were conducted to study the distribution of gene identity as well as to check the validity of the analytical formulas. Effects of selection were also studied by simulations.