Fixation indices in subdivided populations

Abstract

Without restricting the evolutionary forces that may be present, the theory of fixation indices, or F-statistics, in an arbitrarily subdivided population is developed systematically in terms of allelic and genotypic frequencies. The fixation indices for each homozygous genotype are expressed in terms of the fixation indices for the heterozygous genotypes. Therefore, together with the allelic frequencies, the latter suffice to describe population structure. Possible random fluctuations in the allelic frequencies (which may be caused, e.g., by finiteness of the subpopulations) are incorporated so that the fixation indices are parameters, rather than random variables, and these parameters are expressed in terms of ratios of evolutionary expectations of heterozygosities. The interpretation of some measures of population differentiation is also discussed. Ill particular, F(sr) is an appropriate index of gene-frequency differentiation if and only if the genetic diversity is low.