The number of lines of descent and fixation probabilities of alleles in the pure genetic drift process: Analytical approximations

Analysis of diversity between populations diverged from an evolutionarily s mall number of generations cannot be done under the assumption that allele frequencies reflect an equilibrium between genetic drift and mutations. An alternative to analysis through coalescence theory is proposed in this situ ation by developing analytical approximations. Using a Poisson approximatio n of its distribution, the expected number of genes from one generation who se copies make up the population after a number of generations characterize d by fixation index F can be shown to be approximated by 2/F - 1, irrespect ive of population size, and probabilities of fixation of alleles over a fin ite period of time can be also approximated. These expressions, which were checked numerically, should make it possible to calculate approximate likel ihoods for allele frequency distributions promoted by drift. (C) 2000 Acade mic Press.