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 small 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 situation by developing analytical approximations. Using a Poisson approximation of its distribution, the expected number of genes from one generation whose copies make up the population after a number of generations characterized by fixation index F can be shown to be approximated by 2/F−1, irrespective of population size, and probabilities of fixation of alleles over a finite period of time can be also approximated. These expressions, which were checked numerically, should make it possible to calculate approximate likelihoods for allele frequency distributions promoted by drift.