Models and approximations for random genetic drift

Abstract

The multinomial-sampling model of Ethier and Nagylaki (1980) for selection, mutation, and random genetic drift at a single multiallelic locus in a panmictic, monoecious, diploid population with discrete, nonoverlapping generations is described and discussed. Four different approximations for large population number are presented. For frequent alleles, the standard diffusion approximation holds if all the evolutionary forces are comparable ( Ethier and Nagylaki, 1980), whereas there are small Gaussian fluctuations about the deterministic trajectory if the deterministic forces, though still weak, dominate random drift ( Nagylaki, 1986). For rare alleles, it is proved here that a branching process with immigration applies if the allelic numbers are small, whereas a diffusion approximation holds if they are moderate ( Ethier and Nagylaki, 1988). The branching-process limit is established also for autosomal and X-linked loci in a dioecious population. Extensions and open problems are also discussed.