The average number and the variance of generations at particular gene frequency in the course of fixation of a mutant gene in a finite population

Abstract

SUMMARYIn the case of an allele which is going to become fixed in a population, the average number of generations for which the population assumes particular gene frequencies is investigated, using the diffusion approximation. Explicit formulas were obtained and they were checked by computer simulations. As a particular case, it is shown that if a new mutant that is selectively neutral is eventually fixed in a population of sizeN, it spends two generations on average at each of the intermediate frequencies (1/2N, 2/2N, …, (2N−1)/2N), and the variance at each frequency is four generations.