On sojourn times at particular gene frequencies

Abstract

SUMMARYThe distribution of visits to a particular gene frequency in a finite population of sizeNwith non-overlapping generations is derived. It is shown, by using well-known results from the theory of finite Markov chains, that all such distributions are geometric, with parameters dependent only on the set ofbij's, wherebijis the mean number of visits to frequencyj/2N, given initial frequencyi/2N. The variance of such a distribution does not agree with the value suggested by the diffusion method. An improved approximation is derived.