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SUMMARY  The distribution of visits to a particular gene frequency in a finite population of size N with 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 of b ij  's, where b ij  is the mean number of visits to frequency j /2 N , given initial frequency i /2 N . The variance of such a distribution does not agree with the value suggested by the diffusion method. An improved approximation is derived.

On sojourn times at particular gene frequencies