Overdominant alleles in a population of variable size

An approximate method is developed to predict the number of strongly overdominant alleles in a population of which the size varies with time. The approximation relies on the strong-selection weak-mutation (SSWM) method introduced by J. H. Gillespie and leads to a Markov chain model that describes the number of common alleles in the population. The parameters of the transition matrix of the Markov chain depend in a simple way on the population size. For a population of constant size, the Markov chain leads to results that are nearly the same as those of N. Takahata. The Markov chain allows the prediction of the numbers of common alleles during and after a population bottleneck and the numbers of alleles surviving from before a bottleneck. This method is also adapted to modeling the case in which there are two classes of alleles, with one class causing a reduction in fitness relative to the other class. Very slight selection against one class can strongly affect the relative frequencies of the two classes and the relative ages of alleles in each class.