Article,
On the past history of an allele now known to have frequency p
14 (3): 439-450-- (1977)
DOI: DOI: 10.2307/3213447
Abstract
Consider a diploid population of N individuals undergoing random mating and mutation as in the infinite-allele Wright model. Choose a particular gene in generation Q for large Q, and let ft (0 ≦ t ≦ Q) be the frequency of the allelic type of the predecessor of that particular gene (or the gene itself) in generation t. By considering a ‘diffusion approximation' xt of ft, we find the distribution of the age of an allelic type now known to have frequency p, and of its distribution of frequencies since the allele came into existence. A novelty here is that the process xt is not a diffusion, but a process with jumps; it has x = 0 as an inaccessible entrance boundary but periodically jumps to it from the interior of 0, 1. The formulas obtained are the same as those derived by Maruyama and Kimura, who used a totally different approach.
