Ages,extinction times,and first passage probabilities for a multiallele diffusion model with irreversible mutation

We derive some new results for diffusion models in population genetics of the “infinite-alleles” type. Assuming present allelic frequencies known, we find expected values for times which may be interpreted either as the age of the kth oldest allele or the time to extinction of the “kth-to-last” allele to be lost. We also find some conditional expectations and probabilities related to the order of extinction or creation of the alleles. Computations illustrate the dependence of the expected times on the mutation rate.