THE DISTRIBUTION OF RARE ALLELES

Population geneticists have long been interested in the behavior of ra re variants. The definition of a rare variant has been the subject of some debate, centered mainly on whether alleles with small relative fr equency should be considered rare, or whether alleles with small numbe rs should be. We study the behavior of the counts of rare alleles in s amples taken from a population genetics model that allows for selectio n and infinitely-many-alleles mutation structure. We show that in larg e samples the counts of rare alleles - those represented once, twice, ... - are approximately distributed as a Poisson process, with a param eter that depends on the total mutation rate, but not on the selection parameters. This result is applied to the problem of estimating the f raction of neutral mutations.