The population genealogy of the infinitely--many neutral alleles model.

A process analogous to Kingman's coalescent is introduced to describe the genealogy of populations evolving according to the infinitely- many neutral alleles model. The process records population frequencies in old and new classes, and labels the new classes in order of decreasing age. Its marginal distribution is characterized in a form which is amenable to explicit calculations and the transition densities of the associated K-allele models follow readily from this representation.