Allelic frequencies given the sample's common ancestral type
The author considers a population of fixed size N of haploid genes in which K distinct allelic types are possible; it is assumed that the evolution of the population follows a Moran model. Then, looking backward in time, any random sample of n genes eventually has a single common ancestral gene. The probability generating function for the number of times that in a random sample of size n there was a mutation along an individual's genealogical line since the sample's common ancestor is calculated, and from this function the expected proportion of genes in a random sample which are of a particular allelic type, given the allelic type of the sample's common ancestor is derived. It is shown that the same result can be obtained using Kingman's coalescent model. These results are used in the cases of the 2-allele model, the infinitely many alleles model, and the K-alleles model with constant mutation. In the last part, a model with an infinite number of allelic types and stepwise mutation is considered.
scientific article; zbMATH DE number 4074861