Age of an allele and gene genealogies of nested subsamples for populations admitting large offspring numbers

Coalescent processes, including mutation, are derived from Moran type population models admitting large offspring numbers. Including mutation in the coalescent process allows for quantifying the turnover of alleles by computing the distribution of the number of original alleles still segregating in the population at a given time in the past. The turnover of alleles is considered for specific classes of the Moran model admitting large offspring numbers. Versions of the Kingman coalescent are also derived whose rates are functions of the mean and variance of the offspring distribution. High variance in the offspring distribution results in higher turnover and younger age of alleles than predicted by the usual Kingman coalescent.