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

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