Ewens' sampling formula and related formulae: combinatorial proofs, extensions to variable population size and applications to ages of alleles.

Abstract excerpt

Ewens' sampling formula, the probability distribution of a configuration of alleles in a sample of genes under the infinitely-many-alleles model of mutation, is proved by a direct combinatorial argument. The distribution is extended to a model where the population size may vary back in time. The distribution of age-ordered frequencies in the population is also derived in the model, extending the GEM distribution...

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