Abstract
The behaviour of a Pólya-like urn which generates Ewens' sampling formula in population genetics is investigated. Connections are made with work of Watterson and Kingman and to the Poisson-Dirichlet distribution. The order in which novel types occur in the urn is shown to parallel the age distribution of the infinitely many alleles diffusion model and consequences of this property are explored. Finally the urn process is related to Kingman's coalescent with mutation to provide a rigorous basis for this parallel.
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This research was partially supported by the Sloan Foundation under Grant 85-6-14 and by the National Science Foundation
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Hoppe, F.M. The sampling theory of neutral alleles and an urn model in population genetics. J. Math. Biology 25, 123–159 (1987). https://doi.org/10.1007/BF00276386
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DOI: https://doi.org/10.1007/BF00276386