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Asymptotic behavior of the Poisson-Dirichlet distribution for large mutation rate. (English) Zbl 1119.92046

In the context of population genetics, Kingman’s Poisson-Dirichlet distribution describes the equilibrium proportions of different alleles in the infinitely many neutral alleles model. The main result of the paper is a large deviations principle for this distribution when the mutation rate approaches infinity. In particular, at the exponential scale, the differences between different allele proportions are still significant. The large deviations principle detects selection that grows at a linear or greater rate.

MSC:

92D10 Genetics and epigenetics
60F10 Large deviations

Citations:

Zbl 0920.92017
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References:

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