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Quasi-equilibrium theory for the distribution of rare alleles in a subdivided population: Justification and implications. (English) Zbl 0974.92021
Summary: This paper examines a quasi-equilibrium theory of rare alleles for subdivided populations that follow an island-model version of the Wright-Fisher model of evolution. All mutations are assumed to create new alleles. We present four results:
(1) conditions for the theory to apply are formally established using properties of the moments of the binomial distribution; (2) approximations currently in the literature can be replaced with exact results that are in better agreement with our simulations; (3) a modified maximum likelihood estimator of migration rate exhibits the same good performance on island-model data or on data simulated from the multinomial mixed with the Dirichlet distribution, and (4) a connection between the rare-allele method and the Ewens Sampling Formula [W.J. Ewens, Theor. Popul. Biol. 3, 87-112 (1972; Zbl 0245.92009)]; Mathematical population genetics. (1979; Zbl 0422.92011)] for the infinite-allele mutation model is made. This introduces a new and simpler proof for the expected number of alleles implied by the Ewens Sampling Formula.

92D15 Problems related to evolution
62P10 Applications of statistics to biology and medical sciences; meta analysis
Full Text: DOI
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