Quasi-equilibrium theory for the distribution of rare alleles in a subdivided population: justification and implications.
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 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.
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Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
D000483:Alleles; D003198:Computer Simulation; D004641:Emigration and Immigration; D005787:Gene Frequency / Q000235:genetics; D005828:Genetics, Population; D006801:Humans; D008957:Models, Genetic