Migration and mutation in stochastic models of gene frequency change |
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Authors: | Sved J A Latter B D H |
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Affiliation: | (1) School of Biological Sciences, Sydney University, Botany Building A12, 2006, N.S.W., Australia |
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Abstract: | Summary Migration has in the past been introduced deterministically into stochastic gene frequency models. Migration at rate m then reduces the between-population variability by a factor of (1 – m)2 each generation. We show that with stochastic migration, whether of fixed or variable numbers of individuals, a positive term m is added to the variance. As a result of the
m
term, the equilibrium value of the between-population variability is increased compared to the corresponding value for deterministic migration by a factor of approximately (1 – m)–2 for small m. An equivalent result is derived for mutation, using the infinite allele model for a single population. We show in addition that these results may be derived much more simply by use of identity-by-descent probability methods, but only if a modified definition of the probability of identity-by-descent is used, involving the sampling with instead of without replacement of pairs of genes from the population. |
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