Migration and mutation in stochastic models of gene frequency change. I. The island model

Journal of Mathematical Biology
J A Sved, B D Latter

Abstract

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 delta m is added to the variance. As a result of the delta 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.

References

Jun 1, 1975·Theoretical Population Biology·A Jacquard
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Oct 1, 1964·Journal of Cellular Physiology·G E MAGNI
Mar 1, 1951·Annals of Eugenics·S WRIGHT

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Citations

Oct 18, 2013·Journal of Mathematical Biology·Ola Hössjer, Nils Ryman
Sep 19, 2014·Journal of Mathematical Biology·Ola Hössjer
Dec 1, 1988·American Journal of Physical Anthropology·A R Rogers, A W Eriksson
Dec 1, 1988·American Journal of Physical Anthropology·L W Konigsberg
Jul 29, 1995·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·N H Barton, I Wilson
Jun 5, 2013·Evolution; International Journal of Organic Evolution·Michael J Wade
Nov 1, 1986·Evolution; International Journal of Organic Evolution·Alan R Rogers, Henry C Harpending
May 1, 1988·Evolution; International Journal of Organic Evolution·Michael Lynch
Jun 1, 1992·Evolution; International Journal of Organic Evolution·Michael C Whitlock

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