Private alleles in a partially isolated population. II. Distribution of persistence time and probability of emigration

Theoretical Population Biology
N Takahata, M Slatkin

Abstract

Two diffusion limits were derived from a discrete Wright-Fisher model of migration, mutation, and selection with an arbitrary degree of dominance. Instantaneous killing of the process due to emigration of a mutant leads to one of two diffusion processes with a killing term. One (weak gene flow) is the boundary case of the other (strong gene flow), which can cover a wide range of gene flow. The diffusion process subject to strong gene flow is similar to that studied by S. Karlin and S. Tavaré (1983, SIAM J. Appl. Math. 43, 31-41). The spectral decomposition of the transition probability density of "private" allele frequencies is presented in the case of strong gene flow. The fate of mutant in a deme is discussed in terms of the probabilities of survival and emigration.

References

Dec 1, 1973·Proceedings of the National Academy of Sciences of the United States of America·J V Neel
Apr 1, 1981·Theoretical Population Biology·S Karlin, S Tavaré
Oct 1, 1983·Proceedings of the National Academy of Sciences of the United States of America·M Kimura

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Citations

Dec 12, 2002·Journal of Biomedical Informatics·I N SarkarD H Figurski

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