Oct 1, 1983

Diffusion model of intergroup selection, with special reference to evolution of an altruistic character

Proceedings of the National Academy of Sciences of the United States of America
M KIMURA

Abstract

Assume a diploid species consisting of an infinite number of competing demes, each having N(e) reproducing members and in which mating is at random. Then consider a locus at which a pair of alleles A and A' are segregating, where A' is the "altruistic allele," which has selective disadvantage s' relative to A with respect to individual selection, but which is beneficial for a deme in competition with other demes; namely, a deme having A' with frequency x has the advantage c(x - x) relative to the average deme, where c is a positive constant and x is the average of x over the species. Let varphi = varphi(x;t) be the distribution function of x among demes in the species at time t. Then, we have partial differentialvarphi/ partial differentialt = L(varphi) + c(x - x)varphi, where L is the Kolmogorov forward differential operator commonly used in population genetics [i.e., L = (1/2) ( partial differential(2)/ partial differentialx(2))V(deltax) - ( partial differential/ partial differentialx)M(deltax)], and M(deltax) and V(deltax) stand for the mean and variance of the change in x per generation within demes. As to migration, assume Wright's island model and denote by m the migration rate per deme per generation. By investigating th...Continue Reading

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References

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  • Citations1012

Citations

Mentioned in this Paper

Mutation Abnormality
Locus
2,2-dichloro-1,1-difluoroethyl difluoromethyl ether
Alleles

About this Paper

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