Skip to main content
NCBI home page
Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1983 Oct;80(20):6317–6321. doi: 10.1073/pnas.80.20.6317

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

Motoo Kimura 1
PMCID: PMC394288  PMID: 16593383

Abstract

Assume a diploid species consisting of an infinite number of competing demes, each having Ne 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 ϕ = ϕ(x;t) be the distribution function of x among demes in the species at time t. Then, we have ∂ϕ/∂t = L(ϕ) + c(x — ¯x)ϕ, where L is the Kolmogorov forward differential operator commonly used in population genetics [i.e., L = (1/2) (∂2/∂x2)Vδx — (∂/∂x)Mδx], and Mδx and Vδx 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 the steady state, in which mutation, migration, random drift, and intra- and interdeme selection balance each other, it is shown that the index D = c/m — 4Nes′ serves as a good indicator for predicting which of the two forces (i.e., group selection or individual selection) prevails; if D > 0, the altruistic allele predominates, but if D < 0, it becomes rare and cannot be established in the species.

Keywords: population genetics, sociobiology, stochastic process

Full text

PDF
6317

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Boorman S. A., Levitt P. R. Group selection on the boundary of a stable population. Theor Popul Biol. 1973 Mar;4(1):85–128. doi: 10.1016/0040-5809(73)90007-5. [DOI] [PubMed] [Google Scholar]
  2. Crow J. F., Aoki K. Group selection for a polygenic behavioral trait: a differential proliferation model. Proc Natl Acad Sci U S A. 1982 Apr;79(8):2628–2631. doi: 10.1073/pnas.79.8.2628. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. KIMURA M. Stochastic processes and distribution of gene frequencies under natural selection. Cold Spring Harb Symp Quant Biol. 1955;20:33–53. doi: 10.1101/sqb.1955.020.01.006. [DOI] [PubMed] [Google Scholar]
  4. Kimura M. Theoretical foundation of population genetics at the molecular level. Theor Popul Biol. 1971 Jun;2(2):174–208. doi: 10.1016/0040-5809(71)90014-1. [DOI] [PubMed] [Google Scholar]
  5. Leigh E. G. When does the good of the group override the advantage of the individual? Proc Natl Acad Sci U S A. 1983 May;80(10):2985–2989. doi: 10.1073/pnas.80.10.2985. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Ohta T., Kimura M. Linkage disequilibrium between two segregating nucleotide sites under the steady flux of mutations in a finite population. Genetics. 1971 Aug;68(4):571–580. doi: 10.1093/genetics/68.4.571. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Wright S. Evolution in Mendelian Populations. Genetics. 1931 Mar;16(2):97–159. doi: 10.1093/genetics/16.2.97. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Proceedings of the National Academy of Sciences of the United States of America are provided here courtesy of National Academy of Sciences

RESOURCES