Skip to main content
PMC home page
Genetics logoLink to Genetics
. 2002 Aug;161(4):1727–1750. doi: 10.1093/genetics/161.4.1727

General models of multilocus evolution.

Mark Kirkpatrick 1, Toby Johnson 1, Nick Barton 1
PMCID: PMC1462196  PMID: 12196414

Abstract

In 1991, Barton and Turelli developed recursions to describe the evolution of multilocus systems under arbitrary forms of selection. This article generalizes their approach to allow for arbitrary modes of inheritance, including diploidy, polyploidy, sex linkage, cytoplasmic inheritance, and genomic imprinting. The framework is also extended to allow for other deterministic evolutionary forces, including migration and mutation. Exact recursions that fully describe the state of the population are presented; these are implemented in a computer algebra package (available on the Web at http://helios.bto.ed.ac.uk/evolgen). Despite the generality of our framework, it can describe evolutionary dynamics exactly by just two equations. These recursions can be further simplified using a "quasi-linkage equilibrium" (QLE) approximation. We illustrate the methods by finding the effect of natural selection, sexual selection, mutation, and migration on the genetic composition of a population.

Full Text

The Full Text of this article is available as a PDF (256.6 KB).

Selected References

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

  1. Baake E. Mutation and recombination with tight linkage. J Math Biol. 2001 May;42(5):455–488. doi: 10.1007/s002850000077. [DOI] [PubMed] [Google Scholar]
  2. Barton N. H. A general model for the evolution of recombination. Genet Res. 1995 Apr;65(2):123–145. doi: 10.1017/s0016672300033140. [DOI] [PubMed] [Google Scholar]
  3. Barton N. H. Estimating multilocus linkage disequilibria. Heredity (Edinb) 2000 Mar;84(Pt 3):373–389. doi: 10.1046/j.1365-2540.2000.00683.x. [DOI] [PubMed] [Google Scholar]
  4. Barton N. H., Shpak M. The stability of symmetric solutions to polygenic models. Theor Popul Biol. 2000 May;57(3):249–263. doi: 10.1006/tpbi.2000.1455. [DOI] [PubMed] [Google Scholar]
  5. Barton N. H. The effects of linkage and density-dependent regulation on gene flow. Heredity (Edinb) 1986 Dec;57(Pt 3):415–426. doi: 10.1038/hdy.1986.142. [DOI] [PubMed] [Google Scholar]
  6. Barton N. H., Turelli M. Adaptive landscapes, genetic distance and the evolution of quantitative characters. Genet Res. 1987 Apr;49(2):157–173. doi: 10.1017/s0016672300026951. [DOI] [PubMed] [Google Scholar]
  7. Barton N. H., Turelli M. Natural and sexual selection on many loci. Genetics. 1991 Jan;127(1):229–255. doi: 10.1093/genetics/127.1.229. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Bürger R. Moments, cumulants, and polygenic dynamics. J Math Biol. 1991;30(2):199–213. doi: 10.1007/BF00160336. [DOI] [PubMed] [Google Scholar]
  9. Dawson K. J. The decay of linkage disequilibrium under random union of gametes: how to calculate Bennett's principal components. Theor Popul Biol. 2000 Aug;58(1):1–20. doi: 10.1006/tpbi.2000.1471. [DOI] [PubMed] [Google Scholar]
  10. Dawson K. J. The dynamics of infinitesimally rare alleles, applied to the evolution of mutation rates and the expression of deleterious mutations. Theor Popul Biol. 1999 Feb;55(1):1–22. doi: 10.1006/tpbi.1998.1375. [DOI] [PubMed] [Google Scholar]
  11. Fisher W. J. THE BALANCE, THE STEELYARD AND THE CONCEPT OF FORCE. Science. 1918 Nov 1;48(1244):427–433. doi: 10.1126/science.48.1244.427. [DOI] [PubMed] [Google Scholar]
  12. Hill W. G., Robertson A. The effect of linkage on limits to artificial selection. Genet Res. 1966 Dec;8(3):269–294. [PubMed] [Google Scholar]
  13. Kimura M. Attainment of Quasi Linkage Equilibrium When Gene Frequencies Are Changing by Natural Selection. Genetics. 1965 Nov;52(5):875–890. doi: 10.1093/genetics/52.5.875. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Kirkpatrick M., Barton N. H. The strength of indirect selection on female mating preferences. Proc Natl Acad Sci U S A. 1997 Feb 18;94(4):1282–1286. doi: 10.1073/pnas.94.4.1282. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Kirkpatrick M., Servedio M. R. The reinforcement of mating preferences on an island. Genetics. 1999 Feb;151(2):865–884. doi: 10.1093/genetics/151.2.865. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Lande R. Models of speciation by sexual selection on polygenic traits. Proc Natl Acad Sci U S A. 1981 Jun;78(6):3721–3725. doi: 10.1073/pnas.78.6.3721. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Nagylaki T., Hofbauer J., Brunovský P. Convergence of multilocus systems under weak epistasis or weak selection. J Math Biol. 1999 Feb;38(2):103–133. doi: 10.1007/s002850050143. [DOI] [PubMed] [Google Scholar]
  18. Nagylaki T. The evolution of multilocus systems under weak selection. Genetics. 1993 Jun;134(2):627–647. doi: 10.1093/genetics/134.2.627. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Price G. R. Selection and covariance. Nature. 1970 Aug 1;227(5257):520–521. doi: 10.1038/227520a0. [DOI] [PubMed] [Google Scholar]
  20. Slatkin M. On treating the chromosome as the unit of selection. Genetics. 1972 Sep;72(1):157–168. doi: 10.1093/genetics/72.1.157. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Sniegowski P. D., Gerrish P. J., Johnson T., Shaver A. The evolution of mutation rates: separating causes from consequences. Bioessays. 2000 Dec;22(12):1057–1066. doi: 10.1002/1521-1878(200012)22:12<1057::AID-BIES3>3.0.CO;2-W. [DOI] [PubMed] [Google Scholar]
  22. Turelli M., Barton N. H. Genetic and statistical analyses of strong selection on polygenic traits: what, me normal? Genetics. 1994 Nov;138(3):913–941. doi: 10.1093/genetics/138.3.913. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Genetics are provided here courtesy of Oxford University Press

RESOURCES