Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-15T08:59:18.996Z Has data issue: false hasContentIssue false
  • English
  • Français

Inbreeding coefficients and coalescence times

Published online by Cambridge University Press:  14 April 2009

Montgomery Slatkin
Montgomery Slatkin
Affiliation:
Department of Integralive Biology, University of California, Berkeley CA 94720
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

This paper describes the relationship between probabilities of identity by descent and the distribution of coalescence times. By using the relationship between coalescence times and identity probabilities, it is possible to extend existing results for inbreeding coefficients in regular systems of mating to find the distribution of coalescence times and the mean coalescence times. It is also possible to express Sewall Wright's FST as the ratio of average coalescence times of different pairs of genes. That simplifies the analysis of models of subdivided populations because the average coalescence time can be found by computing separately the time it takes for two genes to enter a single subpopulation and time it takes for two genes in the same subpopulation to coalesce. The first time depends only on the migration matrix and the second time depends only on the total number of individuals in the population. This approach is used to find FST in the finite island model and in one- and two-dimensional stepping-stone models. It is also used to find the rate of approach of FST to its equilibrium value. These results are discussed in terms of different measures of genetic distance. It is proposed that, for the purposes of describing the amount of gene flow among local populations, the effective migration rate between pairs of local populations, M^, which is the migration rate that would be estimated for those two populations if they were actually in an island model, provides a simple and useful measure of genetic similarity that can be defined for either allozyme or DNA sequence data.

Information

Type
Research Article
Information
Genetics Research , Volume 58 , Issue 2 , October 1991, pp. 167 - 175
Copyright
Copyright © Cambridge University Press 1991

References

Crow, J. F. & Aoki, K. (1984). Group selection for a polygenic behavioral trait: estimating the degree of population subdivision. Proceedings of the National Academy of Sciences, USA 81, 6073–6077.CrossRefGoogle ScholarPubMed
Crow, J. F. & Kimura, M. (1970). An Introduction to Population Genetics Theory. New York: Harper and Row.Google Scholar
Ewens, W. J. (1990). Population genetics theory – the past and the future. In Mathematical and Statistical Developments of Evolutionary Theory (ed. Lessard, S.), pp. 177–227. Amsterdam: Kluwer.CrossRefGoogle Scholar
Feller, W. (1957). An Introduction to Probability Theory and Its Applications, 2nd edn, vol. 1. New York: Wiley.Google Scholar
Hey, J. (1991). A multi-dimensional coalescent process applied to multi-allelic selection models and migration models. Theoretical Population Biology 39, 30–48.CrossRefGoogle ScholarPubMed
Hudson, R. R. (1990). Gene genealogies and the coalescent process. In Oxford Surveys in Evolutionary Biology (ed. Futuyma, D. J. and Antonovics, J.). Oxford: Oxford University Press (in the press).Google Scholar
Lynch, M. & Crease, T. J. (1990). The analysis of population survey data on DNA sequence variation. Molecular Biology and Evolution 7, 377–394.Google ScholarPubMed
Malécot, G. (1948). Les Mathématiques de l'Hérédité. Paris: Masson et Cie.Google Scholar
Maruyama, T. (1970 a). On the rate of decrease of heterozygosity in circular stepping stone models of populations. Theoretical Population Biology 1, 101–119.CrossRefGoogle ScholarPubMed
Maruyama, T. (1970 b). Effective number of alleles in a subdivided population. Theoretical Population Biology 1, 273–306.CrossRefGoogle Scholar
Maruyama, T. (1971). Analysis of population structure. II. Two-dimensional stepping stone models of finite length and other geographically structured populations. Annals of Human Genetics 35, 179–196.CrossRefGoogle ScholarPubMed
Nei, M. (1972). Genetic distance between populations. American Naturalist 106, 283–292.CrossRefGoogle Scholar
Nei, M. (1973). Analysis of gene diversity in subdivided populations. Proceedings of the National Academy of Sciences, USA 70, 3321–3323.CrossRefGoogle ScholarPubMed
Nei, M. (1982). Evolution of human races at the gene level. In Human Genetics, Part A: The Unfolding Genome, (ed. Bohhe-Tamir, B., Cohen, P. and Goodman, R. N.), pp. 167–181. New York: Alan R. Liss.Google Scholar
Nei, M. (1987). Molecular Evolutionary Genetics. New York: Columbia University Press.CrossRefGoogle Scholar
Slatkin, M. & Barton, N. H. (1989). A comparison of three indirect methods for estimating average levels of gene flow. Evolution 43, 1349–1368.CrossRefGoogle ScholarPubMed
Slatkin, M. & Maddison, W. P. (1989). A cladisic measure of gene flow inferred from the phylogenies of alleles. Genetics 123, 603–613.CrossRefGoogle ScholarPubMed
Slatkin, M. & Maddison, W. P. (1990). Detecting isolation by distance using phylogenies of genes. Genetics 123, 603–613.CrossRefGoogle Scholar
Strobeck, C. (1987). Average number of nucleotide differences in a sample from a single subpopulation: a test for population subdivision. Genetics 117, 149–153.CrossRefGoogle Scholar
Takahata, N. (1983). Gene identity and genetic differentiation of populations in the finite island model. Genetics 104, 497–512.CrossRefGoogle ScholarPubMed
Takahata, N. (1988). The coalescent in two partially isolated diffusion populations. Genetical Research 52, 213–222.CrossRefGoogle ScholarPubMed
Takahata, N. & Palumbi, S. R. (1985). Extranuclear differentiation and gene flow in a finite island model. Genetics 109, 441–457.CrossRefGoogle Scholar
Tavaré, S. (1984). Line-of-descent and genealogical processes and their applications in population genetics. Theoretical Population Biology 26, 119–164.CrossRefGoogle ScholarPubMed
Wright, S. (1922). Coefficients of inbreeding and relationship. American Naturalist 63, 556–561.CrossRefGoogle Scholar
Wright, S. (1951). The genetical structure of populations. Annals of Eugenics 15, 323–354.CrossRefGoogle ScholarPubMed
Wright, S. (1969). Evolution and the Genetics of Population, Volume 2. The Theory of Gene Frequencies. Chicago: University of Chicago Press.Google Scholar