Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-27T23:56:03.406Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimators for pairwise relatedness and individual inbreeding coefficients

Published online by Cambridge University Press:  14 April 2009

Kermit Ritland
Kermit Ritland
Affiliation:
Department of Botany, University of Toronto, Toronto, Ontario M5S 3B2, Canada
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.

Method-of-moments estimators (MMEs) for the two-gene coefficients of relationship and inbreeding, and for thxe four-gene Cotterman coefficients, are described. These estimators, which use co-dominant genetic markers, are most appropriate for estimating pairwise relatedness or individual inbreeding coefficients, as opposed to their mean values in a group. This is because, compared to the maximum likelihood estimate (MLE), they show reduced small-sample bias and lack distributional assumptions. The ‘efficient’ MME is an optimally weighted average of estimates given by each allele at each locus. Generally, weights must be computed numerically, but if true coefficients are assumed zero, simplifiedestimators are obtained whose relative efficiencies are quite high. Population gene frequency is assumed to be assayed ina larger, ‘reference population’ sample, and the biases introduced by small reference samples and/or genetic drift of the reference population are discussed. Individual-level estimates of relatedness or inbreeding, while displaying high variance, are useful in several applications as a covariate in population studies.

Type
Research Article
Information
Genetics Research , Volume 67 , Issue 2 , April 1996 , pp. 175 - 185
Copyright
Copyright © Cambridge University Press 1996

References

Barbujani, G., (1987). Autocorrelation of gene frequencies under isolation by distance. Genetics 117, 777–782.CrossRefGoogle ScholarPubMed
Brown, A. H. D., Barrett, S. C. H., & Moran, G. F., (1985). Mating system estimation in forest trees: models, methods and meanings. In Population Genetics in Forestry, Lecture notes in Biomathematics (ed. Levin, S.), 60, 32–49.CrossRefGoogle Scholar
Chakraborty, R., Meagher, T. R., & Smouse, P. E., (1988). Parentage analysis with genetic markers in natural populations. I. The expected proportion of offspring with unambiguous paternity. Genetics 118, 527–536.CrossRefGoogle ScholarPubMed
Cotterman, C. W., (1940). A Calculus for Slatistico-genetics. Unpublished thesis, Ohio State University, Columbus, Ohio.Google Scholar
Curie-Cohen, M., (1981). Estimates of inbreeding in a natural population: a comparison of sampling properties. Genetics 100, 339–358.CrossRefGoogle Scholar
Crow, J. F., & Kimura, M., (1970). An Introduction to Population Genetics Theory. Burgess, Minneapolis.Google Scholar
Cruzan, M., (1996). Genetic markers in plant evolutionary biology. Ecology (in the Press).Google Scholar
Emigh, T. H., (1980). A comparison of tests for Hardy—Weinberg equilibrium. Biometrics 36, 627–642.CrossRefGoogle ScholarPubMed
Epperson, B. K., (1989). Spatial patterns of genetic variation within plant populations. In Plant Population Genetics Breeding, and Genetic Resources (ed. Brown, A. H. D., Clegg, M. T., Kahler, A. L. and Weir, B. S.). pp. 229–253. Sunderland, Mass.: Sinauer Associates.Google Scholar
Grafen, A., (1985). A geometric view of relatedness. Oxford Survey Evolutionary Biology 2, 28–89.Google Scholar
Jacquard, A., (1974). The Genetic Structure of Populations. Berlin: Springer.CrossRefGoogle Scholar
Li, C. C., & Horvitz, D. G., (1953). Some methods of estimating the inbreeding coefficient. American J. Human Genetics 5, 107–117.Google ScholarPubMed
Loeselle, B., Sork, V., Nason, J., & Graham, C., (1996). spatial genetic structure of a tropical understory shrub, Psychotria officinalis (Rubiaceae). American Journal of Botany (in the Press).Google Scholar
Lynch, M., (1988). Estimation of relatedness by DNA fingerprinting. Molecular Biology and Evolution 5, 584–599.Google ScholarPubMed
Malecot, G., (1969). The Mathematics of Relationship. San Francisco: W. H. Freeman.Google Scholar
Michod, R. D., & Hamilton, W. D., (1980). Coefficients of relatedness in sociobiology. Nature 288, 694–697.CrossRefGoogle Scholar
Morton, N. E., Yee, S., Harris, D. E., & Lew, R., (1971). Bioassay of kinship. Theoreticul Population Biology 2, 507–524.CrossRefGoogle ScholarPubMed
Pamilo, P., & Crozier, R. H., (1982). Measuring genetic relatedness in natural populations: methodology. Theoretical Population Biology 21, 171–193.CrossRefGoogle Scholar
Park, S. K., & Miller, K. W., (1988). Random number generators: good ones are hard to find. Communications of ACM 31, 1192–1201.CrossRefGoogle Scholar
Queller, D. C., & Goodnight, K. F., (1989). Estimating relatedness using genetic markers. Evolution 43, 258–275.CrossRefGoogle ScholarPubMed
Ritland, K., (1996 a). A marker-based method for inferences about quantitative inheritance in natural populations. Evolution (in the Press).CrossRefGoogle ScholarPubMed
Ritland, K., (1996 b). Estimation of individual population divergence, a component of genetic diversity. (Submitted to) Molecular Ecology.Google Scholar
Ritland, K., & Ritland, C., (1996). Inferences about quantitative inheritance based upon natural population structure in the common yellow monkeyflower, Mimulus guttatus. Evolution (in the Press).CrossRefGoogle ScholarPubMed
Robertson, A., & Hill, W. G., (1984). Deviations from Hardy—Weinberg proportions: sampling variances and use in estimation of inbreeding coefficients. Genetics 107, 703–718.CrossRefGoogle ScholarPubMed
Schuster, W. S. F., & Mitton, J. B., (1991). Relatedness within clusters of a bird-dispersed pine and the potential for kin interactions. Heredity 67, 41–48.CrossRefGoogle Scholar
Thompson, E. A., (1975). The estimation of pairwise relationships. Annals of Human Genetics 39, 173–188.CrossRefGoogle ScholarPubMed
Thompson, E. A., (1976). Inference of genealogical structure. Social Sciences Information 15, 477–526.CrossRefGoogle Scholar
Weir, B. S., & Cockerham, C. C., (1984). Estimating Fstatistics for the analysis of population structure. Evolution 38, 1358–1370.Google ScholarPubMed
Weir, B. S., (1990). Genetic Data Analysis. Sunderland, MA.: Sinauer Associates.Google Scholar
Wilkinson, G. S., & McCracken, G. F., (1986). On estimating relatedness using genetics markers. Evolution 39, 1169–1174.CrossRefGoogle Scholar
Wright, S., (1922). Coefficients of inbreeding and relationship. American Naturalist 56, 330–338.CrossRefGoogle Scholar
Wright, S., (1943). Isolation by distance. Genetics 28, 114–138.CrossRefGoogle ScholarPubMed
Wright, S., (1969). Evolution and the Genetics of Populations, vol. 2. The theory of gene frequencies. Chicago: University of Chicago Press.Google Scholar
Yasuda, N., (1968). Estimation of the inbreeding coefficient from phenotypic frequencies by a method of maximum likelihood scoring. Biometrics 24, 915–935.CrossRefGoogle ScholarPubMed