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Estimating gene flow in island populations

Published online by Cambridge University Press:  14 April 2009

Bruce Rannala  and
J. A. Hartigan
Bruce Rannala
Affiliation:
Department of Biology, Center for Computational Ecology
J. A. Hartigan
Affiliation:
Department of Statistics, Yale University, New Haven, Connecticut, 06520, USA
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Summary

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A new method is presented for estimating the rate of gene flow into island populations using the distribution of alleles in samples from a number of islands. The pseudo maximum likelihood estimator (PMLE) that we derive may be applied to species with either discrete or continuous generation times. For Wright's discrete-generation island model, the method provides an estimate of θ = 2Nm where N is the (haploid) population size on each island and m is the fraction of individuals replaced by immigrants in each generation. For a continuous-generation island model, the corresponding parameter φ is the ratio of the immigration rate φ to the individual birth rate λ. Monte Carlo simulations are used to compare the statistical properties of the PMLE with those of two alternative estimatorsof θ derived from Wright's F-statistics. The PMLE is shown to have greatest efficiency (least mean square error) in most cases for a wide range of sample sizes and parameter values. The PMLE is applied to estimate θ using mtDNA haplotypes and allozymes for subdivided populations of African elephants and Channel Island foxes.

Type
Research Article
Information
Genetics Research , Volume 67 , Issue 2 , April 1996 , pp. 147 - 158
Copyright
Copyright © Cambridge University Press 1996

References

Barton, N. H., Halliday, R. B., & Hewitt, G. M., (1983). Rare electrophoretic variants in a hybrid zone. Heredity 50, 139–146.CrossRefGoogle Scholar
Barton, N. H., & Slatkin, M., (1986). A quasi-equilibrium theory of the distribution of rare alleles in a subdivided population. Heredity 56, 409–416.CrossRefGoogle Scholar
Brier, S. S., (1980). Analysis of contingency tables under cluster sampling. Biometrika 67, 591–596.CrossRefGoogle Scholar
Casella, G., & Berger, R., (1990). Statistical Inference. Belmont: Duxbury Press.Google Scholar
Chuang, C., & Cox, C., (1985). Pseudo maximum likelihood estimation for the Dirichlet-multinomial distribution. Communications in Statistics: Theory and Methodology 14, 2293–2311.CrossRefGoogle Scholar
Cockerham, C. C., & Weir, B. S., (1993). Estimation of gene flow from F-statistics. Evolution 47, 855–863.Google ScholarPubMed
Collins, P. W., (1982). Origin and differentiation of the island fox: A study on evolution in insular populations. Master's thesis, University of California, Santa Barbara, CA.Google Scholar
Crow, J. F., & Aoki, K., (1984). Group selection for a polygenic behavioral trait: Estimating the degree of subdivision. Proceedings of the National Academy of Sciences, USA 81, 6073–6077.CrossRefGoogle ScholarPubMed
Edwards, S. V., (1993). Mitochondrial gene genealogy and gene flow among island and mainland populations of a sedentary songbird, the grey-crowned babbler (Pomatostomus temporalis). Evolution 47, 1118–1137.Google ScholarPubMed
Georgiadis, N., Bischof, L., Templeton, A., Patton, J., Karesh, W., & Western, D., (1994). Structure and history of African elephant populations. I. Eastern and southern Africa. Journal of Heredity 85, 100–104.CrossRefGoogle ScholarPubMed
Gong, G., & Samaniego, F. J., (1981). Pseudo maximum likelihood estimation: Theory and applications. The Annals of Statistics 9, 861–869.CrossRefGoogle Scholar
Hudson, R. R., Slatkin, M., & Maddison, W. P., (1992). Estimation of levels of gene flow from DNA sequence data. Genetics 132, 583–589.CrossRefGoogle ScholarPubMed
Johnson, N. L., & Kotz, S., (1972). Distributions in Statistics: Continuous Multivariate Distributions. Wiley and Sons, New York.Google Scholar
Kimura, M., (1953). ‘Stepping-stone’ model of population. Annual Report of the National Institute of Genetics, Japan 3, 62–63.Google Scholar
Kimura, M., & Weiss, G. H., (1964). The stepping stone model of population structure and the decrease of genetic correlation with distance. Genetics 59, 561–576.CrossRefGoogle Scholar
Levin, B., & Reed, J., (1977). Compound multinomial likelihood functions are unimodal: Proof of a conjecture of I. J. Good. The Annals of Statistics 5, 79–87.CrossRefGoogle Scholar
Lewontin, R. C., (1974). The Genetic Basis of Evolutionary Change. New York: Columbia University Press.Google Scholar
Malécot, G., (1948). Les mathématiques de l'hérédité. Freeman, San Francisco, CA., (1969 The mathematics of heredity, Yermanos, D. M. (trans.).)Google Scholar
Maruyama, T., (1970). 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
Mercure, A., Rails, K., Koepfli, K. P., & Wayne, R. K., (1993). Genetic subdivision among small canids: Mitochondrial DNA differentiation of swift, kit and Arctic foxes. Evolution 47, 1313–1328.CrossRefGoogle ScholarPubMed
Mosimann, J. E., (1962). On the compound multinomial distribution, the multivariate β-distribution, and correlations among proportions. Biometrika 49, 65–82.Google Scholar
Nei, M., (1973). Analysis of gene diversity in subdivided populations. Proceedings of the National Academy of Sciences USA 70, 3321–3323.CrossRefGoogle ScholarPubMed
Parke, W. R., (1986). Pseudo maximum likelihood estimation: The asymptotic distribution. The Annals of Statistics 14, 355–357.CrossRefGoogle Scholar
Rannala, B., & Hartigan, J. A., (1995). Identity by descent in island-mainland populations. Genetics 139, 429–437.CrossRefGoogle ScholarPubMed
Slatkin, M., (1985). Gene flow in natural populations. Annual Review of Ecology and Systematics 16, 393–430.CrossRefGoogle Scholar
Slatkin, M., (1994). Gene flow and population structure. In Ecological Genetics, (ed. Real, L.). pp. 3–17. Princeton. NJ: Princeton University Press.Google 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 cladistic measure of gene flow inferred from the phylogenies of alleles. Genetics 123, 603–613.CrossRefGoogle ScholarPubMed
Wayne, R. K., George, S. B., Gilbert, D., Collins, P. W, Kovach, S. D., Girman, D., & Lehman, N., (1991). A morphological and genetic study of the island fox Urocyon littoralis. Evolution 45, 1849–1868.CrossRefGoogle ScholarPubMed
Wehrhahn, C. F., (1989). Proceedings of the ecological genetics workshop. Genome 31, 1098–1099.CrossRefGoogle Scholar
Wehrhahn, C F., & Powell, R., (1987). Electrophoretic variation, regional differences, and gene flow in the coho salmon (Oncorhynchus kisutch) of southern British Columbia. Canadian Journal of Fisheries and Aquatic Sciences 44, 822–831.CrossRefGoogle Scholar
Weir, B. S., & Cockerham, C. C., (1984). Estimating Fstatistics for the analysis of population structure. Evolution 38, 1358–1370.Google ScholarPubMed
Wolfram Research, Inc., (1992). Mathematica. Wolfram Research, Inc., Champaign, IL. Version 2.2.Google Scholar
Wright, S., (1931). Evolution in Mendelian populations. Genetics 16, 97–159.CrossRefGoogle ScholarPubMed
Wright, S., (1949). Adaptation and selection. In Genetics, Paleontology and Evolution, (ed. Jepson, G., Simpson, G. & Mayr, E.). pp. 365–389. Princeton, NJ: Princeton University Press.Google Scholar
Wright, S., (1951). The genetical structure of populations. Annals of Eugenics 15, 323–354.CrossRefGoogle ScholarPubMed
Wright, S., (1969). Evolution and Genetics of Populations. The Theory of Gene Frequencies, vol. 2. Chicago IL: University of Chicago Press.Google Scholar
Zink, R. M., & Remsen, J. V., (1986). Evolutionary processes and patterns of geographic variation in birds. In Current Ornithology, (ed. Johnston, R. F.). pp. 1–69. vol. 4. New York: Plenum.Google Scholar