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Estimation of Divergence from Hardy–Weinberg Form

  • Alan E. Stark (a1)


The Hardy–Weinberg (HW) principle explains how random mating (RM) can produce and maintain a population in equilibrium, that is, with constant genotypic proportions. When proportions diverge from HW form, it is of interest to estimate the fixation index F, which reflects the degree of divergence. Starting from a sample of genotypic counts, a mixed procedure gives first the orthodox estimate of gene frequency q and then a Bayesian estimate of F, based on a credible prior distribution of F, which is described here.


Corresponding author

address for correspondence: Dr Alan E. Stark, Honorary Associate, School of Mathematics and Statistics, F07, University of Sydney, NSW 2006, Australia. E-mail:


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Ayres, K. L., & Balding, D. J. (1998). Measuring departures from Hardy-Weinberg: A Markov chain Monte Carlo method for estimating the inbreeding coefficient. Heredity, 80, 769777.
Balding, D. J., & Nichols, R. A. (1995). A method for quantifying differentiation between populations at multi-allelic loci and its implications for investigating identity and paternity. Genetica, 96, 312.
Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society, 53, 370418.
Cavalli-Sforza, L. L., & Bodmer, W. F. (1971). The genetics of human populations. San Francisco: W. H. Freeman and Company.
Crow, J. F. (1999). Hardy, Weinberg and language impediments. Genetics, 152, 821825.
Edwards, A. W. F. (2008). G. H. Hardy (1908) and Hardy-Weinberg equilibrium. Genetics, 179, 11431150.
Fisher, R. A. (1959). Statistical methods and scientific inference (2nd ed.). Edinburgh: Oliver and Boyd.
Fisher, R. A. (1960). The design of experiments (7th ed.). Edinburgh: Oliver and Boyd.
Good, I. J. (1968). The estimation of probabilities: An essay on modern Bayesian methods. Cambridge, MA: The MIT Press.
Gunel, E., & Wearden, S. (1995). Bayesian estimation and testing of gene frequencies. Theoretical and Applied Genetics, 91, 534543.
Hardy, G. H. (1908). Mendelian proportions in a mixed population. Science, 28, 4950.
Hartl, D. L., & Jones, E. W. (2006). Essential genetics: A genomics perspective (4th ed.). Sudbury, MA: Jones and Bartlett Publishers.
Lange, K. (1995). Applications of the Dirichlet distribution to forensic match probabilities. Genetica, 96, 107117.
Li, C. C. (1988). Pseudo-random mating populations. In celebration of the 80th anniversary of the Hardy-Weinberg law. Genetics, 119, 731737.
Mayo, O. (2008). A century of Hardy-Weinberg equilibrium. Twin Research and Human Genetics, 11, 249–246.
Neel, J. V., & Schull, W. J. (1954). Human heredity. Chicago: The University of Chicago Press.
Penrose, L. S. (1972). The biology of mental defect (4th ed.). London: Sidgwick & Jackson.
Russell, P. J. (2006). iGenetics: A molecular approach (2nd ed.). San Francisco, CA: Pearson Education.
Schull, W. J. (1965). Estimation of genetic parameters in population studies. In Neel, J. V., Shaw, M. W., & Schull, W. J. (Eds.), Genetics and the epidemiology of chronic diseases (pp. 4560). Washington, DC: U. S. Department of Health, Education, and Welfare.
Schull, W. J., Yanase, T., & Nemoto, H. (1962). Kuroshima: The impact of religion on an island's genetic heritage. Human Biology, 34, 271298.
Smith, C. A. B. (1959). Some comments on the statistical methods used in linkage investigations. American Journal of Human Genetics, 11, 289304.
Stark, A. E. (1980). Inbreeding systems: Classification by a canonical form. Journal of Mathematical Biology, 10, 305.
Stark, A. E. (2006a). A clarification of the Hardy-Weinberg law. Genetics, 174, 16951697.
Stark, A. E. (2006b). Stages in the evolution of the Hardy-Weinberg law. Genetics and Molecular Biology, 29, 589594.
Stark, A. E., & Seneta, E. (2012). On S. N. Bernstein's derivation of Mendel's law and ‘rediscovery’ of the Hardy-Weinberg distribution. Genetics and Molecular Biology, 35, 388394.
Stark, A. E., & Seneta, E. (2013). A reality check on Hardy-Weinberg. Twin Research and Human Genetics, 16, 782789.
Stark, A. E., & Seneta, E. (2014). Hardy-Weinberg equilibrium as foundational. International Journal of Statistics in Medical Research, 3, 198202.
Stern, C. (1943). The Hardy-Weinberg law. Science, 97, 137138.
Weinberg, W. (1908). Über den Nachweis der Vererbung beim Menschen. Jahreshefte d. Vereins f. vaterländische Naturkunde in Württemberg, 64, 369382.
Weinberg, W. (1909). Johannsen, W. Elemente der exakten Erblichkeitslehre. Deutsche wesentlich erweiterte Ausgabe. IV. u. 516 S. JenaFischer [Review]. Archiv. für Rassen-und Gesellschafts-Biologie, 6, 553555.
Weir, B. S. (1996). Genetic data analysis II. Sunderland, MA: Sinauer Associates.



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