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Assortative mating for a quantitative character

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Abstract

Phenotypic assortative mating is investigated for a character determined by additive loci without dominance and a stochastically independent environment. Conditional-expectation arguments are used to calculate the equilibrium values of the phenotypic variance and the correlation between sundry relatives. For the latter, it suffices to suppose that the regressions of an individual's genotype on his phenotype and of his phenotype on that of his mate are linear. For the former, linearity of the regression of the allelic effects on the phenotype is also posited. The biological implications of these assumptions are discussed.

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References

  • Abramowitz, M.: Elementary analytical methods. In: Abramowitz, M., Stegun, I. A. (eds.): Handbook of mathematical functions, pp. 9–63. Washington: National Bureau of Standards 1964

    Google Scholar 

  • Bulmer, M. G.: The mathematical theory of quantitative genetics. Oxford: Oxford University Press 1980

    Google Scholar 

  • Cavalli-Sforza, L. L., Bodmer, W. F.: The genetics of human populations. San Francisco: Freeman 1971

    Google Scholar 

  • Cloninger, C. R., Rice, J., Reich, T.: Multifactorical inheritance with cultural transmission and assortative mating. II. A general model of combined polygenic and cultural inheritance. Am. J. Hum. Genet. 31, 176–198 (1979)

    Google Scholar 

  • Crow, J. F., Felsenstein, J.: The effect of assortative mating on the genetic composition of a population. Eugen. Quart. 15, 85–97 (1968)

    Google Scholar 

  • Denniston, C.: An extension of the probability approach to genetic relationship: One locus. Theoret. Population Biology 6, 58–75 (1974)

    Google Scholar 

  • Falconer, D. S.: Introduction to quantitative genetics. New York: Ronald Press 1960

    Google Scholar 

  • Fisher, R. A.: The correlation between relatives on the supposition of Mendelian inheritance. Trans. Roy. Soc. Edinb. 52, 399–433 (1918)

    Google Scholar 

  • Gimelfarb, A.: Evolving populations: Mathematical analysis of some dynamical properties. Dissertation, University of Wisconsin, Madison, 1979

    Google Scholar 

  • Gimelfarb, A.: A general linear model for the genotypic covariance between relatives under assortative mating. J. Math. Biol. 13, 209–226 (1981a)

    Google Scholar 

  • Gimelfarb, A.: Analysis of “nontraditional” relationships under assortative mating. J. Math. Biol. 13, 227–240 (1981b)

    Google Scholar 

  • Jensen, A. R.: Genetic and behavioral effects of nonrandom mating. In: Nobel, C. E., Osborne, R. T., Weyl, N. (eds.), pp. 51–105. Human variation: Biogenetics of age, race, and sex. New York: Academic Press 1978

    Google Scholar 

  • Johnson, N. L., Kotz, S.: Distributions in statistics: Discrete distributions. Boston: Houghton Mifflin 1969

    Google Scholar 

  • Johnson, N. L., Kotz, S.: Distributions in statistics: Continous multivariate distributions. New York: Wiley 1972

    Google Scholar 

  • Kempthorne, O.: An introduction to genetic statistics. New York: Wiley 1957

    Google Scholar 

  • Kendall, M. G., Stuart, A.: The advanced theory of statistics, 3rd edition, Vol. 2. London: Griffin 1973

    Google Scholar 

  • Lande, R.: The influence of the mating system on the maintenance of genetic variability in polygenic characters. Genetics 86, 485–498 (1977)

    Google Scholar 

  • Lande, R.: The minimum number of genes contributing to quantitative variation between and within populations. Genetics 99, 541–553 (1981)

    Google Scholar 

  • Lukacs, E.: Characteristic functions, 2nd edition. London: Griffin 1970

    Google Scholar 

  • Malécot, G.: Théorie mathématique de l'hérédité mendelienne généralisée. Paris: Guilhot 1939; Reprinted in Malécot, G.: Probabilités et hérédité. Paris: Presses Universitaires de France 1966

    Google Scholar 

  • Moran, P. A. P., Smith, C. A. B.: Commentary on R. A. Fisher's paper on “The correlation between relatives on the supposition of Mendelian inheritance.” Eugen. Lab. Mem. 46, 1966

  • Nagylaki, T.: Selection in one- and two-locus systems. Berlin: Springer 1977

    Google Scholar 

  • Nagylaki, T.: The correlation between relatives with assortative mating. Ann. Hum. Genet. 42, 131–137 (1978)

    Google Scholar 

  • Risch, H.: The correlation between relatives under assortative mating for an X-linked and autosomal trait. Ann. Hum. Genet. 43, 151–165 (1979)

    Google Scholar 

  • Spuhler, J. N.: Assortative mating with respect to physical characteristics. Eugen. Quart. 15, 128–140 (1968)

    Google Scholar 

  • Vandenberg, S. G.: Assortative mating, or who marries whom? Behav. Genet. 2, 127–157 (1972)

    Google Scholar 

  • Wilson, S. R.: The correlation between relatives under the multifactorial model with assortative mating. Ann. Hum. Genet. 37, 189–204, 205–215 (1973)

    Google Scholar 

  • Wright, S.: Systems of mating. III. Assortative mating based on somatic resemblance. Genetics 6, 144–161 (1921)

    Google Scholar 

  • Wright, S.: Evolution and the genetics of populations. Vol. II. Chicago: The University of Chicago Press 1969

    Google Scholar 

  • Wright, S.: Evolution and the genetics of populations. Vol. IV. Chicago: The University of Chicago Press 1978

    Google Scholar 

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Supported by National Science Foundation Grant DEB81-03530

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Nagylaki, T. Assortative mating for a quantitative character. J. Math. Biology 16, 57–74 (1982). https://doi.org/10.1007/BF00275161

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  • DOI: https://doi.org/10.1007/BF00275161

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