Summary
According to Hardy-Weinberg, for a single autosomal locus, a population achieves equilibrium in one generation of random mating if allelic frequency is the same in the sexes, or in two generations if the frequency is not. For a single X-chromosomal locus, however, the approach to equilibrium oscillates and is gradual. Covariances between relatives for autosomal and for X-chromosomal loci are in the literature for a random mating population in equilibrium. Although assumption of equilibrium is defensible for an autosomal locus, it is less defensible for an X-chromosomal locus. Covariances between collateral and between lineal relatives are derived for X-chromosomal loci in a random mating population not in equilibrium. Collateral relatives such as sibs are of the same generation, and lineal relatives such as parent-offspring are of different generations. Coefficient of co-ancestry between relatives, based on identity by descent, was used in this development. Results are applicable to crossbreeding in livestock and poultry, and also to haplo-diploid organisms, such as the honeybee, in which the entire genome is equivalent to being X-chromosomal.
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References
Bohidar NR (1964) Derivation and estimation of variance and covariance components associated with covariance between relatives under sex-linked transmission. Biometrics 20:505–521
Crow JF, Kimura M (1970) An introduction to population genetics theory. Harper and Row, New York/NY, pp 132–136
Falconer DS (1981) Introduction to quantitative genetics, 2nd ed. Longman, New York/NY
Grossman M, Eisen EJ (1989) Inbreeding, coancestry and covariance between relatives for X-chromosomal loci. J Hered 80:137–142
Hogben L (1932) Filial and fraternal correlations in sex-linked inheritance. Proc R Soc Edinburgh 52:331–336
James JW (1973) Covariances between relatives due to sex-linked genes. Biometrics 29:584–588
Jennings HS (1916) The numerical results of diverse systems of breeding. Genetics 1:53–89
Kempthorne O (1969) An introduction to genetic statistics. Iowa State University Press, Ames/IA
Kempthorne O, Folks L (1971) Probability, statistics, and data analysis. Iowa State University Press, Ames/IA
Li CC (1976) First course in population genetics. Boxwood Press, Pacific Grove/CA
Malécot G (1969) The mathematics of heredity. Freeman, San Francisco/CA
Marx JL (1988) A parent's sex may affect gene expression. Science 239:352–353
Melchinger AE (1988) Means, variances, and covariances between relatives in hybrid populations with disequilibrium in the parent populations. In: Weir BS, Eisen EJ, Goodman MM, Namkoong G (eds) Proc 2nd Int Conf Quant Genet. Sinauer, Sunderland/MA, pp 400–415
Weir BS, Cockerham CC (1977) Two locus theory in quantitative genetics. In: Pollak E, Kempthorne O, Bailey TB, Jr (eds) Proc Int Conf Quant Genet. Iowa State University Press, Ames/IA, pp 247–269
Wright S (1969) The theory of gene frequencies. Evolution and the Genetics of Populations, vol. 2. University of Chicago Press, Chicago/IL
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Communicated by E. J. Eisen
Supported in part by the Illinois Agricultural Experiment Station, Hatch Project 35-0367
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Grossman, M., Fernando, R.L. Covariance between relatives for X-chromosomal loci in a population in disequilibrium. Theoret. Appl. Genetics 77, 311–319 (1989). https://doi.org/10.1007/BF00305821
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DOI: https://doi.org/10.1007/BF00305821