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The study of multiallelic genetic systems by matrix methods

Published online by Cambridge University Press:  14 April 2009

C. Cannings
C. Cannings
Affiliation:
Department of Statistics, University of Aberdeen
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A matrix notation is developed to facilitate study of natural selection in large populations. The processes of mating (taking into account differences between genotypes in fertility in both sexes), segregation, and differential viabilities are each expressed in matrix notation. Assortative mating and non-random segregation can also be described by the method. The separate processes can then be combined to give simple equations relating the genic and genotypic frequencies in one generation to those in the previous generation. This will facilitate computer treatment of natural selection processes.

The method can also be used to study equilibria and the conditions of their stability by examining the latents roots of the matrix. Several special cases of selection at an autosomal locus are examined. The method can be extended to sex-linked loci and two special cases are discussed.

Information

Type
Research Article
Information
Genetics Research , Volume 14 , Issue 3 , December 1969 , pp. 167 - 183
Copyright
Copyright © Cambridge University Press 1969

References

REFERENCES

Bennett, J. H. (1963). Random mating and sex-linkage. J. theoret. Biol. 4, 28–36.CrossRefGoogle ScholarPubMed
Birkhoff, G. & MacLane, S. (1959). A Survey of Modern Algebra. Macmillan.Google Scholar
Bodmer, W. F. (1965). Differential fertilities in population genetics models. Genetics 51, 411–424.CrossRefGoogle ScholarPubMed
Cannings, C. (1967). Equilibrium, convergence and stability at a sex-linked locus under natural selection. Genetics 56, 613–618.CrossRefGoogle Scholar
Cannings, C. (1968 a). Differential fertilities between homogamous and heterogamous matings. Genet. Res., Camb. 11, 289–301.CrossRefGoogle Scholar
Cannings, C. (1968 b). Equilibrium under selection at a multiallelic sex-linked locus. Biometrics 24, 187–189.Google Scholar
Cannings, C. (1969). Unisexual selection at an autosomal locus. Genetics (in the Press).CrossRefGoogle ScholarPubMed
Cormack, R. M. (1964). A boundary problem arising in population genetics. Biometrics 20, 785–793.CrossRefGoogle Scholar
Kingman, J. F. C. (1961). A mathematical problem in population genetics. Proc. Camb. Phil. Soc. 57, 574–582.CrossRefGoogle Scholar
Li, C. C. (1955). Population Genetics. University of Chicago Press.Google Scholar
Li, C. C. (1967). The maximization of average fitness by selection for a sex-linked locus. Proc. natn. Acad. Sci. U.S.A. 57, 1260–1261.CrossRefGoogle ScholarPubMed
Littlewood, L. E. (1957). A Mathematician's Miscellany, 2nd ed.Methuen.Google Scholar
Mandel, S. P. H. (1959 a). The stability of a multiple allelic system. Heredity 13, 289–302.CrossRefGoogle Scholar
Mandel, S. P. H. (1959 b). Ph.D. thesis, Cambridge University Library.Google Scholar
Mirsky, L. (1955). An Introduction to Linear Algebra. Oxford University Press.Google Scholar
Mulholland, H. P. & Smith, C. A. B. (1959). An inequality arising in genetical theory. Am. math. Monthly 66, 673–683.CrossRefGoogle Scholar
Owen, A. R. G. (1953). A genetical system admitting of two distinct stable equilibria under natural selection. Heredity 7, 97–102.CrossRefGoogle Scholar
Sprott, D. A. (1957). The stability of a sex-linked allelic locus. Ann. Hum. Genet. 22, 1–6.CrossRefGoogle Scholar
Tallis, G. M. (1966). Equilibrium under selection for K-alleles. Biometrics 22, 121–127.CrossRefGoogle Scholar