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Multiple gene identities

Published online by Cambridge University Press:  01 July 2016

E. A. Thompson
E. A. Thompson*
Affiliation:
University of Cambridge
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Extract

The relationships between individuals may be specified by the genes which they have in common, where two genes are considered to be the same only if they are identical by descent from some common ancestor. Relationships between two individuals have been extensively studied by, amongst many others, Cotterman (1940), Malécot (1948) and Li and Sacks (1954). Less progress has been made with the more general problem of relationships between an arbitrary number of individuals. Elandt-Johnson (1971) has considered the special case of joint genotype distributions in a sibship, and Hilden (1970) has constructed an algebraic method of combining information on several individuals to give the conditional distribution of a single unborn relative, but neither of these approaches provides a general solution to the problem.

Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 1 , March 1975 , pp. 26 - 27
Copyright
Copyright © Applied Probability Trust 1975 

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References

Cotterman, C. W. (1940) A calculus for statistico genetics. . Ohio State University, Columbus, Ohio.Google Scholar
Elandt-Johnson, R. C. (1971) Joint genotype distributions of s children and a parent, and of s siblings. Multiple alleles. Amer. J. Hum. Genet. 23, 442–461.Google Scholar
Hilden, J. (1970) GENEX — an algebraic approach to pedigree probability calculus. Clinical Genetics 1, 319–348.Google Scholar
Jacquard, A. (1972) Genetic information given by a relative. Biometrics 28, 1101–1114.CrossRefGoogle ScholarPubMed
Li, C. C. and Sacks, L. (1954) The derivation of joint distribution and correlation between relatives by the use of stochastic matrices. Biometrics 10, 347–360.Google Scholar
Malécot, G. (1948) Les mathématiques de l'hérédité. Masson et Cie, Paris.Google Scholar
Thomson, E. A. (1974) Gene identities and multiple relationships. Biometrics. To appear.CrossRefGoogle Scholar