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Gene Identities and Multiple Relationships

E. A. Thompson
Biometrics
Vol. 30, No. 4 (Dec., 1974), pp. 667-680
DOI: 10.2307/2529231
Stable URL: http://www.jstor.org/stable/2529231
Page Count: 14
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Gene Identities and Multiple Relationships
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Abstract

Relationships between individuals may be specified by the genes that they have in common, where two genes are considered to be the same only if they are identical by descent from some common ancestor, or in the terminology of Cotterman [1940] "derivative". The concepts of gene identity and genetically distinct states and the derivation of joint and conditional phenotype distributions have been extensively studied for the case of two individuals, by, amongst many others, Cotterman [1940], Malecot [1948], Li and Sacks [1954], and Jacquard [1972]. In this paper it is shown how these ideas may be extended to relationships between any number of individuals. Problems regarding the specification of genetically distinct gene identity states are resolved by considering the group structure of the set of all identity states. A genealogical relationship between any number of individuals is regarded as a probability distribution over the space of genetically distinct states, and hence expressions for the joint genotype distributions of several relatives may be found.

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