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Analyse des pedigrees et calcul des coefficients d'identité par les arbres géniques
Author(s) -
Vu Khang J. Tien,
de Rochambeau H.,
Chevalet C.,
Gillois M.
Publication year - 1979
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710210406
Subject(s) - gene , genetics , combinatorics , biology , zygote , locus (genetics) , identity by descent , gene family , mathematics , allele , genome , haplotype , embryogenesis
Two genes in a pedigree are identical by descent if they are two copies of a common ancestor gene. To obtain an unambiguous definition of the set of genes, at some autosomal locus, any gene is defined as an ordered pair of zygotes: the zygote who carries the gene, and the parent who transmitted it. The natural ordered structure on the set of zygotes yields an ordered structure upon the set of genes. Any event of the mendelian segregation splits down the set of genes into non‐overlaping classes of identical genes: when considered as an ordered sub‐set of genes, each class is shown to have the algebraic properties of a tree. Given a sub‐set of genes, a family of exclusive events ensuring identity between all genes of is identified as a family of genic trees with some property. This relationship between segregational events and genic trees is extended to the case where two sub‐sets and ′ of genes are considered together. As a consequence, a general method is obtained to compute either identity coefficients involving any number of genes splitted into one or two identity classes, or the fifteen coefficients defined among four genes, whichever the relationships between zygotes and genes might be. Using this approach to deal with the allelic structure in a set of genes carried by related zygotes is suggested.