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Ibd Configuration Transition Matrices And Linkage Score Tests For Unilineal Relative Pairs, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

Properties of transition matrices between IBD configurations are derived for four general classes of unilineal relative pairs obtained from the grand-parent/ grand-child, half-sib, avuncular, and cousin relationships. In this setting, IBD configurations are defined as orbits of groups acting on a set of inheritance vectors. Properties of the transition matrix between IBD configurations at two linked loci are derived by relating its infinitesimal generator to the adjacency matrix of a quotient graph. The second largest eigenvalue of the infinitesimal generator and its multiplicity are key in determining the form of the transition matrix and of likelihood-based linkage tests such as …