#### Abstract

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 score tests.

#### Disciplines

Genetics | Statistical Methodology | Statistical Theory

#### Suggested Citation

Dudoit, Sandrine, "IBD Configuration Transition Matrices and Linkage Score Tests for Unilineal Relative Pairs" (February 2003). *U.C. Berkeley Division of Biostatistics Working Paper Series.* Working Paper 128.

http://biostats.bepress.com/ucbbiostat/paper128