Calculation of identity-by-descent probabilities of short chromosome segments

For some purposes, identity-by-descent (IBD) probabilities for entire chromosome segments are required. Making use of pedigree information, length of the segment and the assumption of no crossing-over, a generalization of a previously published graph theory oriented algorithm accounting for nonzero IBD of common ancestors is given, which can be viewed as method of path coefficients for entire chromosome segments. Furthermore, rules for setting up a gametic version of a segmental IBD matrix are presented. Results from the generalized graph theory oriented method, the gametic segmental IBD matrix and the segmental IBD matrix for individuals are identical.