Simple and rapid inversion of additive relationship matrices incorporating parental uncertainty.

Animals bred in pastoral systems are often part of multiple-sire groups, introducing uncertainty into pedigrees. Genetic evaluation of sires and dams in such instances is complicated by the uncertainty of parenthood. This article defines a simple and rapid algorithm to compute the inverse of a numerator relationship matrix under uncertain parenthood. The algorithm can accommodate inbreeding and uncertainty of parenthood on both paternal and maternal sides of the pedigree.