Inverse of Single Trait Additive Genetic Covariance Matrix with Unequal Variances Across Additive Genetic Groups

Recursive procedures are presented to compute the additive genetic covariance matrix and its inverse for a single trait when additive genetic variances differ across genetic groups. They are extensions of well-known recursive methods that assume equal 'additive variances for all genetic groups in a population. These procedures facilitate animal evaluation with mixed model analysis when animals being evaluated belong to different subpopulations within a breed or to different breeds and crossbred groups, especially when animals belonging to different genetic groups are related. Models should inciude additive and nonadditive fixed (group) and random effects depending on the trait being evaluated.