Use of Relationships Among Sires to Increase Accuracy of Sire Evaluation

Sire evaluation methods that invoke best linear unbiased prediction have not utilized information available from known relationships among sires. Principles for doing this have been known, but computations were too costly, involving the inverse of a large numerator relationship matrix. In a method for writing this inverse rapidly without computing the relationship matrix, all relationships can be used with little additional labor. Also records of female ancestors can be incorporated easily. Further, the number of equations for groups to account for genetic trend and for differences among subpopulations is reduced.