Derivation of Henderson's Method of Incorporating Artificial Insemination Sire Evaluations into Intraherd Prediction of Breeding Values

A derivation is given for the method proposed by Henderson to incorporate evaluations of sires based on daughter records in other herds into the intraherd prediction of breeding values. The derivation consists of pretending the daughters in other herds have records which have been adjusted for the herd-year-season effects of their origin. These equations then are absorbed into the equation for the sire which is tied to both sets of daughters by elements of the inverse of the matrix of relationships.