Theoretical Weights for Regression of a Son's Genetic Evaluation on His Sire's and His Dam's Genetic Evaluations

Theoretical weights for prediction of a son's genetic evaluation from genetic evaluations of his sire and dam are derived. Weights for sire and dam are equal and depend on number of daughters of the son when the bull evaluation is from his daughters alone and cow evaluation is from her records alone. Mixed model procedures which incorporate records of other relatives change theoretical weights. When records of daughters of both the son and his sire are used in evaluations of both, theoretical weights for the sire to predict the son's evaluation are about .50 for many combinations of daughter numbers of the bulls. Including the evaluation of the sire of the cow in her evaluation changes the theoretical weight to predict the son's evaluation from the dam's evaluation only slightly from the situation when only the dam's records are used. In addition, the theoretical weight for the maternal g/andsire is nearly zero. DISCUSSION The purpose of this note is to show theoretical weights for predicting a son's evaluation from those of his parents. Theoretical weights for the sire's genetic evaluation and dam's genetic evaluation for predicting a progeny are both .5, but when they are used to predict the progeny's evaluation, unless the number of records in the progeny's evaluation is extremely large, the weights are usually less than .5 but may be equal. For example, theoretical weights are equal when records in evaluating the sire are only from his daughters and in evaluating the dam are only from her records. The Northeast Artificial Insemination Sire Comparison (NEAISC), however, uses records of daughters of a sire and daughters of his son to evaluate both the sire and son. The use of the maternal grandsire model (7) complicates the theoretical regression but will not be considered here because sire evaluation in pedigree analyses previously have not considered the maternal grandsire model (1, 2, 4, 5, 6, 8).