Bias and Mean Square Error from Ignoring Genetic Groups in Mixed Model Sire Evaluation

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Abstract
Criteria based on mean square error were developed to determine whether differences among genetic groups ought to be included in sire [bull] evaluation. Simulation was used for a population of 2000 1st lactations from daughters of 50 sires with 25 sires/group. Designs were simulated for semen exchanges between groups of 5, 10, 25 and 50% 1-directional and reciprocal. Analyses were with and without the inverse of a matrix of numerator relationships among sires. The matrix averaged 10.3 and 5.8% related sire pairs within and between groups, respectively. For unrelated sires, mean square error of sire evaluation ignoring genetic groups was less than including genetic groups when true genetic differences between groups were less than 176.7, 132.4, 103.1 or 93.9 kg for 1-way exchanges of 5, 10, 25 or 50% and 126.0, 102.8, 84.6 or 79.3 kg for reciprocal exchanges. For related sires corresponding genetic differences were 179.8, 137.1, 109.5 or 100.5 for 1-way exchanges and 131.1, 109.1, 92.1 or 87.2 for reciprocal exchanges. For 2 groups, ignoring genetic groups leads to smaller mean square error of sire evaluation if the true genetic difference is less than the SE of estimate of the difference between groups.