Prediction of Merits of Potential Matings from Sire-Maternal Grandsire Models with Nonadditive Genetic Effects

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Abstract
Models for BLUP of matings under a nonadditive genetic model were derived for two equivalent models. These models were, first, an animal model with missing data on dams and, second, a sire-maternal grandsire model. The second model results in a marked decrease in the order of the mixed model equations and produces predictions identical to those of the animal model. The sire-maternal grandsire model first predicts merits of mating groups. Then a back solution can be used to predict individuals within mating groups. Also, minimum variance quadratic unbiased estimation for the sire-maternal grandsire model was found to produce the same estimates as those obtained employing the animal model for minimum variance quadratic unbiased estimation.