Research-Article| Volume 72, ISSUE 10, P2592-2605, October 1989

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

      This paper is only available as a PDF. To read, Please Download here.


      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.


        • Allaire F.R.
        • Henderson C.R.
        Specific combining abilities among dairy sires.
        J. Dairy Sci. 1965; 48: 1096
        • Allaire F.R.
        Mate selection by selection index theory.
        Theor. Appl. Genet. 1980; 57: 267
        • Cockerham C.C.
        An extension of the concept of partitioning hereditary covariance for analyses of covariance among selections when epistasis is present.
        Genetics. 1954; 39: 859
        • Henderson C.R.
        Estimation of changes in herd environment.
        J. Dairy Sci. 1949; 32 (Abstr.): 706
        • Henderson C.R.
        Best linear unbiased predictions of breeding values not in the model for records.
        J. Dairy Sci. 1977; 60: 783
        • Henderson C.R.
        ANOVA, MIVQUE, REML, and ML algorithms for estimation of variances and covariances. Statistics: An appraisal.
        in: David H.A. David H.T. Proc. 50th Anniv. Conf. Iowa State Univ. Press, Ames1984
        • Henderson C.R.
        Best linear unbiased prediction of nonadditive genetic merits in noninbred populations.
        J. Anim. Sci. 1984; 60: 111
        • Henderson C.R.
        MIVQUE and REML estimation of additive and nonadditive genetic variances.
        J. Anim. Sci. 1985; 61: 113
        • Henderson C.R.
        Equivalent linear models to reduce computations.
        J. Dairy Sci. 1985; 68: 2267
        • Quaas R.L.
        • Pollak E.J.
        Mixed model methodology for farm and ranch beef cattle testing programs.
        J. Anim. Sci. 1980; 51: 1277
        • Rao C.R.
        Minimum variance quadratic unbiased estimation of variance components.
        J. Multivar. Anal. 1971; 2: 445
        • Wright S.
        Coefficients of inbreeding and relationship.
        Am. Nat. 1922; 56: 330