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Research-Article| Volume 72, ISSUE 3, P664-670, March 1989

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Inverse Numerator Relationship Matrix Approximation1

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      Abstract

      Genetic evaluation by BLUP requires knowledge of the inverse numerator relationship matrix among breeding values. When pedigree information is complete, the true relationship matrix can be determined and an exact inverse found. When pedigree information is incomplete, an exact inverse of an approximate relationship matrix is obtainable. The usual algorithm for the inverse numerator relationship matrix may be derived assuming each unidentified parent to be a different base population animal.

      References

        • Everett R.W.
        • Keown J.F.
        Mixed model sire evaluation with dairy cattle—experience and genetic gain.
        J. Anim. Sci. 1985; 59: 529
        • Famula T.R.
        • Pollak E.J.
        • Van Vleck L.D.
        Genetic groups in dairy sire evaluation under a selection model.
        J. Dairy Sci. 1983; 66: 927
        • Henderson C.R.
        Use of relationships among sires to increase accuracy of sire evaluation.
        J. Dairy Sci. 1975; 58: 1731
        • Henderson C.R.
        Best linear unbiased estimation and prediction under a selection model.
        Biometrics. 1975; 31: 423
        • Henderson C.R.
        A simple method for computing the inverse of a numerator relationship matrix used in prediction of breeding values.
        Biometrics. 1976; 32: 69
        • Kennedy B.W.
        • Schaeffer L.R.
        • Sorenson D.A.
        Genetic properties of animal models.
        J. Dairy Sci. 1988; 71: 17
        • Pollak E.J.
        • Quaas R.L.
        Definition of group effects in sire evaluation models.
        J. Dairy Sci. 1983; 66: 1503
      1. Quaas, R. L. 1984. Linear prediction in Use of mixed models for prediction and for estimation of (co)variance components. BLUP school handbook. R. L. Quaas, R. D. Anderson, and A. R. Gilmour, ed. Anim. Genet. Breeding Unit, Univ. New England, Armidale, NSW, 2351, Australia.

        • Quaas R.L.
        Additive genetic model with groups and relationships.
        J. Dairy Sci. 1988; 71: 1338
        • Quaas R.L.
        • Pollak E.J.
        Modified equations for sire models with groups.
        J. Dairy Sci. 1981; 64: 1868
        • Robinson G.K.
        Group effects and computing strategies for models for estimating breeding values.
        J. Dairy Sci. 1986; 69: 3106
        • Thompson R.
        Sire evaluation.
        Biometrics. 1979; 35: 339