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Use of an Average Numerator Relationship Matrix for Multiple-Sire Joining¹

University of Illinois², Urbana 61801 and University of New England^,3, New South Wales 2351, Australia

Abstract

Some breeding programs practice multiple joining of sires to a group of females. Consequently, the sire of a progeny is not known. This creates a problem in sire evaluation and in employment of the animal model or its equivalent, the reduced animal model. This paper suggests the use of an average numerator relationship matrix derived under the assumption of particular probabilities for the sires in the group. An easy method for computing the inverse of this average matrix without writing the original matrix is derived. Thus, this inverse can be used in mixed-model equations for evaluations in a sire model, an animal model or a reduced animal model.

¹ Financial support for research in Australia during January–March, 1987, was provided by the Reserve Bank of Australia. This support was much appreciated.

² Dept. of Anim. Sci.

³ Anim. Genetics and Breeding Unit.

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