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Mixed Model Evaluation of Related Sires for Milk Yield Eliminating Age and Interaction of Sire with Herd-Year-Season¹

Department of Dairy Science, University of Illinois, Urbana 61801

ABSTRACT

A method of best linear unbiased evaluation of related sires for milk yield considering age and interaction of sire with herd-year-season was developed. It was based on simplification of mixed model equations for multiple traits and multiple random classifications when all traits are recorded for each individual and design matrices are the same for all traits. The resulting modified least squares equations were used for milk yield and age at calving under a model with sire, herd-year-season, and sire by herd-year-season. For unrelated sires, this permits consideration of an arbitrarily large number of classes of herd-year-seasons and sires by herd-year-season. Absorption involves inversion of matrices of order t for t traits and unrelated sires. For groups of c related sires inverses of order tc are needed. Resulting absorbed equations of order ts for s sires must be solved. Sire, sire by herd, and error components of variance and covariance for first lactation milk yield and age at calving were used to examine implications for sire evaluation. Conditions justifying evaluation with only actual milk yield or only age-corrected milk yield were derived.

¹ Supported in Part by the Illinois Agricultural Experiment Station.