Sire Evaluations with Parities as Correlated Traits and Comparison with Single-Trait Evaluations1

All lactation records are included in sire evaluations for milk components by mixed model methodology by the United States Department of Agriculture. To increase accuracy of these evaluations, procedures were investigated for processing information from different parities as correlated traits rather than as a repeated single trait. The current model for mature equivalent records, which includes fixed group, random sire, fixed herd-year-season, and random cow effects, was modified to include a separate sire effect for each of first three parities. Residual variances for different parities were assumed uncorrelated and of equal variance and, therefore, could be factored out of mixed model equations. Cows and herd-year-seasons were absorbed prior to iteration. Sire equations then were augmented by addition of direct product of the inverse of the relationship matrix and the inverse of the matrix of genetic variance among parities. Sire solutions were obtained by block iteration, with blocks consisting of group equations and three equations for each sire. Evaluations were computed for 591 Ayrshire sires with 13,551 daughter records for milk and fat yields and 447 Guernsey sires with 10,817 daughter records. Computation time for multitrait evaluation was four times that for single trait multi parity evaluation, and convergence was .57 as fast. Correlations between multi parity evaluations and those based only on first lactation records ranged from .85 to .90. Correlations between single trait multi parity and multitrait evaluations ranged from .97 to .99 for sires with more than 10 daughters. Therefore, although inclusion of later lactation records increases accuracy of evaluations, little additional gain is achieved by multitrait evaluation.