Heterogeneity of (Co)Variance Components for Jersey Type Traits

Heterogeneity of (co)variances for US Jersey linear and final scores was investigated with data from February 2000 USDA genetic evaluations. (Co)variances were estimated from datasets defined by parity, contemporary group size, and mean final score. First-appraisal scores during first or second parity from records that included all traits were studied. Contemporary groups within each parity were classified by size, based on number of cows in a given parity for that herd appraisal date: 5 to 15, 30 to 55, and 100. Groups were further classified as high (above parity-size class mean) or low (below parity-size class mean) for final score. The parity, group size, and final score classifications resulted in 12 datasets, which contained appraisal information from 8111 to 23,692 cows. (Co)variance components were estimated using expectationmaximization REML and canonical transformation. Across all traits and independent of herd size, phenotypic variances tended to be higher for low-scoring contemporary groups and during second parity. Similar or larger heterogeneities existed for genetic variances, but those heterogeneities were not as consistent across trait and contemporary group size class. Associated mean relative differences were defined as the mean of the ratios of the Frobenius norms of the differences between a given matrix and an overall mean matrix to the Frobenius norm of the mean matrix. For variance matrices, covariances were ignored. Mean differences for phenotypic variances were 18% during first and 20% during second parity, and for genetic variances were 26 and 31% for first and second parity, respectively. The different patterns for genetic and phenotypic variances led to significant differences in estimated heritabilities. Mean relative differences for covariances were found to be similarly heterogeneous: 20% for first parity and 23% for second parity, for phenotypic covariance, and 32 and 36% for first and second parities, respectively, for genetic covariance. This heterogeneity resulted more from variance heterogeneity than from differences among associated correlation matrices (phenotypic: 11% first and 12% second parity; genetic: 20% first and 26% second parity). (