**N. Gengler,* ^{,}† T. Dusseldorf,† G. R.
Wiggans,‡ J. R. Wright,‡ and T. Druet*^{,}†**

*National Fund for Scientific Research, B-1000 Brussels, Belgium †Animal Science Unit, Gembloux Agricultural University, B-5030 Gembloux, Belgium ‡Animal Improvement Programs Laboratory, Agricultural Research Service, USDA, Beltsville, MD 20705-2350

**ABSTRACT** 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 data sets 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 is more than or equal to 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
data sets, which contained appraisal information from 8111 to 23,692 cows.
(Co)variance components were estimated using expectation-maximization 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, and 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), especially for phenotypic
covariances.

(**Key words: **genetic evaluation, heterogeneous variance,
variance estimation)

**2001 J. Dairy Sci. 84:1772**

© 2001, by the American Dairy Science Association. All rights reserved.