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Adjustment for Heterogeneous Covariance due to Herd Milk Yield by Transformation of Test-Day Random Regressions

¹ National Fund for Scientific Research, B-1000 Brussels, Belgium
² Animal Science Unit, Gembloux Agricultural University, B-5030 Gembloux, Belgium
³ Animal Improvement Programs Laboratory, Agricultural Research Service, USDA, Beltsville, MD 20705

Corresponding author: N. Gengler; e-mail: gengler.n{at}fsagx.ac.be .

A method of accounting for differences in covariance components of test-day milk records was developed based on transformation of regressions for random effects. Preliminary analysis indicated that genetic and nongenetic covariance structures differed by herd milk yield. Differences were found for phenotypic covariances and also for genetic, permanent environmental, and herd-time covariances. Heritabilities for test-day milk yield tended to be lower at the end and especially at the start of lactation; they also were higher (maximum of ~25%) for high-yield herds and lower (maximum of 15%) for low-yield herds. Permanent environmental variances were on average 10% lower in high-yield herds. Relative herd-time variances were ~10% at start of lactation and then began to decrease regardless of herd yield; high-yield herds increased in midlactation followed by another decrease, and medium-yield herds increased at the end of lactation. Regressors for random regression effects were transformed to adjust for heterogeneity of test-day yield covariances. Some animal reranking occurred because of this transformation of genetic and permanent environmental effects. When genetic correlations between environments were allowed to differ from 1, some additional animal re-ranking occurred. Correlations of variances of genetic and permanent-environmental regression solutions within herd, test-day, and milking frequency class with class mean milk yields were reduced with adjustment for heterogeneous covariance. The method suggests a number of innovative solutions to issues related to heterogeneous covariance structures, such as adjusted estimates in multibreed evaluation.

Key Words: heterogeneous covariance · covariance structure · test-day yield · random regression

Abbreviations: EM = expectation maximization · HC = heterogeneous covariance · RRM = random regression model.