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United States Department of Agriculture

Agricultural Research Service

Title: Estimation of (Co)variance Function Coefficients for Test Day Yields with Aexpectation-Maximazation Restriced Maximum Likelihood Algorithm

Authors
item Gengler, N - GEMBLOUX AGRIC UNIV
item Tanji, A - GEMBLOUX AGRIC UNIV
item Wiggans, George
item Misztal, I - UNIV OF GEORGIA

Submitted to: Journal of Dairy Science
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: June 3, 1999
Publication Date: N/A

Interpretive Summary: For several years, the direct use of test-day yields instead of computed or estimated lactation yields has been considered the next step in the evolution of genetic evaluation systems for dairy animals. Two types of test day models have been suggested: multitrait and random regression. However, a challenge for both types of methods is to obtain the variance components required for developing a test-day evaluation system. A (co)variance function can be defined as a continuous function that represents the variance and (co)variance of traits measured at different points on a trajectory. (Co)variance functions are particularly useful for phenomena that are time dependent, such as lactation. This study used the statistical techniques of expectation-maximization restricted maximum likelihood and random regression on polynomials to estimate (co)variance function coefficients for milk, fat, and protein yields over the entire lactation. The results showed that further research on general comparison of models is needed as well as on alternative ways of modeling the average and the (co)variances between test days before an accurate test day model can be developed and implemented.

Technical Abstract: Coefficients for (co)variance functions were obtained via random regression models using the expectation-maximization restricted maximum likelihood algorithm. Data included milk, fat, and protein yields from 176,495 test days of 22,943 first lactation cows that calved in Pennsylvania and Wisconsin from 1990 through 1996. Three approximately equal-sized data sets were created: one for Pennsylvania and two for Wisconsin. Random regressions were on third order Legendre's polynomials. Genetic and permanent environmental (co)variances each were described by three coefficients. The model contained a fixed effect for age, season, and lactation stage rather than a fixed regression. Fixed contemporary groups were based on herd, test day, and milking frequency. The coefficient matrices were dense and included around 70,000 equations. Estimated (co)variance function coefficients, as well as the heritabilities and correlations computed from them, were quite variable across data sets. Heritabilities were at a minimum(0.14 for milk and fat and 0.13 for protein) around peak yield, increased to a maximum (0.24 for milk and protein and 0.21 for fat) around 245 d in milk, and declined slightly afterwards. Genetic correlations between early and late lactation were low (values of <0.10), especially for protein. Phenotypic correlations among test day yields were between 0.21 and 0.99.

Last Modified: 7/30/2014
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