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United States Department of Agriculture

Agricultural Research Service

Title: Calculation of Lactation Yields and Lactation Weights from Test Day Yields and Correlations Using Best Prediction

item Vanraden, Paul

Submitted to: Journal of Dairy Science
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: May 28, 1997
Publication Date: N/A

Interpretive Summary: Milk recording in the United States is less uniform than in the past with several familiar plans and many more innovative plans. Monthly testing and sampling until now provided test day data that fit into fairly simple formulas that gave accurate and consistent lactation records. New test plans with varying test intervals, incomplete data on test day, reduced supervision, and electronic recording can provide lactation records with lower or higher accuracy. Widely varying plans can provide useful data for genetic evaluations, but data should be weighted according to accuracy and combined using improved formulas that adapt to data design. The best prediction statistical method was used to compute and to plot lactation yields and provided a flexible theory to calculate 305-day yields and accuracies of those yields as measured under many different test plans. Computations were more difficult than for the test interval method but are now affordable. Multiple-day averages, partial-day estimates, missing traits, lack of supervision, and mixtures of test plans were accounted for in the equations. Lactation weights that reflect the accuracy of any particular record were derived. The scale for lactation weights may need to be changed so that the maximum weight of 1 represents 305 supervised test days and 305 samples instead of just 10 as in the past. The heritability should be raised at the same time to offset the new, lower lactation weights and to reflect the smaller measurement error in the standard lactation. Because test day data and genetic evaluations may become available soon, predictions, plots, and accuracy calculations from the best prediction method will help dairy breeders better understand and use information from the new evaluation method.

Technical Abstract: Lactation records are calculated from milk, fat, and protein data obtained from one or more milkings on several days during the cow's lactation. The test interval method, which estimated missing daily milk yields by simple interpolation, was used for many years for standard monthly data but may not be as useful for the wider variety of test plans now proposed. More accurate 305-day yields can be computed using best prediction, which has optimum properties if means are known and distribution is multivariate normal. The 305-day yield is estimated as the mean 305-day yield plus covariance of test day and 305-day yields multiplied by the inverse of the test day (co)variance matrix multiplied by the test day deviation vector. The correlation of true and estimated 305-day yields, which is needed to calculate lactation weights, can be obtained by similar algebra. Computing times were affordable but not trivial; they ranged from 0.001 to 1 second per lactation. Equations were modified to account for differing accuracies of partial-day data, multiple-day means, and unsupervised data.

Last Modified: 4/19/2014
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