Variances of Prediction Errors for Differences of Estimated Genetic Values of Cows in the Same and in Different Herds

A modification of the evaluation method for cows in the northeast United States allowed simultaneous evaluation of cows in pairs of herds and computation of variances of prediction errors of differences of genetic potential between pairs of cows within and across herds. These variances were examined for 20 pairs of herds in Holstein, Jersey, and Brown Swiss breeds. Current evaluations of cows are nearly as accurate for comparing cows from different herds as they are for comparing cows from the same herd. I N T R O D U C T I O N Cows in Dairy Herd Improvement Association (DHIA) herds in the northeast United States currently are evaluated by the Northeast A -1 estimated transmitting ability (NEA -1 ETA) procedure (2, 5). This method uses Henderson's mixed model equations (3) to obtain best linear unbiased predictions (BLUP) of the additive genetic values of all c o w s in a particular herd. The predicted genetic values then are halved to arrive at predictions of cows' transmitting abilities. The procedure uses all records on all cows in a herd and incorporates information from proofs of any artificial insemination (AI) sires having progeny in that herd, including the sires' predicted transmitting abilities and the number of daughter records used to evaluate the bulls (5,6). The NEA -1 ETA evaluations aid the dairyproducer in choosing which cows to rebreed so that they may have another lactation and also which cows to breed to produce replacement females. The evaluations also might be used by an AI organization for selecting dams of bulls. The AI stud wants to mate its best bulls to the best cows in the population, keeping the male offspring for progeny testing. Because an AI buli has the possibility for wide use, the best possible parents should be chosen for such a sire. The primary objective of this study was to examine the accuracy of the NEA -1 ETA evaluations when they are used to compare genetic values of cows from different herds as against comparing genetic values of cows from within the same herd. If there is not a substantial loss of accuracy when cows from different herds are compared, then an AI stud may use these evaluations to select dams of bulls with more confidence. For Henderson's mixed model equations and BLUP of random effects, a measure of accuracy associated with these predictions is the variance of prediction errors, i.e., var(~ u), where u is a random effect in the model with mean 0 and variance O2u. Variance of prediction errors is a desirable standard of accuracy, because it gives a measure of dispersion of the predictors about the true predictands and can be calculated from the elements of the inverse of the coefficient matrix of the mixed model equations (3, 4). In our study, cows from pairs of herds were evaluated simultaneously by the NEA -1 ETA procedure, and variances of prediction errors of differences of genetic value between cows from different herds were compared to variances of prediction errors of differences of genetic value between cows from the same herd. Received October 14, 1982. 1 Department of I~iostatistics, University of Washington, Seattle 98195. M O D E L OF COW E V A L U A T I O N The additive genetic model in the NEA -1 ETA cow evaluation can be written 1983 J Dairy Sci 66:1370-1376 1370 VARIANCES OF PREDICTION ERRORS 1371