Validation of simultaneous deregression of cow and bull breeding values and derivation of appropriate weights.

Training of genomic prediction in dairy cattle may use deregressed proofs (DRP) as phenotypes. In this case, DRP should be estimated breeding values (EBV) corrected for information of relatives included in the data used for genomic prediction, and adjusted for regression to the mean (i.e., their reliability). Deregression is especially important when combining animals with EBV with low reliability, as commonly the case for cows, and high reliability. The objective of this paper, therefore, was to compare the performance of different deregression procedures for data that include both cow and bull EBV, and to develop and test procedures to obtain the appropriate deregressed weights for the DRP. Considered DRP were EBV: without any adjustment, adjusted for information of parents and regression to the mean, or adjusted for information of all relatives and regression to the mean. Considered deregressed weights were weights of initial EBV: without any adjustment, adjusted for information of parents, or adjusted for information of all relatives. The procedures were compared using simulated data based on an existing pedigree with 1,532 bulls and 13,720 cows that were considered to be included in the data used for genomic prediction. For each cow, 1 to 5 records were simulated. For each bull, an additional 50 to 200 daughters with 1 record each were simulated to generate a source of data that was not used for genomic prediction. The simulated trait had either a heritability of 0.05 or 0.3. The validation involved 3 steps: (1) computation of initial EBV and weights, (2) deregression of those EBV and weights, (3) using deregressed EBV and weights to compute final EBV, (4) comparison of the initial and final EBV and weights. The methods developed to compute appropriate weights for the DRP were either very precise and computationally somewhat demanding for larger data sets, or were less precise but computationally trivial due their approximate nature. Adjusting DRP for all relatives, known as matrix deregression, yields by definition final EBV that are identical to the original EBV. Matrix deregression is therefore preferred over other approaches that only correct for information of parents or not performing any deregression at all. It is important to use appropriate weights for the DRP, properly corrected for information of relatives, especially when individual reliabilities of final EBV are computed based on the prediction error variance of the model.