Methods of Calculating Prediction Error Variance and Prediction Accuracy for Restricted Best Linear Unbiased Prediction of Breeding Values

Prediction error variance (PEV) and prediction accuracy (PA) of breeding values (BVs) are essential for formulating breeding plans and predicting response to selection. However, restricted best linear unbiased prediction method (RBLUP method) carries many unknowns: in particular, the formulas for calculating PEV and PA are not clear. New findings were obtained using the RBLUP method. The uniqueness of RBLUP of BVs was proven. The formulas of PEV and PA for the RBLUP of BVs were derived from restricted mixed model equations. A method was also devised for easily calculating the PEV and PA for the RBLUP of BVs. Finally, the relationship between the RBLUP and ordinary BLUP of BVs was derived. It has become easier to calculate the PEV and PA for the RBLUP of BVs. This method is particularly effective for calculating the PEV and PA when applying the RBLUP method to achieve relative desired changes in all traits. This has also made it possible to predict the response to selection using the RBLUP method.