Accuracies of estimated breeding values from ordinary genetic evaluations do not reflect the correlation between true and estimated breeding values in selected populations.

The accuracy of estimated breeding values (EBVs) is an important parameter in livestock genetic improvement. It is used to calculate response to selection and to express the credibility of individual EBVs. Although it is well-known that selection reduces accuracy, this effect is not well-studied and accuracies from genetic evaluations are not adjusted for selection. This work investigates the effect of selection on accuracy of EBVs estimated using best linear unbiased predictors. Results show that accuracies in a selected population may be considerably smaller than the ordinary accuracy from genetic evaluation. Accuracy of the parent average is dramatically reduced by selection, up to a factor of three. Expressions for equilibrium accuracies in selected populations are presented and depend only on the unselected accuracy and the intensity of selection. Thus, schemes with the same unselected accuracy and intensity of selection also have the same equilibrium accuracy and response to selection. At the same unselected accuracy, therefore, schemes based on between-family information do not show greater reduction in response and accuracy because of the Bulmer effect. An example shows that benefit of genomic selection may be underestimated when the effect of selection on accuracy is ignored. Finally, this work argues that the SE of an EBV and the correlation between true and EBVs are different things, and that accuracies should not be adjusted for selection when they primarily serve to indicate the SEs of EBVs.