8.11: Accuracy of estimated breeding values

The accuracy of an estimated breeding value indicates how well the estimate represents the true breeding value. In other words: it represents the correlation between the estimated and the true breeding value. Unlike a normal correlation, because of some underlying assumptions, this correlation cannot become negative. It can have values between 0 (totally inaccurate estimate) to 1 (estimated breeding value is the perfect predictor of the true breeding value). The accuracy is indicated by the symbol r_IH. The r represents the fact that it is a correlation, the I represents the estimated breeding value, and the H represents the true breeding value.

From the table it becomes clear that with only information on the parents, or even grand-parents, the accuracy of the EBV can never be as large as what can be achieved with own performance. In the absence of a common environmental effect (c²), the maximum accuracy that can be achieved can be determined by assuming a very large n. If n becomes very large, then the maximum r_IH that can be achieved with full sib information is equal to which equals 0.707. In other words, for any trait with heritability larger than 0.5, selection on own performance gives a higher accuracy than selection on information collected on an infinitely large number of full sibs. Likewise, the maximum accuracy that can be achieved with half sib information, in the absence of a common environmental effect, is  which equals 0.5. So for any trait with heritability larger than 0.25, selection on own performance gives a higher accuracy than that based on an infinitely large number of half sibs. When there is a common environmental effect, these maximum achievable accuracies for full or half sib selection become smaller. From the formula it becomes clear that a common environmental effect decreases the accuracy of selection.