Prediction of genetic gain in finite populations with heterogeneous predicted breeding values accuracies

The algebraic expression of the genetic selection differential (expected genetic superiority of breeders after a selection on their Predicted Breeding Values) was derived when a limited number of individuals were selected from a limited sample of candidates on the basis of their predicted genetic value, with heterogeneous reliabilities. A formula is proposed for situations in which these reliabilities can be clustered in a few classes. We show that the expected genetic selection differential increases with the number of classes, the mean reliability being constant. In the panel of cases simulated, this increase reached up to 18% of the values obtained in the homogeneous situation. We used the proposed formulae to estimate selection differentials and compared it numerically with performing simulations. In terms of speed of computation, our algebraic formulae performed better than simulations in populations of limited size.