Prediction of genetic gain from quadratic optimisation with constrained rates of inbreeding

There are selection methods available that allow the optimisation of genetic contributions of selection candidates for maximising the rate of genetic gain while restricting the rate of inbreeding. These methods imply selection on quadratic indices as the selection merit of a particular individual is a quadratic function of its estimated breeding value. This study provides deterministic predictions of genetic gain from selection on quadratic indices for a given set of resources (the number of candidates), heritability, and target rate of inbreeding. The rate of gain was obtained as a function of the accuracy of the Mendelian sampling term at the time of convergence of long-term contributions of selected candidates and the theoretical ideal rate of gain for a given rate of inbreeding after an exact allocation of long-term contributions to Mendelian sampling terms. The expected benefits from quadratic indices over traditional linear indices (i.e. truncation selection), both using BLUP breeding values, were quantified. The results clearly indicate higher gains from quadratic optimisation than from truncation selection. With constant rate of inbreeding and number of candidates, the benefits were generally largest for intermediate heritabilities but evident over the entire range. The advantage of quadratic indices was not highly sensitive to the rate of inbreeding for the constraints considered.