Using Monte Carlo simulation, two schemes of restricted selection were compared under various combinations of genetic parameters and constraints on the genetic gains. The first selection scheme is the combination of best linear unbiased prediction (BLUP) evaluation and linear programming technique (BLUP + LP), and the second one is based on the restricted BLUP selection (RBLUP). Selection for two traits was supposed, in which animals were selected to maximize the genetic gain in trait 2 (Δg2) under a proportional restriction on the genetic gain in trait 1 (Δg1) to satisfy the intended ratio (Ag,:Ag2). Little differences were found between the two selection schemes with respect to the genetic gains averaged over replicates. However, in all the cases studied, the variance of genetic gains among replicates under BLUP + LP selection was smaller and less sensitive to the genetic parameters and the intended restriction than RBLUP selection. Under the situations of antagonistic selection, the difference tended to be larger. When the heritabilities of the two traits were different, RBLUP selection remarkably increased the variance of genetic gain in a trait with a higher heritability. These results suggest that BLUP + LP selection should always be preferable to RBLUP selection because of the smaller risk of selection. This choice is especially important for the situation where the genetic parameters act as limiting factors for the achievement of intended genetic gains.
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