A method of computing restricted best linear unbiased prediction of breeding values for some animals in a population.

Restricted BLUP (R-BLUP) is derived by imposing restrictions directly within a multiple-trait mixed model. As a result, the R-BLUP procedure requires the solution of high-order simultaneous equations. If restrictions are imposed on breeding values for only some animals in a population, calculations become more complex. A new procedure for computing the R-BLUP of breeding values was derived when constraints were imposed on the additive genetic values of only some animals in a population. Rules for including records when proportional constraints are imposed were developed based on the traits that are recorded for an animal. The technique was better than the previous method in both memory requirement and central processing unit time.