Abstract
A mixed model method (BLUP) [best linear unbiased prediction] is introduced for the estimation of breeding values for multiple traits of all animals included in a dataset, by utilizing the complete genetic relationship. Considerable computational simplifications are obtained by linear transformation of the variates, thus enabling the equations to be solved separately for each trait. The method is illustrated by an example. Undesirable effects of sampling variance on estimated genetic parameters are discussed and a recent method (bending) for the improvement of defective variance matrices is recommended. Recent advances in ML [maximum likelihood] estimation of genetic parameters are briefly reviewed.