A review of theoretical aspects in the estimation of breeding values for multi-trait selection

The natural links between best linear unbiased prediction and selection indices are reviewed. These links allow a simple interpretation of the estimation equations and allow results from selection index theory to be used in investigating the accuracy of predictors. The gain in accuracy in prediction for one trait from using other correlated traits is partitioned into a direct gain from measuring other traits and a gain because fixed effects are estimated more precisely. There will be a loss of accuracy in predictors and loss of selection response when variance parameters are not known exactly. A regression argument is used to explain this phenomenon and formulae to quantify the loss of selection response are interpreted using canonical variates. Often predictors and variance parameters are derived from selected populations. The relevance of procedures developed for unselected populations is discussed and unsolved problems indicated.