Prediction of Breeding Value Under Henderson's Selection Model: A Revisitation

Prediction of breeding value by maximization of the joint density of the random effects and of the data was studied in a conditional selection scheme proposed by Henderson. Dispersion parameters were assumed known. In this setting, a condition under which selection can be ignored is that the distribution of the selection variable must not depend on the location parameters being estimated; the conditional distribution of the selection variable given the data and the random effects also must be ancillary. Selection can be ignored when culling is based on linear or nonlinear functions of the data that do not depend on the fixed effects. Contrary to results needed for unbiased estimation and prediction, selection can be ignored when it is based on linear or nonlinear functions of the residuals or of the random effects. The question of what type of predictor should be used in order to maximize expected genetic progress remains open.