C. R. Henderson: contributions to predicting genetic merit.

The contributions of C. R. Henderson to the genetic evaluation of livestock have been widely accepted, utilized, and enhanced by animal breeders and statisticians. Not well known are the possible alternatives to BLUP that have been suggested by Henderson, such as biased predictors and Bayesian methodology to incorporate prior information. A search for rapid methods of inverting dominance and additive by additive genetic relationship matrices has taken place since Henderson first described his method for computing the inverse of the additive genetic relationship matrix. Accounting for inbreeding and selected base populations continues to be a problem. There is a need to derive accurate descriptions of selection processes and the appropriate selection model in order to solve the problems of cow culling, nonrandom association of sires with herd-year-seasons, and preferential treatment. Henderson solved many animal breeding problems and left hints for solving others, but there are still many difficult problems to be tackled that will have to be resolved without the availability of his generous advice.