Approximate prediction error covariances among multiple estimated breeding values for individuals

INTRODUCTION Today’s genetic evaluation schemes involve models comprising multiple, correlated additive genetic effects for each animal. These can be multi-trait (MT) models or random regression (RR) models which model trajectories in traits recorded repeatedly per animal through a set of RR coefficients. Often we are interested in linear functions of the resulting breeding value (EBV) estimates. These may be selection indexes combining EBVs for individual traits. For instance, BREEDPLAN, the Australian genetic evaluation scheme for beef cattle currently considers 22 traits (Johnston et al., 1999). The companion program, BREEDOBJECT (Barwick and Henzell, 1998) provides a range of customised selection indexes from the EBVs generated by BREEDPLAN. For RR models, estimates of the genetic RR coefficients describe the complete trajectory of genetic merit for each animal. EBVs for any point on the longitudinal scale can be obtained by evaluating the regression equations. Hence, like selection indexes, such derived point EBVs are linear functions of multiple, estimated EBVs which are correlated.