Approximating prediction error covariances among additive genetic effects within animals in multiple-trait and random regression models

A method for approximating prediction error variances and covariances among estimates of individual animals' genetic effects for multiple-trait and random regression models is described. These approximations are used to calculate the prediction error variances of linear functions of the terms in the model. In the multiple-trait case these are indexes of estimated breeding values, and for random regression models these are estimated breeding values at individual points on the longitudinal scale. Approximate reliabilities for terms in the model and linear functions thereof are compared with corresponding reliabilities obtained from the inverse of the coefficient matrix in the mixed model equations. Results show good agreement between approximate and 'true' values.