On selection criteria and estimation of parameters when the variance is heterogeneous.

Procedures for ranking candidates for selection and for estimating genetic and environmental parameters when variances are heterogeneous are discussed. The best linear unbiased predictor (BLUP) accounts automatically for heterogeneous variance provided that the covariance structure is known and that the assumptions of the model hold. Under multivariate normality BLUP allowing for heterogeneous variance maximizes expected genetic progress. Examples of application of BLUP to selection when residual or genetic variances are heterogeneous are given. Restricted maximum likelihood estimation of heterogeneous variances and covariances via the expectation-maximization algorithm is presented.