A reparameterization of a genetic selection index to locate its sampling properties

A transformation is proposed of the variables used for constructing genetic selection indices, such that the reparameterized phenotypic covariance matrix is identity and the genetic covariance matrix is diagonal. These diagonal elements play the role of heritabilities of the transformed variables. The reparameterization enables sampling properties of the index weights to be easily computed and formulae are given for data from half-sib families. The index is likely to be least stable when the transformed variables of low heritability have high economic weights, and the weights will have highest sampling variance when these heritabilities are nearly equal. It is suggested that the sample roots of the determinantal equation be inspected when constructing an index in order to give some guide to its accuracy.