Relationships between genotype x environment interaction and genetic correlation of the same trait measured in different environments.

Relationships between genotype x environment interaction and genetic correlation of the same trait measured in different fixed environments are derived by comparing the variance-covariance structures of observations between a one-way multiple-trait linear model and a two-way single-trait mixed linear model. In the latter model, heterogeneity of interaction variances among environments and non-zero covariances among interactions are assumed, in addition to the heterogeneity of error variances and non-zero covariances between genetic-group effects and interactions that were accommodated in earlier work. The results are applicable to more than two environments and to unbalanced data. This paper is a generalization and a correction of earlier works.