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In plant breeding, multienvironment trials (MET) may include sets of related genetic strains. In self‐pollinated species the covariance matrix of the breeding values of these genetic strains is equal to the additive genetic covariance among them. This can be expressed as an additive relationship matrix, A, multiplied by the additive genetic variance. Using Mixed Model Methodology, the genetic covariance matrix can be estimated and Best Linear Unbiased Predictors (BLUPs) of the breeding values obtained. The effectiveness of exploiting relationships among strains tested in METs and usefulness of these BLUPs of breeding values for simultaneously modeling the main effects of genotypes and genotype × environment interaction (GE) have not been thoroughly studied. In this study, we obtained BLUPs of breeding values using genetic variance–covariance structures constructed as the Kroneker product (direct product) of a structured matrix of genetic variances and covariances for sites and a matrix of genetic relationships between strains, A. Results are compared with those from traditional fixed effects and random effects models for studying GE ignoring genetic relationships. A CIMMYT international wheat trial was used for illustration. Results showed that direct products of factor analytic structures with matrix A efficiently model the main effects of genotypes and GE. These models showed the lowest standard error of the BLUPs SE(BLUP) of breeding values. Genotypes that were related to other genotypes had small SE(BLUP). Related genotypes can clearly be visualized in biplots.
Crossa et al. (Wed,) studied this question.