The phenomenon of genotype × environment (G×E) interaction in plant breeding decreases selection accuracy, thereby negatively affecting genetic gains. Several genomic prediction models incorporating G×E have been recently developed and used in genomic selection of plant breeding programs. Genomic prediction models for assessing multi-environment G×E are extensions of a single-environment model, and have advantages and limitations. In this study, we propose two multi-environment Bayesian genomic models: the first model considers genetic effects (
u) that can be assessed by the Kronecker product of variance-covariance matrices of genetic correlations between environments and genomic kernels through markers under two linear kernel methods, linear (GBLUP) and Gaussian (GK). The other model has the same genetic component as the first one (u) plus an extra component, f, that captures random effects between environments that were not captured by the random effects (u). We used five CIMMYT
data sets (one maize and four wheat) that were previously used in different studies. Results show that models with G×E always have superior prediction accuracy than single-environment models, and the higher prediction accuracy of multi-environment models with
u and f over the multi-environment model with only occurred in 85% of the time with GBLUP and 45% with GK across the five data sets. This last result indicated that the inclusion of the random effect f is still beneficial for increasing prediction accuracy after adjusting by the random effect u.
