A novel matrix multiplication framework for modeling genotype-by-environment interaction in genomic prediction

Accurate modeling of genotype-by-environment (G×E) interaction is critical for genomic prediction in plant breeding but remains challenging due to complex interaction structures. Conventional models often use the Hadamard product of genotype and environment covariance matrices to capture joint similarity, which may not fully represent G×E complexity. Here we propose a novel framework that derives covariance structures from the matrix multiplication of genotype and environment kernels, decomposing these into symmetric components incorporated as random effects in mixed models. Evaluated for 11 wheat and rice multi-environment datasets and across, this approach consistently outperformed the traditional Hadamard-based model, improving prediction accuracy by up to 13.2% in Pearson’s correlation and enhancing top-selection accuracy. Combining both methods yielded the highest performance, indicating complementary information capture. This framework offers a flexible, interpretable, and computationally feasible extension for modeling G×E interaction, potentially enhancing genomic selection effectiveness under diverse environmental conditions.