Genomic Prediction of Genotype × Environment Interaction Kernel Regression Models

In genomic selection (GS), genotype × environment interaction (G × E) can be modeled by a marker × environment interaction (M × E). The G × E may be modeled through a linear kernel or a nonlinear (Gaussian) kernel. In this study, we propose using two nonlinear Gaussian kernels: the reproducing kernel Hilbert space with kernel averaging (RKHS KA) and the Gaussian kernel with the bandwidth estimated through an empirical Bayesian method (RKHS EB). We performed single‐environment analyses and extended to account for G × E interaction (GBLUP‐G × E, RKHS KA‐G × E and RKHS EB‐G × E) in wheat ( Triticum aestivum L.) and maize ( Zea mays L.) data sets. For single‐environment analyses of wheat and maize data sets, RKHS EB and RKHS KA had higher prediction accuracy than GBLUP for all environments. For the wheat data, the RKHS KA‐G × E and RKHS EB‐G × E models did show up to 60 to 68% superiority over the corresponding single environment for pairs of environments with positive correlations. For the wheat data set, the models with Gaussian kernels had accuracies up to 17% higher than that of GBLUP‐G × E. For the maize data set, the prediction accuracy of RKHS EB‐G × E and RKHS KA‐G × E was, on average, 5 to 6% higher than that of GBLUP‐G × E. The superiority of the Gaussian kernel models over the linear kernel is due to more flexible kernels that accounts for small, more complex marker main effects and marker‐specific interaction effects.