Genomic Prediction of Genotype x Environment Interaction Kernel Regression Models

In genomic selection (GS), genotype x environment interaction (G x E) can be modeled by a marker x environment interaction (M x E). The G x 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 x E interaction (GBLUP-G x E, RKHS KA-G x E and RKHS EB-G x 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 x E and RKHS EB-G x 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 x E. For the maize data set, the prediction accuracy of RKHS EB-G x E and RKHS KA-G x E was, on average, 5 to 6% higher than that of GBLUP-G x 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.