Non-linear kernel methods for genomic prediction of soybean yield and quality in multi-environment trials

Nonlinear kernels improve the accuracy of genomic prediction while preserving the inferential framework of quantitative genetics. Improving the predictive accuracy of genomic prediction (GP) for complex genetic architectures involving non-additive effects and genotype-by-environment interactions (GEI) requires alternative approaches beyond conventional linear models such as Genomic Best Linear Unbiased Prediction (GBLUP). In this study, we evaluated grain yield, protein content, and oil content in the SoyNAM population, comprising 1,379 genotypes evaluated across six environments, to compare four non-linear kernels (Laplacian, Gaussian, Bessel, and Polynomial) with the GBLUP and Random Forest a Machine Learning model. Two variance structures (main effects and main plus interaction effects) were evaluated under three cross-validation schemes: CV1 (predicting untested genotypes in observed environments), CV2 (predicting tested genotypes in observed environments), and CV0 (predicting tested genotypes in unobserved environments). In addition, we tested the same models in a epistatic trait simulated dataset. The inclusion of GEI effects substantially improved predictive accuracy for grain yield under CV1 and CV2, whereas only modest gains were observed for protein and oil content. Across traits and validation schemes, the nonlinear kernels consistently matched or outperformed GBLUP, with the greatest advantage observed for oil content and under the CV0 scheme. No single nonlinear kernel consistently outperformed the others, indicating that kernel performance was environment dependent. Compared with Random Forest, the non-linear kernels achieved comparable or superior predictive accuracy while preserving the mixed-model framework, enabling the estimation of variance components. Moreover, in the extra dataset, the Laplacian kernel consistently showed high predictive accuracy across all scenarios, supporting its use as a promising option to the widely used Gaussian kernel. Therefore, non-linear kernel methods provide a robust and interpretable alternative for GP.