A Two-Step Hybrid Statistical and Machine-Learning Framework with Full Genetic Effects for Multi-Environment Genomic Prediction in Maize

Abstract

Accurate genomic prediction across environments remains challenging because phenotypic variation is jointly influenced by environmental conditions, genetic effects, and genotype-by-environment interactions. We developed a two-step hybrid statistical and machine-learning framework for multi-environment genomic prediction in maize (Zea mays L.). A trait-specific mixed model was first used to statistically decompose phenotypic variation into adjusted environmental means and residuals, after which the environmental component was predicted from environmental metadata and covariates, while the residual component was modeled using genomic main effects (G), genotype-by-environment effects (G×E), and pairwise epistatic effects (G×G). The framework was evaluated for grain yield, pollen DAP, silk DAP, and anthesis–silking interval (ASI) using environment-grouped five-fold cross-validation and an independent 2022 temporal test. On the 2022 test set, the best two-step models increased global Pearson correlation coefficients from 0.578, 0.559, 0.573, and 0.277 to 0.652, 0.635, 0.644, and 0.362, respectively. An ablation using arithmetic environmental means showed that the two-step formulation itself improved ranking performance, while mixed-model adjustment provided additional gains. Five-fold cross-validation showed the strongest and most stable improvements for pollen DAP and silk DAP, with global PCC increasing by 62.3% and 71.9% and global RMSE decreasing by 33.5% and 37.8%, respectively. Adding G×E produced only modest, trait-dependent gains, whereas G×G provided no consistent benefit. Overall, the proposed statistical decomposition and component-wise modeling improved the use of environmental and genomic information, although the magnitude and source of predictive gains were strongly trait-dependent.