Joint Modeling of Grain Yield and Root Lodging in Maize Using Multi-Output Neural Network and Machine Learning Models Under Defined Environmental Conditions

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We evaluated a multi-output neural network framework for jointly analyzing maize grain yield (GY) and root lodging percentage (LP) using above-ground morphological traits measured under defined environmental conditions. To address model robustness, the multi-output neural network was compared with linear regression, elastic net, random forest, and XGBoost using repeated five-fold cross-validation, an 80/20 holdout split, and independent year-wise validation. Under repeated cross-validation, XGBoost provided the strongest average predictive performance for both traits, with R2 values of 0.57 for GY and 0.67 for LP. The multi-output neural network showed moderate performance, with R2 values of 0.49 for GY and 0.57 for LP. Final holdout performance for the neural network for GY and LP was R2 = 0.64 and R2 = 0.92, respectively. Year-wise validation showed weak temporal transferability because the two seasons differed not only in environmental conditions, but also in lodging mechanism. Repeated permutation importance identified ear width (EW), kernel row number (RNE), thousand kernel mass (KM1000), and kernel number per ear (KNE) as important predictors of GY, while LP prediction was most strongly associated with internode major diameter (IDmajor), ear length (EL), and the number of green leaves (NGL). Across both permutation importance and SHAP, only RNE and NGL were consistently shared between GY and LP. Supplementary ALE diagnostics indicated that RNE showed increasing model-estimated effects for both predicted GY and LP, whereas NGL showed a positive association with predicted GY but a decreasing or nonlinear association with predicted LP. These results show that joint modeling can support exploratory trait interpretation, but the predictive relationships remain environment-specific and should not be interpreted as causal or broadly transferable without further multi-environment validation.

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