Navigating yield-density trade-offs in maize production: A Bayesian-ML framework for uncertainty attribution and management

Context Optimizing planting density is a key agronomic strategy for improving maize yield, yet its response remains highly uncertain due to the combined influence of genotype, environment, and management (G–E–M) factors. Traditional models often overlook uncertainty and fail to fully account for the contributions of these factors, limiting their practical utility. Objective This study aims to quantify the probabilistic response of maize yield to planting density, and systematically attribute the uncertainty of this response to key G–E–M factors across China. Methods The dataset was compiled from 997 field trials conducted in China between 1999 and 2022. A Bayesian hierarchical model was employed to probabilistically estimate three key descriptors: optimal planting density (OPD), yield at OPD (YOPD), and density efficiency (DE). The eXtreme Gradient Boosting (XGBoost) machine learning (ML) algorithm was then used to evaluate the contribution of genetics, climate, soil, and management to the estimates and their uncertainties. Results The median OPD, YOPD, and DE were 7.40 × 10 4 plants ha −1 , 11.06 Mg ha −1 , and 154.45 g plant −1 , with considerable uncertainties (2.65 ×10 4 plants ha −1 , 2.06 Mg ha −1 , and 57.97 g plant −1 , respectively). ML revealed that climate factors dominated YOPD prediction (54.59%), while plant architecture was the primary factor for OPD (14.34%) and a leading driver of its uncertainty. Management practices, particularly row spacing and nitrogen rate, were the largest contributors to overall uncertainty (up to 34.06% for OPD uncertainty), whereas soil properties provided crucial buffering effects, mitigating variability. Conclusions The maize density-yield relationship is inherently probabilistic, not deterministic. Plant architecture sets the biological potential for density tolerance, while climate defines the attainable yield, and management practices are the primary source of predictive uncertainty. Implications Our findings advocate for tailoring planting density based on cultivar-specific architecture and local environmental conditions, with optimized management to reduce production uncertainty, thereby enhancing sustainable intensification of maize systems.