Soybean [Glycine max (L.) Merr.] seeding rate research across North America is typically conducted in small geo-political regions where environmental effects on the seeding rate × yield relationship are minimized. Data from 211 individual field studies (∼21,000 data points, 2007-2017) were combined from across North America ranging in yield from 1,000-7,500 kg ha −1 . Cluster analysis was used to stratify each individual field study into similar environmental (soil × climate) clusters and into high (HYL), medium (MYL), and low (LYL) yield levels. Agronomically optimal seeding rates (AOSR) were calculated and Monte Carlo risk analysis was implemented. Within the two northern most clusters the AOSR was higher in the LYL followed by the MYL and then HYL. Within the farthest south cluster, a relatively Abbreviations: AOSR, agronomically optimal seeding rate; CIPAR, cumulatively intercepted photosynthetically active radiation; HYL, high yield level; LYL, low yield level; MYL, medium yield level; NCCPI, national commodity crop productivity index; PAR, photosynthetically active radiation; VRS, variable rate seeding.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

The timing of crop development has significant impacts on management decisions and subsequent yield formation. A large intercontinental dataset recording the timing of soybean developmental stages was used to establish ensembling approaches that leverage both knowledge-based, human-defined models of soybean phenology and data-driven, machine-learned models to achieve accurate and interpretable predictions. We demonstrate that the knowledge-based models can improve machine learning by generating expert-engineered features. The collection of knowledge-based and data-driven models was combined via super learning to both improve prediction and identify the most performant models. Stacking the predictions of the component models resulted in a mean absolute error of 4.41 and 5.27 days to flowering (R1) and physiological maturity (R7), providing an improvement relative to the benchmark knowledge-based model error of 6.94 and 15.53 days, respectively, in cross-validation. The hybrid intercontinental model applies to a much wider range of management and temperature conditions than previous mechanistic models, enabling improved decision support as alternative cropping systems arise, farm sizes increase and changes in the global climate continue to accelerate.

The timing of crop development has significant impacts on management decisions and subsequent yield formation. A large intercontinental dataset recording the timing of soybean developmental stages was used to establish ensembling approaches that leverage both discrete-time dynamical system models of soybean phenology and data-driven, machine-learned models to achieve accurate and interpretable predictions. We demonstrate that the knowledge-based, dynamical models can improve machine learning by generating expert-engineered features. Combining the predictions of the diverse component models via super learning resulted in a mean absolute error of 4.12 and 4.55 days to flowering (R1) and physiological maturity (R7), providing an improvement relative to the best benchmark model error of 6.90 and 15.47 days, respectively. The hybrid intercontinental model applies to a much wider range of management and temperature conditions than previous mechanistic models, enabling improved decision support as alternative cropping systems arise, farm sizes increase, and changes in the global climate continue to accelerate.