Bootstrap multimodel aggregation for estimating optimum nitrogen rates in agricultural crops

Abstract

For several (non-legume) crops, nitrogen (N) fertilization is key to maximize grain yield and farmers’ profit. The N rate that balances production and income is the economic optimum nitrogen rate (EONR). Estimating the EONR is a model-based process, and results vary depending on the data and selected model. Therefore, multimodel inference can improve both accuracy (bias) and precision (variance) of EONR estimation. In this study, we propose for the first time the use of bootstrap-based multimodel aggregation (BbMA), a simple machine learning algorithm, as a multimodel inference technique to estimate optimal N rates. The objectives were to: (i) evaluate the ability of BbMA to estimate the true EONR under different data generating models and experimental designs using simulated data, and (ii) apply this approach to field data. Simulation results showed that BbMA reduced both bias and variance of EONR estimates compared to individual models, even when the true model was included among candidates. These improvements were more pronounced with higher data quality (i.e., more observations and N rates). In the field data example, BbMA estimates fell within the range of individual model estimates and produced wider confidence intervals. This BbMA framework for grain yield response to N fertilization provides a simple and robust method to estimate EONR (or other derived quantities) while accounting for model uncertainty.