Toward a standardized statistical methodology comparing optimum nitrogen rates among management practices: A bootstrapping approach

Abstract

There are a range of approaches to compare differences between or among optimum nitrogen (N) fertilizer rates resulting from different management practices; however, this goal lacks statistical standardization. To provide the statistical rigor needed to give clear recommendations for greater or less N need based on specific management practices, we propose a bootstrapping approach that resamples residuals with replacement. While bootstrapping is not new to data processing in agronomic fields, we provide an example of how to conduct residual-resampled bootstrapping with nonlinear regression to identify differences in response curves, optimum N rates, and maximum yields using the FertBoot package in R. Our example dataset provides clear evidence of the value of the bootstrapping approach, as it can aid in determining significant differences between even relatively small differences in optimum N rate. We encourage adoption of this approach as a way to accurately evaluate differences in optimum fertilizer levels between or among treatments to better inform future agronomic decision making. INTRODUCTIONA common objective of fertilizer research is to determine how management practices affect the optimum nitrogen (N) fertilizer rate. Examples of such practices include, but are not limited to, tillage, manure application, residue management, and cover cropping, with the difference in optimum N rates between the treatment and the control being considered the N fertilizer replacement value of an input or practice. A common experimental design to address this objective is a randomized complete block, split-plot design with the agronomic management treatment as the main plot factor and N rate asThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

How can we estimate optimum fertilizer rates with accuracy and precision?

“…We used the approach described in Archontoulis and Miguez (2015) to fit the nonlinear models. In the supplemental material, we present an example using data from Francis et al., 2021 and, in addition, consider generalized additive models (Wood, 2017).…”