Evaluating boundary line fitting approaches for detecting yield-limiting factors and critical soil nutrient concentrations

Closing the crop yield gap is critical to meeting rising global food demand driven by population growth. The boundary line (BL) methodology is widely used to assess yield gaps and identify its causes. However, the lack of a standard BL fitting method can lead to inconsistencies in outputs and recommendations. This study compared four BL fitting methods, binning, BOLIDES, quantile regression (QR), and the censored bivariate normal model (cbvn), in determining the most-limiting factor and critical values (𝑥crit) across three datasets from England (Dataset 1), East Africa (Dataset 2), and a nutrient omission-trial from Ethiopia (Dataset 3). The most-limiting factor was identified using the Law of the Minimum and experimentally via omission-trials. Agreement among BL fitting methods and between BL methodology and omission-trials was tested using Cohen/Fleiss 𝜅-statistic. The consistency of 𝑥crit from BL fitting methods was assessed using the 95% confidence interval (CI) of cbvn and compared to RB209 guidelines (Dataset 1 only). Additionally, stakeholder preferences/opinions on BL fitting methods were gathered via workshops in Nairobi and Harare. Results showed BL fitting methods generally identified the most-limiting factor consistently (𝜅 > 0.4), but inconsistencies were observed for binning and QR methods. Experimentally-determined most-limiting factors were inconsistent with BL outputs (𝜅 < 0.2). While most 𝑥crit estimates fell within the cbvn CI, deviations occurred, especially in Dataset 2. BL fitting methods often underestimated 𝑥crit compared to RB209 guidelines. Stakeholder exercise showed no evidence (p = 0.56) against the null hypothesis of uniform ranking of BL fitting methods. The study highlights that while BL fitting methods show general consistency, discrepancies with experimentally determined results exist. Despite consistent results, cbvn is recommended for critical nutrient estimation due to its uncertainty quantification, supporting probabilistic insights for agronomic decisions.