Comparison of statistical methods to characterize yield response to phosphorus

Determining whether phosphorus (P) fertilization will increase grain yield (i.e., responsiveness) is a major challenge in soil fertility. The critical soil test value (CSTV) is a threshold commonly used to determine responsiveness. Despite the widespread use of CSTV, its ability to predict responsiveness has not been fully evaluated yet. The objective of this study was to evaluate five statistical methods that predict responsiveness with soil test phosphorus (STP): (i-ii) linear-plateau (using raw or ANOVA-based relative yield), (iii-iv) quadratic-plateau (using raw or ANOVA-based relative yield), and (v) logistic regression that estimates the probability of response along a STP gradient. Methods (i-iv) represent common practices that yield a CSTV, and (v) is proposed as an alternative. We compared the methods with a simulation study across 18 scenarios varying the number of site-years (10−100) and P rate levels (4, 5, 7), and with a case study. The simulation results showed that model performance became more consistent as the number of site-years increased. Overall, the plateau-based response models (i.e., methods i-iv) showed performances ranging 67.6% - 76.3% accuracy and 65.5% - 74.7% precision. Logistic regression showed 57.5% accuracy and 85.5% precision. Our results suggest that plateau-based response models remain useful for predicting site-year responsiveness, with no single plateau model clearly outperforming the others. The logistic regression approach: (i) shows performance comparable to other traditional methods, but (ii) maps a probability of response along a gradient of STP, and (iii) allows rethinking the way we conceptualize and communicate P responsiveness using probabilities instead of point estimates for thresholds.