Establishing a critical phosphorus dilution curve for potato in semi-arid regions based on a Bayesian analysis

Phosphorus (P) fertilizer use efficiency in potato production is relatively low in semi-arid regions, wasting P resources and increasing environmental risks. Therefore, improving P use efficiency (PUE) is critical for sustainable potato production. The critical P dilution curve (CPDC) and P nutrition index (PNI) have proven to be robust diagnostic tools for assessing crop P status and aiding in improving P fertilizer management. Several potato CPDCs have been established, however, few studies have been conducted to establish a CPDC for potato (<i>Solanum tuberosum</i> L.) under ridge planting with drip irrigation, a planting pattern that has been increasingly adopted in semi-arid regions. In addition, the different CPDCs established using the conventional Jestus statistical model cannot discriminate the true variability across scenarios or have become linked to estimation errors. Therefore, the objectives of this study were to (1) establish a potato CPDC based on a Bayesian statistical method and (2) evaluate the relationship between potato yield and PNI. Three years of field experiments with five levels of P₂O₅ application (0, 80, 160, 240, 320 kg ha^-1) were conducted in Inner Mongolia, China. No significant differences were found between CPDCs across the year × site for the assessed scenarios, and thus, a generic CPDC for potatoes in the region was derived as Pc = 0.616 DM^-0.296, and it can be used to calculate the PNI. Further analysis showed that at each growth stage, the PNI exhibits a significant plateauing linear relationship with relative potato tuber yield. Thus, it provides a standard for diagnosing the P nutritional status in potatoes and lays a robust foundation for precise P recommendations in the region.