Diagnosis of Macro and Micro Nutrients Balance in Sugar Beet Using ahalanobis Distance, Aitchison Distance, and Pan Balance

Soil, water, and plant test data can be used to optimize fertilizers use, increase the quantity and quality of crops yields, and to protect the environment from the negative effects of excess fertilizers. To achieve these goals, the analysis of these data should be based on a systematic and comprehensive approach, especially in terms of nutrients’ interactions and separation of nutrients synergistic and antagonistic effects. DRIS and CNDclr can diagnose D number of components, while D-1 could be diagnosed in the D-compositional “Hilbert space” across CNDilr. The objective of this paper was to compare “Aitchison” and “Mahalanobis” distances (as a predictor) across ilr coordinates as measures of nutrient imbalance, as well as determination of macro and micro reference norms for sugar beet using CND-ilr and “Pan Balance ” technique for diagnosing nutrients status. We collected 170 root yield and foliar samples in fall sugar beet fields of Khuzestan province in Iran and analyzed seven nutrients in leaf (N, P, K, Fe, Mn, Zn, and Cu). Then, nutrients were arranged into ten balances: ilr1: [Fe|Cu, Zn, Mn], ilr2: [Mn|Zn, Mn], ilr3: [Zn|Cu], ilr4: [P | N], ilr5: [NP | K], ilr6: [Fe | Mn], ilr7: [Zn | CU], ilr8: [Fe,Mn| Zn,Cu], ilr9: [N,P,K|Mn,Zn,Fe,Cu], and ilr10: [FV|N,P,K,Mn,Zn,Fe,Cu], which were computed as isometric log ratios (ilr). Total population of observations’ classification performed by a customized <> procedure (ROC technique) showed that a critical “Mahalanobis” distance of 4.2 separated balanced (low yield) from imbalanced (high yield) specimens about yield cut-off of 60.32 t/ha with test performance of 85%, as measured by the area under the ROC curve for ilr4 to ilr10. Comparing the “Mahalanobis” distance with the “Aitchison” distance showed that they were similar. By using Pan balance technique, comparing total nutrient balance between reference (TN) and none reference (TP) group of total fields by Tukey’s test showed seven significant differences (P ≤ 0.05), except ilr7. Results showed that in order to increase sugar beet root yield in the study area, it was not necessary to use iron fertilizers and N-fertilization should be reduced, while potassium fertilizer should be increased.