Various aspects of analysis, interpretation and diagnosis of nutrient status using PCA, CND-clr and CND-ilr methods (a case study on sugar beet)

Background and Objectives: Optimizing fertilizer use through plant analysis requires robust nutrient standards based on growth stage and a thorough understanding of nutrient interactions (the plant ionome). Statistical methods based on Compositional Data Analysis (CDA)—such as Principal Component Analysis (PCA) and Compositional Nutrient Diagnosis (CND)—overcome major limitations of single-factor approaches, provided they minimize bias in result interpretation. In this study, nutrient concentrations and root yield data from 170 sugar beet fields were compared using three models: PCA, CND-clr, and CND-ilr. This research aims to: (1) introduce the theoretical foundations of PCA, CND-clr, and CND-ilr; (2) validate nutrient indices through two interpretive  approaches (minimum limit-maximum limit, LMi-LMa, and lower limit-upper limit, LL-LU) within the CND-clr model; (3) derive critical concentrations and sufficiency ranges using CND-clr indices; (4) validate CND-ilr reference standards and compare them with other models; and (5) assess nutrient status using PCA and compare it with CND-clr and CND-ilr.
 

 



Materials and Methods: Leaf concentrations of N, P, K, Fe, Mn, Zn, and Cu, along with root yield, were collected from 170 sugar beet farms in Khuzestan Province, southwestern Iran. Leaf samples were taken from plants aged 90–120 days, washed, oven-dried at 65 °C for 48 h, ground, and sieved. Nutrients were analyzed using standard laboratory methods: micro-Kjeldahl for N, spectrophotometry for P, flame photometry for K, and atomic absorption spectrophotometry for Fe, Mn, Zn, and Cu. At harvest, average root yield per hectare was recorded. The study area soils had a saturated extract pH of 7.5–7.8, salinity <1 dS m⁻¹, lime content of 30–50%, and silty loam to silty clay loam textures.
Results: Principal Component Analysis using absolute nutrient concentrations showed that four components explained approximately 85 % of the total variance (eigenvalues > 1). In the first principal component (PC1), potassium, zinc, and copper exhibited the highest positive correlations, while nitrogen showed the highest negative correlation with root yield. However, interpreting nutrient status based on the nutrient index (IX) within the PCA framework led to bias. In contrast, the same nutrient index produced unbiased results when used with Pearson correlation. Consequently, PCA is capable of prioritizing nutrient–yield correlations at a macro scale (regional level) but lacks standard criteria for plot, farm, or orchard scale evaluation. Using the CND-clr method, critical concentrations and sufficiency ranges for N, P, K, Fe, Mn, Zn, and Cu were established. Validation of these standards on multiple farms using the two approaches revealed that the lower limit-upper limit (LL-LU) approach is more stringent than the minimum-maximum (LMi-LMa) approach. After determining CND-ilr reference standards, farm level validation effectively detected nutrient balances indicating synergistic and antagonistic effects, with the CND-ilr method providing the most diagnostically informative outputs. Comparative analysis demonstrated that both CND-clr and CND-ilr, supported by credible reference standards, are capable of assessing plant nutritional status at both micro scale (individual field) and macro scale (regional) levels.

 



Conclusion: PCA is a valuable tool for macro scale prioritization of nutrient yield correlations, but its lack of micro scale evaluation standards limits its application at the farm level. By contrast, the CND-clr and CND-ilr methods, equipped with robust reference standards, effectively assess nutrient status across both spatial scales. Critical concentrations and sufficiency ranges for N, P, K, Fe, Mn, Zn, and Cu were determined as reference standards indicative of nutrient interactions. The LL-LU validation approach proved more stringent than LMi-LMa. Furthermore, the CND-ilr method enabled a more accurate diagnosis of synergistic and antagonistic nutrient interactions, making it particularly suitable for site-specific nutrient management.