Compositional nutrient diagnosis of corn using the Mahalanobis distance as nutrient imbalance index

Abstract

Compositional nutrient diagnosis (CND) provides a plant nutrient imbalance index (CND - r2) with assumed χ2 distribution. The Mahalanobis distance D2, which detects outliers in compositional data sets, has a χ2 distribution. The objective of this paper was to compare D2 and CND – r2 nutrient imbalance indexes in corn (Zea mays L.). We measured grain yield as well as N, P, K, Ca, Mg, Cu, Fe, Mn, and Zn concentrations in the ear leaf at silk stage for 210 calibration sites in the St. Lawrence Lowlands [2300–2700 corn thermal units (CTU)] as well as 30 phosphorus (2300–2700 CTU; 10 sites) and 10 nitrogen (1900–2100 CTU; one site) replicated fertilizer treatments for validation. We derived CND norms as mean, standard deviation, and the inverse covariance matrix of centred log ratios (clr) for high yielding specimens (≥9.0 Mg grain ha–1 at 150 g H2O kg–1 moisture content) in the 2300–2700 CTU zone. Using χ2 = 17 (P < 0.05) with nine degrees of freedom (i.e., nine nutrients) as a rejection criterion for outliers and a yield threshold of 8.6 Mg ha–1 after Cate-Nelson partitioning between low- and high-yielders in the P validation data set, D2 misclassified two specimens compared with nine for CND –r2. The D2 classification was not significantly different from a χ2 classification (P > 0.05), but the CND – r2 classification differed significantly from χ2 or D2 (P < 0.001). A threshold value for nutrient imbalance could thus be derived probabilistically for conducting D2 diagnosis, while the CND – r2 nutrient imbalance threshold must be calibrated using fertilizer trials. In the proposed CND –D2 procedure, D2 is first computed to classify the specimen as possible outlier. Thereafter, nutrient indices are ranked in their order of limitation. The D2 norms appeared less effective in the 1900–2100 CTU zone. Key words: Nutrient balance, simplex closure, variance-covariance matrix, χ2 distribution, grain corn, nitrogen and phosphorus fertilization