Plant Nutrient Norms Based On Nutrient Balances Using Compositional Data Analysis.

Plant tissue diagnosis has roots in Sprengel’s  Law of Minimum (1828) and chemical analysis of soils and plant tissues by Boussingeault (1836) as later improved by Justus von Liebig, E.A. Mitscherlich and others. The first representation of tissue analytical data in a closed compositional space has been drawn by Lagatu and Maume in 1934 using a N-P-K ternary diagram. The concept of critical percentage above which there is luxury consumption of nutrient and below which there is poverty adjustment was introduced by Macy in 1936 and improved by Ulrich in 1943 and 1967. The latter showed the importance of considering nutrient balance and change in concentration over time in tissue nutrient diagnosis. DRIS was elaborated by Beaufils in 1973 using dual ratios as binary representations of nutrient interactions. The DRIS computation procedure was rearranged by Parent and Dafir in 1992 to fit into the centered log ratio transformation approach developed by Aitchison en 1986 for compositional data analysis. Indeed, tissue analytical data are compositional data intrinsically biased by redundancy, scale dependency and non normal distribution due to the closure problem of the constant sum. Balances were defined as isometric log ratios (ilr) by Egozcue et al. in 2003 from sequential binary partitions of orthogonally arranged groups of components that avoid numerical biases. This unbiased procedure was applied to tissue analytical data by Parent in 2011 for tissue diagnosis. A number of D-1 balances can be defined from a composition of D parts based on sound theory in agronomy and the principle of orthogonality. The balances are projected into the Euclidean space as ilr coordinates to allow computing distances between reference and diagnosed compositions. The ilrs can be tested for time stationarity. We present a step-by step procedure to build, calibrate and validate unbiased nutrient balance models using survey and experimental data with example.