Application of the “Delapuente” Equation in Field Trials of Wheat

Abstract

The equation, y = bx ^α + cx ^2α is used to describe the incidence of nutrients in the leaf at flowering in terms of dry matter production. The results for five fields of wheat were extremely satisfactory and gave the following results: of 15 possible combinations (five fields × three distinct leaves) the equation fitted well to 13 in the case of nitrogen, 11 for calcium and nine for iron; for phosphorus the results were good in seven cases, with six each for the nutrients potassium, magnesium and manganese. The best fits were for nitrogen, and declined in terms of goodness of fit in the order magnesium, calcium, potassium, manganese, iron, and phosphorus. Other forms of equation that are typically used in this work were less applicable and of poorer statistical significance. The action of a nutrient on the plant defines the parameters b (of positive sign, indicating stimulation) and c (usually negative implying inhibition) and the exponent α, responsible for the shape of the curve. In passing from leaf 1 to leaf 3, α generally declines, so that the first leaf (where the point of inflexion is closest to the maximum) is very close to its maximum development and at a late stage as a sink. The other leaves, particularly the third, are in a declining dry matter phase and therefore “source” organs. The different physiological state of the leaves is also reflected in the values of the parameters b and c; particularly well here in that large differences can be observed according to the different nutrients. Thus, in the case of nitrogen, both parameters increase (in absolute terms) according to leaf number thereby indicating greater effects, both stimulatory and inhibitory, on the dry matter content of the third leaf for a given nutrient concentration. The contrary is the case for calcium and magnesium. The high values of the parameters for magnesium indicate a strong influence on the plant. The three parameters, then, quantify the action of a nutrient, including all the conditions of the plant culture. However, the form of the curve will be more strictly related to the specific organ and its physiological state.

Keywords:

• Mathematical model
• Equation
• Quadratic
• Square‐root
• Mineral nutrition
• Production

Acknowledgments

We thank John Fenlon for his assistance in statistics and in the English translation of the mathematical terminology, and Dionisio Gonzalez for his technical help.