A SIMPLE MATHEMATICAL MODEL FOR DIAGNOSIS OF NUTRIENT CONTENT AND DRY MATTER PRODUCTION IN WHEAT

Abstract

The equation y = a + bx ^α + cx ^2α proposed as a general function of nutrition to describe the relationship between the concentration of nutrients in a plant and the production of dry matter. The function has a maximum if b>0˜ and ˜c≤0, which corresponds to the optimal nutritional value; depending on the value of the parameter α it may have a point of inflexion which can occur before or after the maximum and at varying distances from it. The parameter a can be set to zero if necessary in which case the function passes through the origin. Hence its parametric form is flexible and suitable for describing the incidence of nutrients in dry matter production. Furthermore, it is very simple and easy to use. Its use in describing leaves of field-grown wheat at different stages of growth seems to indicate that it has some applicability compared with other commonly used functions, and given its flexibility it can offer advances in the understanding of mineral nutrition in plants. Although further assays are necessary, so that the physiological stage of the plant sample can be accurately defined, it seems that the value of α may define the physiological state of the plant, the particular circumstances of cultivation defining the parameters b and c. Thus, for example, in 1987, in experimental trials of wheat close to flowering, the value of α for nitrogen in the flag leaf was 1.75, for the second leaf 1.25, and 1.00 for the third. The corresponding stages of growth, although not very precisely defined, were close to the maximum for the first leaf, slightly declining in the second, but more so for the third. Post-anthesis, nitrogen in the first leaf had an α-value of 0.75; its physiological state now corresponding to a sharp decline in foliar weight. Other situations would give characteristic values of α, whose calibration over several carefully conducted trials would be used in plant nutrition diagnosis.

ACKNOWLEDGMENTS

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