MODIFIED-QUADRATIC PLATEAU MODEL FOR DESCRIBING PLANT-RESPONSES TO FERTILIZER

Accurate estimation of optimal fertilizer rates is becoming more critical because of growing economic and environmental concerns associated with fertilizer use. Curve-fitting techniques are often used to estimate optimal fertilizer rates, but significant problems exist in selecting a proper model for a particular cropping situation. One solution is to develop a model sufficiently general to preclude the need for selecting a proper model for each cropping situation. We developed a modified-quadratic/plateau (MQ/P) segmented model (four or five parameters) and demonstrated its general applicability compared with the quadratic/plateau (Q/P) segmented model (three parameters) for describing fertilizer responses. The MQ/P model contains an efficiency index (E(x)) that is a quadratic function of the applied rate of nutrient X. In the Q/P model, E(x) remains constant relative to the rate of nutrient X. The MQ/P and Q/P segmented models set yield equal to the maximum yield (Y(m)) when the rate of nutrient X is greater than that required to achieve Y(m). The general applicability of the MQ/P model in comparison with the Q/P model was evaluated by determining how well these models fit hypothetical input data calculated with linear/plateau (L/P), Mitscherlich (M), and square root/plateau (SR/P) functions. The MQ/P model gave R2 values > 0.99 and predicted economically optimum fertilizer rates (i.e., rates at which the first derivative of yield response functions equaled the fertilizer/crop price ratio) close to those calculated with the input functions. The Q/P model gave R2 values ranging from 0.95 to 0.99, but gave poor predictions of economically optimum fertilizer rates. The ability of the MQ/P model to fit functions as diverse as L/P, M, and SR/P, and to predict economically optimum N rates associated with these functions, suggests that the MQ/P model has utility as a general curve-fitting technique for responses in which the right-hand segment is a plateau. An advantage of the MQ/P model is that the regression parameters can be interpreted as physically meaningful constants.