A QUADRATIC MODEL FOR FERTILIZER RECOMMENDATIONS BASED ON RESULTS OF SOIL ANALYSES

The establishment of a quantitative relationship between crop yields a nd amounts of applied nutrients is essential for fertilizer recommenda tions. A model was developed that uses yield goals, results of a soil analysis, and cost/value ratios for the calculations of rates of nitro gen (N), phosphorus (P), and potassium (K) to apply to corn. The coeff icients for the equation: Y = a(0) + a(1) X + a(2)X(2), are calculated by: a(0) = Y-0 = Y-m x SI; a(1) = [2 (Y-m - Y-0)]/X(m); a(2) = (Y-0 - Y-m)/X(m)(2). In these equations, Y-m stands for maximum yield, X(m) is the quantity of applied nutrient correspondent to the maximum yield , Y-0 is the yield without application of the nutrient, and SI is the sufficiency index calculated from soil analysis calibration curves. Ex perimental results of 25 NPK experiments with corn were used to evalua te the model. Model estimated values of optimal nutrient rates and yie ld increases were, on the average, slightly higher than the experiment al values for the three nutrients, with pronounced differences for iso lated cases. However, profits calculated with the response curves, con sidering the experimental optima and the most economical rates given b y the model, were quite close. The model can be applied using yield go als and organic matter, P and K given by soil analysis as inputs, givi ng calculations of optimal rates of nutrients, expected yield increase s, and profits.