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# A quadratic model for fertilizer recommendations based on results of soil analysis

A quadratic model for fertilizer recommendations based on results of soil analysis

Communications in soil science and plant analysis7(5-8): 1595-1610

The establishment of a quantitative relationship between crop yields and amounts of applied nutrients is essential for fertilizer recommendations. A model was developed that uses yield goals, results of a soil analysis, and cost/value ratios for the calculations of rates of nitrogen (N), phosphorus (P), and potassium (K) to apply to corn. The coefficients for the equation: Y = a0 + a1X + a2X2, are calculated by: a0 = Y0 = Ym X SI; a, = [2 (Ym - Y0)]/Xm; a2 = (Y0 - Ym)/Xm2. In these equations, Ym stands for maximum yield, Xm is the quantity of applied nutrient correspondent to the maximum yield, Y0 is the yield without application of the nutrient, and SI is the sufficiency index calculated from soil analysis calibration curves. Experimental results of 25 NPK experiments with corn were used to evaluate the model. Model-estimated values of optimal nutrient rates and yield increases were, on the average, slightly higher than the experimental values for the three nutrients, with pronounced differences for isolated cases. However, profits calculated with the response curves, considering the experimental optima and the most economical rates given by the model, were quite close. The model can be applied using yield goals and organic matter, P and K given by soil analysis as inputs, giving calculations of optimal rates of nutrients, expected yield increases, and profits.

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Accession: 013073482

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