Quadratic and Quadratic‐Plus‐Plateau Models for Predicting Optimal Nitrogen Rate of Corn: A Comparison

Abstract

Based on quadratic response models, the University of Illinois recommends 22 kg fertilizer N Mg⁻¹ corn (Zea mays L.) grain yield, with adjustments for cropping history, manure, and planting date. Recent work suggests recommendations based on the quadratic model are excessive. This field study evaluated the quadratic‐plus‐plateau and quadratic models and the current recommendation for a 10‐ to 12‐yr, two‐location, two‐crop‐sequence data set with 5 N fertilizer rates in Illinois. For all location‐sequences, we detected a systematic bias with the quadratic model as compared with the quadratic‐plus‐plateau model. The quadratic response model predicted a maximum grain yield of 3 to 6% larger and an optimal N fertilizer rate 5 to 60% larger than that predicted by the quadratic‐plus plateau model and decreased profit from $0.61 to $17.12 ha⁻¹ yr⁻¹. Current University of Illinois recommendations differed by from − 6 to + 104 kg N ha⁻¹ from the amount predicted by the quadratic‐plus‐plateau and resulted in a profit reduction of $0.01 to $31.42 ha⁻¹ yr⁻¹. These analyses indicate that the quadratic‐plus‐plateau is preferable to the quadratic model for predicting N fertilizer requirements of corn. Economic analysis indicates that the consequences of using the quadratic model rather than quadratic‐plus‐plateau model can be large, but not in all cases. Furthermore, the general recommendation of 22 kg N Mg⁻¹ of expected grain yield minus rate adjustments is not appropriate in all cases. Site‐specificity plays a large role in determining optimal N rates.