From a point to a range of optimum estimates for maize plant density and nitrogen rate recommendations

The interaction between nitrogen (N) rate, plant density, and hybrid on net return to seed and fertilizer cost remains unknown but important to be addressed given the multi-input decision process corn growers make every year. We collected grain yield from a factorial experiment with five N rates (0-291 kg N ha-1), five plant densities (3.7-11.4 plants m-2), and four hybrids (old vs. new) over 2 years in Iowa. Data were sufficiently modeled with a quadratic plateau model with continuous covariate terms to include N x plant density interactions (R2 = 0.925, n = 387). We found a wide range of plant densities (6.7-8.4 plants m-2) and N rate (150-212 kg N ha-1) combinations to achieve 99% of the maximum net revenue. The economic optimum N rate increased with increasing plant density from 4 to 7 plants m-2. The fundamental relationships between grain yield response to N fertilizer and plant density were similar across old and new hybrids; however, the absolute values were different, with newer hybrids having 20% higher economic optimum N rate and 23% higher yield than the older hybrids. We concluded that by accounting for two inputs into the revenue equation, a larger range of combinations was found to achieve 99% of the maximum net revenue. Our study offers new insights into N rate by plant density by hybrid interaction to assist future research. The greatest economic risk occurs at high plant density and low N rates. A wide range of optimum N rate (150-210 kg N ha-1) and plant density (6.7-8.4 plants m-2) reached 99% of max revenue. New hybrids had 10% higher optimum plant density, 20% higher optimum N rate, and 23% higher yield than old hybrids. The optimum N rate varied the most and the optimum plant density the least across years and hybrids. The relationship between optimum yield and optimum N rate depends on the choice of the fitted regression model.