Selecting Cotton Yield Response Function to Estimate Profit-Maximizing Potassium Fertilization Rates for Cotton Production in Tennessee
Harmon, X., C. Boyer, C. O. Gwathmey, J. A. Larson, and R. K. Roberts.  2017.  Journal of Plant Nutrition, 40,11:1547-1556.

Abstract:
Recent research has shown stochastic yield response functions fit data better than deterministic yield response functions; however, little research exists comparing profit-maximizing fertilizer rates for upland cotton (Gossypium hirsutum L.) using stochastic and deterministic yield response functions. The objective of this research was to determine the most appropriate yield response functional form from which to determine the profit-maximizing potassium (K) rate for cotton in Tennessee. Data were used from a nine-year K fertilizer experiment in Jackson, Tennessee. Quadratic, quadratic-plus-plateau, linear response plateau, and linear response stochastic plateau response functions were estimated to determine the yield response function that best fit the data. The linear response stochastic plateau function was the most suitable yield response function for the data. The profit-maximizing K rate ranged from 65.2 to 74.3 kg K ha−1. Misspecification of the yield response function recommended over-application of K fertilizer and decreased producer's short term profits.