Crop yield response functions in nutrient application: A review

Abstract The question of the optimal nutrient application in agricultural production continues to gather attention because of its relevance in increasing the profitability of crop production and protecting the environment. Economically optimal nutrient application decision rules are commonly derived by fitting crop yield functions to nutrients. The choice of the appropriate yield functional form thus is critical for estimating unbiased and more precise nutrient recommendations. This review explores recent developments in yield response functions to the nutrient application. We first introduce the concept of the economic theory of production and yield response functions. We then explain, with mathematical equations, some commonly used functional forms: quadratic response, Mitscherlich–Baule, deterministic, and stochastic plateau functions. We also summarize the strengths and weaknesses of each functional form and its implications for nutrient management strategies from an economic perspective. In recent studies, researchers have suggested that stochastic plateau functional forms, both linear and quadratic, could explain yield response to the nutrient application in a better way. Finally, we recommend fitting stochastic plateau functions in conjunction with carryover information in a dynamic optimization setting may yield more accurate optimal nutrient levels. Future research should continue to investigate whether these functional forms perform better in different crop and soil environments.