Phosphorus and Nitrogen Yield Response Models for Dynamic Bio-Economic Optimization: An Empirical Approach

Nitrogen (N) and phosphorus (P) are both essential plant nutrients. However, their joint response to plant growth is seldom described by models. This study provides an approach for modeling the joint impact of inorganic N and P fertilization on crop production, considering the P supplied by the soil, which was approximated using the soil test P (STP). We developed yield response models for Finnish spring barley crops (Hordeum vulgare L.) for clay and coarse-textured soils by using existing extensive experimental datasets and nonlinear estimation techniques. Model selection was based on iterative elimination from a wide diversity of plausible model formulations. The Cobb−Douglas type model specification, consisting of multiplicative elements, performed well against independent validation data, suggesting that the key relationships that determine crop responses are captured by the models. The estimated models were extended to dynamic economic optimization of fertilization inputs. According to the results, a fair STP level should be maintained on both coarse-textured soils (9.9 mg L−1 a−1) and clay soils (3.9 mg L−1 a−1). For coarse soils, a higher steady-state P fertilization rate is required (21.7 kg ha−1 a−1) compared with clay soils (6.75 kg ha−1 a−1). The steady-state N fertilization rate was slightly higher for clay soils (102.4 kg ha−1 a−1) than for coarse soils (95.8 kg ha−1 a−1). This study shows that the iterative elimination of plausible functional forms is a suitable method for reducing the effects of structural uncertainty on model output and optimal fertilization decisions