Application of saturated D-optimal design for optimum fertilization in the production of high protein soybean

Objectives The production of high protein soybean is an important industry in the supply-side reform in modern agriculture system. Optimal fertilization plays a vital role in the efficient production of high protein soybean. The saturated D-optimum design method was attempted in the fertilization management in high-protein soybean production in Huang-Huai-Hai region.

Methods A field experiment was conducted using a high-protein soybean cultivar of Jidou21 as the tested crop. Fertilizers of nitrogen, phosphate and potassium were designed using the two factors' saturating D-optimal design. Each factor included 10 levels and with three replicates. The total of 30 experimental plots were randomly arranged. All fertilizers were applied in batches at the flowering stage of soybean. Both the soybean yield and protein contents were determined at the maturity stage.

Results Using the obtained data, a ternary quadratic polynomial mathematical model was established, with the applied amounts of N, P and K as independent variables, and the soybean yield and protein content as the target functions. The analysis of model showed that application of N, P, and K significantly influenced soybean yield and protein content, and N exhibited better effect than K and P did. When the levels of N, P and K reached 95.46, 183.8 and 128.7 kg/hm², the marginal yield effect became zero; When the levels of N, P and K reached 120.8, 178.4 and 141.3 kg/hm², the marginal protein effect became zero. There were interactions among the N, P and K rates and the yield and protein content of soybean. Under the experimental conditions, to obtain above 3104 kg/hm² of soybean yield with more than 46%of protein content, the optimum fertilization rate was N 76.1−101.1 kg/hm², P 131.1−168.5 kg/hm² and K 104.9−134.8 kg/hm².

Conclusions The fertilizer function model established using the saturated-D method is satisfactory in clearly expressing the continue change of the relationship between the NPK fertilization and the yields and protein contents of soybean, and the interaction of the three fertilizers. Suitable rates of NPK fertilizers are effectively in improving the yield and protein content of the tested soybean cultivar. The optimal rate of fertilizers is N 76.1−101.1 kg/hm², P 131.1−168.5 kg/hm² and K 104.9−134.8 kg/hm² for the soybean cultivar in the experimental area.