Objectives Ternary quadratic polynomial fertilizer response model (TPFM) has low success rate due to setting bias and multicollinearity. A ternary non-structural fertilizer response model (TNFM) was established to expand the model applicability and precision of fertilizer recommendation in rice production.

Methods Thirteen rice field NPK fertilizer experiments were chosen in Pinghe County and Xianyou County, Fujian Province. Design of “3414” was used in all the thirteen experiments, the treatments were as following: 1) N₀P₀K₀; 2) N₀P₂K₂; 3) N₁P₂K₂; 4) N₂P₀K₂; 5) N₂P₁K₂; 6) N₂P₂K₂; 7) N₂P₃K₂; 8) N₂P₂K₀; 9) N₂P₂K₁; 10) N₂P₂K₃; 11) N₃P₂K₂; 12) N₁P₁K₂; 13) N₁P₂K₁; 14) N₂P₁K₁. Of them, “2” represented current recommended nutrient levels, “1” and “3” represented 50% and 150% of those, and “0” represented no nutrient input. The TPFM and TNFM were established for each experiment. Extra 668 rice field results were collected all over Fujian Province, and used for the verification of the fitting effect and the reliability of fertilization recommendation of the two kinds of models.

Results Among the established 13 TPFMs, two failed to achieve statistical significance levels and three resulted in non-typical model. While all the 13 TNFMs were typical models, showing less setting bias and multicollinearity. The TPFMs recommended higher nutrient rates than the practical ones, while the TNFMs verified with the 668 field experiments results, 30.1% of the TPFMs failed to pass the significance test, but 23.4% of the TNFMs did not. In the non-typical model that made the recommended fertilization rate by extrapolation, the proportion of the TPFMs was only 4.0%, while that of the TNFMs was increased to 30.7%. In the two types of non-typical models of unreasonable coefficient symbol and without maximum yield point, the proportion of the TPFMs reached to 32.3% and 14.4%, respectively. However, the TNFMs were reduced to 6.9% and zero, respectively, and the proportion of typical model by the TPFMs was only 19.5%. In contrast, using the TNFMs made the proportion of the typical model increase to 39.1%, which was twice of the TPFMs. Hence, the new model significantly improved the modeling success rate.

Conclusions The ternary non-structural fertilizer response model (TNFM) has a higher fitting accuracy and wider application scope in the modeling of nitrogen, phosphorus and potassium fertilization response of paddy rice.