Objectives The fitting of different fertilizer effect function models of the fertilizer application rate and yield of maize in Northeast China was compared, and the effect function model with the best fitting effect was found out, which provided an important theoretical basis for the recommended fertilizer application of spring maize in Northeast China.

Methods Four functional effect models, quadratic term model, linear plus platform model, exponential model and spherical model were used to study the “3414” field experiments of soil testing and formula fertilizer project in Northeast China since 2010, including brown soil, alibic soil, meadow soil, chernozem, aeolian soil, black soil and alluvial soil, according to the relative yield of less than 80%, 80%–90% and more than 90%. 417 field experiments with low, medium and high fertility levels were fitted. The recommended fertilizer application rate, target yield and determination coefficient (R²) under the four functional effect models were analyzed and compared, and the model with the best fitting effect was found out.

Results After considering the fitting degree of fertilizer effect function, recommended fertilizer application and target yield, on low-fertility ·brown soil, chernozem, aeolian soil, black soil and alluvial soil, the fitting effect was as follows: linear plus platform model > spherical model > quadratic term model > exponential index model, and compared with the spherical model, quadratic term model and exponential model, the linear plus platform model saved 60–93, 73–95 and 84–114 kg/hm² nitrogen, respectively. On low fertility albic soil and meadow soil, the fitting effect was as follows: linear plus platform model > spherical model > exponential model > quadratic term model, and compared with the spherical model, quadratic term model and exponential model, the linear plus platform model saved 68–73, 84–87 and 89–91 kg/hm² nitrogen, respectively. On medium fertility brown soil, chernozem, black soil and aeolian soil, the fitting effect was as follows: linear plus platform model > spherical model > quadratic term model > exponential model, and compared with the spherical model, quadratic term model and exponential model, the linear plus platform model saved 72–93, 75–103 and 89–113 kg/hm² nitrogen, respectively. On middle fertility albic soil, meadow soil and alluvial soil, the fitting effect was as follows: linear plus platform model > spherical model > exponential model > quadratic term model, and compared with the spherical model, quadratic term model and exponential model, the linear plus platform model saved 78–100, 97–103 and 85–126 kg/hm² nitrogen, respectively. On high-fertility albic soil and black soil, the fitting effect was as follows: linear plus platform model > quadratic term model > spherical model > exponential model, and compared with the spherical model, quadratic term model and exponential model, the linear plus platform model saved 105–118, 121–134 and 165–168 kg/hm² nitrogen, respectively. On high fertility chernozem, the fitting effect was as follows: linear plus platform model > spherical model > quadratic term model > exponential model, and compared with the spherical model, the quadratic term model and the exponential model, the linear plus platform model saved 154, 154 and 155 kg/hm² nitrogen, respectively.

Conclusions Considering the fit of the fertilizer effect function, the recommended rate of fertilizer and target yield, the fitting effect of the linear plus platform model is the best in seven soils, and the other three kinds of fertilizer effect function are different according to soil type and soil fertility.