*2.1. Site Descriptions*

The study was conducted in Lishu County (43◦02–43◦46 N, 123◦45–124◦53 E), Jilin Province in Northeast China. Two field locations within the study site with contrasting soil types were selected for this study: one field with a black soil (loamy clay) equivalent to typical Haploboroll and the other field with an aeolian sandy soil (loamy sand) equivalent to typical Cryopsamments according to the USDA Soil Taxonomy [42]. In Lishu County, about 54,700 hectares of black soil fields and about 13,900 hectares of aeolian sandy soil fields are used to grow spring maize [15]. The black soil field was fertile and fine-textured with higher field capacity (0.39 cm cm<sup>−</sup>3), total N (1.35 g kg−1), and SOM (26.2 g kg−1) than the coarse-textured aeolian sandy soil field with lower field capacity (0.13 cm cm<sup>−</sup>3), total N (0.65 g kg−1), and SOM (9.7 g kg−1) [43]. The daily precipitation (mm) and daily mean temperature (◦C) during three maize growing seasons from 2015 to 2017 were reported in the previous study in Lishu County [43]. According to accumulated precipitation (APP) of maize growth season, year 2015, 2016, and 2017 were considered as dry (347.3 mm), wet (660.6 mm), and normal (509.9 mm) years, respectively.

#### *2.2. Field Experiments and N Management Strategies*

The same field experiment was conducted from 2015 to 2017 in the black soil and aeolian sandy soil fields. The experiment used a two-factor randomized complete block design with three replicates involving six N rates (from 0 to 300 kg N ha−<sup>1</sup> for maize with an increment of 60 kg N ha−1) with three planting densities (D1: 55,000 plants ha−1, D2: 70,000 plants ha−1, D3: 85,000 plants ha−1) in each field. The plot size was 9 × 8 m<sup>2</sup> with wide-narrow row planting spacing of 0.40–0.80 m. For each N treatment, one-third of the N fertilizer in the form of urea and all the phosphorus in the form of calcium superphosphate (at rate of 90 kg P2O5 ha−1) and potassium in the form of potassium sulphate (at rate of 90 kg K2O ha−1) fertilizers were blended into the top 20 cm soil as basal fertilizers before planting. The remaining two-thirds of the N fertilizer was side-dressed at the V8 growth stage.

To compare different N managemen<sup>t</sup> strategies, we defined the treatments of 300 kg N ha−<sup>1</sup> with 55,000 plants ha−<sup>1</sup> and 240 kg N ha−<sup>1</sup> with 70,000 plants ha−<sup>1</sup> as the farmer N rate (FNR) and regional optimal N rate (RONR) managemen<sup>t</sup> strategies, respectively. The treatment of 0 kg N ha−<sup>1</sup> with 55,000 plants ha−<sup>1</sup> was defined as check plot (CK). Three EONR managemen<sup>t</sup> strategies were evaluated in this study: (1) soil-specific EONR (SS-EONR) adjusts N application rates according to different soil types; (2) soil- and year-specific EONR (SYS-EONR) adjusts N application rates according to different soil types and each year's weather conditions; and (3) soil-year-density-specific EONR (SYDS-EONR) adjusts N application rates according to different soil types, each year's weather conditions and different planting densities. The EONR was defined as the rate of N application where \$1 of additional N fertilizer returned \$1 in grain yield, and was based on the assumption that N fertilizer was the only variable cost and all other costs were fixed [44]. The optimal plant density was empirically determined at 70,000 and 55,000 plants ha−<sup>1</sup> for the black and aeolian sandy soil fields, respectively. The SS-EONR, SYS-EONR and SYDS-EONR were determined based on the maize yield responses to the N application rate for specific soil, specific soil- and year, and specific soil-, year and density situations, respectively.

The local maize variety-Liangyu 66 was used in both fields. No irrigation was applied in the black soil field, while one-time irrigation of about 50 mm of water was applied before the anthesis growth stage in the aeolian sandy soil field each year. All plots were kept free of weeds, insects, and diseases with chemicals based on standard practices.

#### *2.3. Sample Collection and Data Calculation*

Before the start of the experimental series in 2015, soil samples were collected from each plot to determine the soil physical and chemical characteristics. At maize harvest stage (R6) for each growing season, three plant samples were randomly collected from each plot and split into stalks, leaves and grains. These three parts of plant samples were dried in the oven at 105 ◦C for one hour and then at 85 ◦C to a constant weight to determine dry aboveground biomass (AGB), which was the sum dry weight of talks, leaves and grains. Then they were ground into fine powder to determine plant N concentration (PNC) by the Kjeldahl digestion method [45], and the plant nitrogen uptake (PNU) was determined by multiplying PNC by AGB. Finally, the N nutrition index (NNI) for each plot was determined by the ratio of actual and critical PNC at harvest stage [46]. The critical PNC was calculated as following equation:

$$\text{PNC.c} = 36.5 \times \text{W}^{-0.48} \tag{1}$$

where PNCc is the critical plant N concentration expressed as "g kg−<sup>1</sup> dry matter (DM)" and W is the AGB expressed in "t DM ha−1".

After sampling, grain yield was determined by harvesting the middle 20 m<sup>2</sup> area of each plot and standardized to 14% grain moisture content. Later, partial factor productivity (PFP), agronomic efficiency (AE), and recovery e fficiency (RE) were calculated using the following equations:

$$\text{PFP [kg kg}^{-1}\text{]} = \text{Y}\_{\text{N}}/\text{N}\_{\text{F}} \tag{2}$$

$$\text{AE}\left[\text{kg}\,\text{kg}^{-1}\right] = (\text{Y}\_{\text{N}} - \text{Y}\_{0}) / \text{N}\_{\text{F}}\tag{3}$$

$$\text{RE I} \left[ \% \right] = \left( \text{PNU}\_{\text{N}} - \text{PNU}\_{0} \right) / \text{N}\_{\text{F}} \tag{4}$$

where Y N and Y0 are the yield in N fertilizer application plots and 0 kg N ha−<sup>1</sup> plots, respectively, and PNU N and PNU0 are the plant N uptake (PNU) in N application plots and 0 kg N ha−<sup>1</sup> plots, respectively, and NF is the applied N fertilizer rate.

The economic income, defined as net return (NR, \$ ha−1), was calculated according to Formula (4):

$$\text{NR} = \text{GY} \times \text{GP} - \text{Cost} \tag{5}$$

where GY is the grain yield (kg ha−1), GP is the grain price (0.25 \$ kg−1), and the Cost included field tillage (100 \$ ha−1), sowing (127 \$ ha−1), irrigation (423 \$ ha−1), pesticide (100 \$ ha−1), herbicide (100 \$ ha−1), harvest (155 \$ ha−1), N fertilizer (0.92 \$ N kg−1), phosphorus fertilizer (0.52 \$ P2O5 kg−1), potassium fertilizer (0.52 \$ K2O kg−1), and maize seeds (1.05 \$ 1000 seeds−1).
