Field experiments were carried out in 2014 and 2015 at the Wuqiao Experiment Station of China Agricultural University, Hebei province, China (37° 41′ N, 116° 36′ E). In the upper 0.4 m of the clay-loam soils, pH was 8.3 with a bulk density of 1.45 g cm^-3, and they contained 12.36 g kg^-1 of soil organic matter, 1.04 g kg^-1 of total nitrogen (N), 37.71 mg kg^-1 of readily available phosphorous (P), and 94.22 mg kg^-1 of readily available potassium (K). The soil pH, organic matter, total N, available P and K were analyzed by following procedures of Piper (1950), Bremner (1965), Kjeldahl method, Stanford and English (1949) and Olsen et al. (1954), respectively. Preceding crop was winter wheat. A standard agro-meteorological station automatically recorded meteorological conditions in the experimental fields; air temperature and rainfall data during the study period growing seasons are provided in Figure 1. The light and temperature condition in 2015 was better than that in 2014, which benefited maize production.

The experimental design was a split-plot with three replicates: two planting densities treatments were applied as the main plots, and three N treatments were designated as sub-plots. The size of the main plot was 20 m × 15 m, and the sub-plot size was 20 m × 5 m. A common maize hybrid – Zhengdan 958, the main maize cultivar in NCP, was planted at two planting densities (67,500 plants ha^-1 and 90,000 plants ha^-1) with equal row spacing of 0.6 m. The N application rates were as follows: control (N0), 180 kg N ha^-1 (N180), and 360 kg N ha^-1 (N360). As recommended by Liu et al. (2003), the N180 treatment was set in two stages: 90 kg N ha^-1 at the three-leaf stage and 90 kg N ha^-1 at the silking stage. The N360 treatment was set at 360 kg N ha^-1 at the time of planting; this is the traditional N management protocol used by farmers in NCP (Zhang et al., 2008). Urea was applied 0.1 m deep into the soil with a furrowing machine according to the N application rates. In addition, all plots received 130 kg P₂O₅ ha^-1 in the form of calcium superphosphate (P₂O₅ 12%) and 130 kg K₂O ha^-1 in the form of potassium sulfate (K₂O 60%) at the time of planting. Maize was planted on June 15, 2014 and on June 19, 2015, after winter wheat crops were harvested. Each plot was irrigated with 75 mm of water immediately after sowing. The maize grains were harvested on October 5 in both years before winter wheat planting.

Three plant samples were randomly selected from the center of each plot during the silking stage and at the time of harvest. Plants were dissected into leaf + husk, stalk + cob, and grain (only at the time of harvest). All separated components were oven-dried at 80°C to a constant weight; they were then weighed to record dry matter accumulation (DMA, kg ha^-1) and milled into a powder. Total N was measured using the Kjeldahl method, and NUE (kg kg^-1), agronomic N efficiency (AEN, kg kg^-1), and N partial productivity (PFP_N, kg kg^-1) were calculated using the methods of Dobermann (2005).

Based on the DMA and N accumulation measurements, we calculated the following parameters (Mi et al., 2003; Chen Y. et al., 2014):

To determine the green leaf area at the silking stage and 10, 20, 30, 40, and 50 days after silking (DAS), leaf length (L, cm), and maximum width (W, cm) were measured to calculate green leaf area (Montgomery, 1911) and leaf area index (LAI).

Direct N₂O emission (kg N ha^-1), NH₃ volatilization (kg N ha^-1), and NO₃^- leaching (kg N ha^-1) were calculated using the methods of Cui et al. (2013).

X is the N application rate (kg N ha^-1). The indirect N₂O emissions can be estimated by following the IPCC methodology (IPCC, 2006) where 1 and 0.75% of the volatilized N-NH₃ and leached N-NO₃ is lost as N₂O-N. Using the above N loss-N input response curve, we calculated the direct, indirect, and total N₂O emissions (kg N ha^-1), and N₂O emission intensity (N₂O emission per unit maize yield, kg N Mg^-1).

Total greenhouse gas emissions (kg CO₂ eq; including CO₂, CH₄, and N₂O) during the life cycle of maize production are represented in three components: emissions during N fertilizer application; emissions during N fertilizer production and transportation; and emissions during the production and transportation of P and K fertilizer, and pesticides, and diesel fuel use in farming operations such as sowing, tilling, and harvesting. Components were calculated according to the methods of Cui et al. (2013).

EF in the equation 14 is coefficient of greenhouse gas emissions. The values of EF_p, EF_k, EF_pest., EF_fuel., and EF_elec. were 0.79, 0.55, 19.13, 3.75, and 1.14 kg CO₂ eq per unit input, respectively. The value of Pest_.input and Fuel_.input were estimated to be 4.13 and 72.7 kg ha^-1, respectively. We then calculated the total greenhouse gas emission (also known as global warming potential, kg CO₂ eq ha^-1) and greenhouse gas intensity (kg CO₂ eq Mg^-1).

At the time of harvest, maize GY (14% water content) was measured within a randomly selected 7.2 m² sub-plot (4 m × 1.8 m) in each plot. Kernel number was measured on 10 randomly selected ears from each plot. Thousand-kernel weight (TKW) was determined after drying thousand-kernel samples at 80°C in a forced-draft convention oven to a constant weight.

The effects of the treatments and years on the measured parameters [including GY, N utilization, N₂O emission intensity, and greenhouse gas intensity] were evaluated using univariate analysis of variance (ANOVA) procedures. After verifying the homogeneity of error variances, all the data across planting densities and N application rates were pooled for use in the ANOVA. Differences were compared using the least significant difference test (LSD) at a 0.05 level of probability. All analyses were conducted using SPSS 17.0 (SPSS Inc., Chicago, IL, United States).

Grain yields and yield components were significantly affected by planting density, N application rate, and the interaction of planting density × N application rate (Table 1 and Supplementary Figure S1). As planting density increased from 67,500 to 90,000 plants ha^-1, GY was significantly increased by 7% (from 9,556.5 to 10,184.5 kg ha^-1) across years and N application rates. No significant difference in GY was observed between N180 and N360 treatments across years and two densities (Table 1).

Increased planting density produced a significant 23% increase of average ear number; kernel number and TKW displayed significant decreases of 7 and 4%, respectively (Table 1). No significant differences in the three yield components were observed between N180 and N360 treatments.

Planting density, N application rate, and the interaction of planting density × N application rate had a significantly influence on NUE, AEN and PFP_N (Table 2 and Supplementary Figure S2). As planting density increased from 67,500 to 90,000 plants ha^-1, NUE, AEN, and PFP_N significantly increased by 4, 25, and 9%, respectively. Across years and planting densities, the average NUE was ranked in the following order: 44.4 kg kg^-1 for N180 > 41.8 kg kg^-1 for N360 > 32.5 kg kg^-1 for N0. The AEN and PFP_N in N180 were 24.7 and 63.0 kg kg^-1, respectively, which displayed significant increases of 96 and 99%, respectively, compared to N360 (Table 2).

Planting density and N application rate had a significant influence on N accumulation at silking and harvest, and the N distribution ratio at the time of harvest (Tables 3, 4).

As planting density increased from 67,500 to 90,000 plants ha^-1, N accumulation at silking and harvest of summer maize were significantly increased by 11 and 3%, respectively, across years and N applying rates. At silking, a planting density of 90,000 plants ha^-1 displayed increases in N accumulation in leaf + husk and stalk + cob of 8 and 16%, respectively, relative to a summer maize planted at a density of 67,500 plants ha^-1. At harvest, the higher planting density resulted in significantly increased N accumulation in grains, however, the N accumulation in leaf + husk and stalk + cob were decreased by 4 and 5%, respectively (Tables 3, 4).

Across years and planting densities, we observed increased total N accumulation at silking, N accumulation in each organ at silking, total N accumulation at harvest, and N accumulation in each organ at harvest with increasing N application rates (Tables 3, 4).

Planting density, N application rate, and the interaction of planting density × N application rate significantly influenced N remobilization and N remobilization efficiency from vegetative organ to grain after silking (Table 4).

N remobilization of total, leaf + husk, and stalk + cob was increased by 34, 21, and 39% as planting density increased from 67,500 to 90,000 plants ha^-1, respectively; in addition, N remobilization efficiency of total, leaf + husk, and stalk + cob was also increased by 21, 13, and 41%, respectively (Table 4). No significant differences in N remobilization of total, leaf + husk, and stalk + cob were observed between N180 and N360 treatments. However, N remobilization efficiency of total, leaf + husk, and stalk + cob in N360 treatment was decreased by 2, 11, and 5% relative to summer maize of N180 treatment (Table 4).

Pre-silking, post-silking, and total DMA were significantly affected by planting densities and N application rates (Table 5 and Supplementary Figure S3).

With the higher planting density, the pre-silking, post-silking, and total DMA were significantly increased by 11, 4, and 6%, respectively, across years and N application rates. The post-silking and total DMA were significantly increased by N application, but we observed no significant differences in pre-silking, post-silking, and total DMA when comparing N180 and N360 treatments (Table 5). In addition, significant positive correlations were observed between N accumulation and DMA at harvest in both planting densities (Figure 2).

The LAI of maize gradually decreased after silking. The LAI after silking in N360 treatment was always higher than that in N180 treatment under both planting densities. Given the same N application rate, the LAI in planting density of 90,000 plants ha^-1 was always higher (Figure 3). In addition, significant negative correlations were observed between N remobilization efficiency and LAI at harvest in both planting densities (Figure 4).

N₂O emission intensity and greenhouse gas intensity were both strongly affected by planting density, N application rate, and the interaction of planting density × N application rate (Table 6 and Supplementary Figure S4).

As planting density increased from 67,500 to 90,000 plants ha^-1, the direct, indirect, and total N₂O emission intensity were significantly decreased by 7, 8, and 7%, respectively, across years and N application rates. The direct, indirect, and total N₂O emission intensity were significantly increased by N application. The direct, indirect, and total N₂O emission intensity in N360 treatments were significantly increased by 182, 198, and 187%, respectively, relative to the N180 treatment (Table 6). The higher planting density also produced significantly lower (4%) greenhouse gas intensity across years and N application rates. Greenhouse gas intensity significantly increased with N application; we observed a significant increase of 86% in greenhouse gas intensity in the N360 treatment compared to the N180 treatment (Table 6).

Selecting high-yield maize varieties that are tolerant of high planting densities has become an increasingly popular field of research for breeders (Troyer and Rosenbrook, 1983; Tollenaar and Lee, 2002). Previous studies have reported that increases in maize yields are mainly dependent on the breeding of high-yield varieties and high planting densities (Tokatlidis et al., 2011; Van Ittersum and Cassman, 2013). In this study, GY was significantly higher at a planting density of 90,000 plants ha^-1 (Table 1 and Supplementary Figure S1), which is much higher than the planting densities typically employed by local farmers (<60,000 plants ha^-1; Chen et al., 2009) and more comparable to planting densities commonly used in North America (>80,000 plants ha^-1; Lee and Tollenaar, 2007). However, the kernel number and TKW were decreased (Table 1), which was in agreement with most previous studies (Andrade et al., 2002; Borrás et al., 2004). Under high planting density, interplant competition for resources is exacerbated, which produces a lower number of kernel per ear and lower TKW (Tollenaar et al., 2006; Boomsma et al., 2009); GY increases are attributable to the increased number of ear per area (Grassini et al., 2011; Van Ittersum and Cassman, 2013). Thus, for GY, the positive effects of high planting densities surpassed the negative effects of interplant competition. Improving kernels per ear and TKW are two potential paths to increase maize yields in high planting density conditions in the future.

Nitrogen can affect crop yields through its influence on the yield components (kernel per ear, TKW, and ear per unit area; Raun and Jhonson, 1999; Van Ittersum and Cassman, 2013). In this study, the GY and yield components were significantly increased by the application of N (N180 and N360 kg N ha^-1); however, we observed no significant differences in maize GY and yield components between N180 and N360 kg N ha^-1 treatments (Table 1). These observations are consistent with previous studies demonstrating that the response of maize GY to increasing N apply followed a parabolic curvilinear relationship (Cui et al., 2009; Meng et al., 2013). Previous studies have demonstrated that the metabolism of N and carbon in plants are affected by the activity of nitrate reductase (NR) and sucrose phosphate synthetase (SPS; Lawlor and Cornic, 2002; Shen et al., 2007). The activity of these two enzymes shows an increasing trend with increased N applications within a certain range, thus, they enhance the accumulation of photoproduct and transshipment; however, the activity of SPS decreases when the N is excessively applied, which can explain observed decreases in the number of kernel per ear and TKW (Shen et al., 2007; Li et al., 2012), leading to low GY (Table 1 and Supplementary Figure S1).

Nitrogen utilization can be increased by better-integrated agronomic management practices, such as fertilizing and crop cultivation techniques, which can better ensure maximized crop production and N efficiency (Chen et al., 2006; Cui et al., 2009). Our results demonstrated that high NUE, AEN, and PFP_N are obtainable through increased planting density (from 67,500 to 90,000 plants ha^-1) or decreased N applications (from 360 to 180 kg N ha^-1; Table 2 and Supplementary Figure S2). Using the same N application rate, the highest NUE, AEN, and PFP_N values were obtained with a planting density of 90,000 plants ha^-1; using the same planting density, the highest NUE, AEN, and PFP_N values were both obtained in the N180 treatment. The highest NUE, AEN, and PFP_N values among the six treatments were obtained at a planting density of 90,000 plants ha^-1 with an N application rate of 180 kg N ha^-1 (Supplementary Figure S2), which is comparable to the recommended high-yield maize in China (100,000 plants ha^-1 with 237 kg N ha^-1; Chen et al., 2011) and in Nebraska, United States (75,000 plants ha^-1 with 183 kg N ha^-1; Grassini et al., 2011).

For N absorption, the correlation analysis indicated that N accumulation had a significant and positive relationship with DMA (Figure 2). This is consistent with previous studies that demonstrated that N-uptake and DMA improved simultaneously (Liu et al., 2014). In this study, DMA was greater with higher planting density and N application rates (Table 5). Interplant competition at high density contributes to reduced DMA per-plant (Tollenaar et al., 2006; Boomsma et al., 2009). However, maize biomass production at 90,000 plants ha^-1 treatment increased under field level in the present study (Table 3), which is consistent with previous results of Lee and Tollenaar (2007) who found that higher biomass accumulations were obtained at relatively higher densities (75,000–90,000 plants ha^-1), thus, a high rate of N-uptake was observed in the positive relation between N accumulation and DMA. In addition, higher N concentration and accumulation were mainly due to higher N application rates (Liu et al., 2014). Not surprisingly, higher N accumulation was observed with a planting density of 90,000 plants ha^-1 and the N360 treatments in this study.

Regarding N-transfer, we observed a decreased efficiency in N remobilization from vegetative organs to grains with increased rates of N, and N remobilization and N remobilization efficiency improved under the higher planting density of summer maize (Table 4). Previous researchers indicated that 33–65% of N concentrated in grains comes from N remobilization that was stored in vegetative organs before silking (Ciampitti and Vyn, 2013; Kosgey et al., 2013), especially the leaves, which contributed up to 45–65% (Chen Y. et al., 2014); N remobilization and N efficiency in our study were within those ranges, respectively (Table 4). Previous studies showed that high N application rates (e.g., 300 and 400 kg N ha^-1) contributed to the high N uptake capacity but low N remobilization efficiency because the leaves always maintained a “stay-green” state (Lee and Tollenaar, 2007; Ciampitti and Vyn, 2012). The negative correlation between N remobilization efficiency and LAI in this study reinforces the above conclusion (Figure 4). However, under relatively high planting densities (e.g., 90,000 plants ha^-1 in this study), the N application for each plant was relatively low, and thus the N was not available in excess for each plant.

Global N fertilizer consumption is expected to reach 250 Mt yr^-1 by 2050 (Tilman et al., 2011), which will lead to massive releases of greenhouse gas, water pollution, and other major environmental problems (Tilman et al., 2011; Lu and Tian, 2013). The future of agricultural production not only needs sustainable yield increases, but it must also limit environmental harm caused by excessive N application (Cui et al., 2013; Chen X. et al., 2014). We observed total N₂O emissions of was 1.99 and 5.74 kg N ha^-1 in the recommended N management practice (N180; Liu et al., 2003) and the traditional N dose (N360) treatments, respectively; this also confirmed that excessive N fertilizer applications can lead to substantial fertilizer N losses with N entering ecosystems through nitrification-denitrification processes (Robertson and Vitousek, 2009; Sutton et al., 2011). The emission factor was 1.10% in N180 in our study, which was comparable to the 1.20% estimated by Cui et al. (2013) and 1.06% estimated by Linquist et al. (2012). The N180 treatment achieved similar GY with a 62% reduction in N₂O emission intensity and a 46% reduction in greenhouse gas intensity compared to the N360 treatment (Table 6); we attributed this result to competitive GY. In addition, the 7% reduction in N₂O emission intensity and a 4% reduction in greenhouse gas intensity in crops at a planting density of 90,000 plants ha^-1 compared to 67,500 plants ha^-1 were also attributed to the improved crop yields achieved through higher planting densities.

In the present study, compared with farmer practice, the labor costs in comprehensive management practice (increasing planting density and reducing N application) was increased, however, the N input was decreased with higher GY. In brief, the annual profit in comprehensive management practice increased by ¥ 503 per ha compared with farmer practice. In actual maize production, field demonstrations of the revised fertilizer regime could be used to validate the research findings and be used to train farmers to ensure uptake of the new recommendations of best practice.