## 2 Materials and Methods  
### Study Site, Field Experimental Design and Management Practices  
The field experiment was carried out in 2017 and 2018 at the Dryland Farming and Water-saving Station of Hebei Academy of Agricultural and Forestry Sciences in Henghui (Hebei, China: latitude 37\({}^{\circ}\)44\({}^{\prime}\) N, longitude 115\({}^{\circ}\)42\({}^{\prime}\) E, elevation 20 m above sea level). The study area has a warm-temperate sub-humid continental monsoon climate with an annual mean temperature of 13.3 \({}^{\circ}\)C and annual precipitation of 487 mm from 1980-2019, with 76% falling in June-September. The monthly precipitation totals and mean air temperature during experimental years (2017-2018) and the 40-yr average (1980-2019) are shown in Figure 1. Cumulative precipitation during silage corn growing season from June through September totaled 324 mm in 2017 and 339 mm in 2018, which were generally below 40-yr normal (365 mm). The 2017 season was the wetter year with a total rainfall amount of 521 mm, and there was a considerable amount of rainfall in October (149 mm) after corn harvesting. The precipitation in 2018 (502 mm) was more concentrated in growing seasons from March through August, with a pronounced peak (202 mm) in August. Mean monthly air temperature of the corn growing period from July through September was 0.3 \({}^{\circ}\)C and 0.5 \({}^{\circ}\)C higher than the 40-yr average in 2017 and 2018, respectively. The soil was a silt loam with pH of 7.75, organic matter of 14.4 g kg\({}^{-1}\), alkali-hydrolyzable N of 74.0 mg kg\({}^{-1}\), soil available phosphorus of 19.4 mg kg\({}^{-1}\), soil available potassium of 202.1 mg kg\({}^{-1}\) within the top 20-cm soil. The soil of the study site was relatively rich in nutrients and it can represent the local level of medium and high yield fields. The preceding crop was sorghum-sudangrass grown with an annual N application rate of 250 kg N ha\({}^{-1}\) from 2012-2016. The field experiment was established in March 2017. Alfalfa-silage corn intercropping system (AC) with four N application rates (whole-plot factor) and three corn plant densities (sub-plot factor) were assigned according to split-plot design with three replications. Monocultured corn (CK) managed according to local farmers' practices was included in one whole plot per replicate as a control. The subplot size was 40 m\({}^{2}\) (5 m \(\times\) 8 m) with 1.5 m walkways to separate subplots. For the alfalfa-silage corn intercropping system, a local variety of alfalfa \"Zhongmu number 1\" mixed with rhizobia was sown with a drill on March 16, 2017 in the seeding rate of 22.5 kg ha\({}^{-1}\). An alternating row spacing of 20-40-20-40 cm was employed. After the alfalfa harvest in mid-June, a summer dual-purpose corn hybrid (Zhengdan 958) was drilled into the 40 cm wide gap between alfalfa rows at plant densities of 30,000 (D30), 45,000 (D45), 60,000 (D60) plants per hectare. Urea (46% N) was broadcasted by hand after corn sowing at 0 (N0), 60 (N60), 120 (N120), and 180 (N180) kg N ha\({}^{-1}\). To eliminate phosphorus and potassium limitation, all plots of AC received 100 kg P\({}_{2}\)O\({}_{5}\) ha\({}^{-1}\) as granular superphosphate and 100 kg K\({}_{2}\)O ha\({}^{-1}\) as potassium sulfate before alfalfa seeding in 2017 by broadcasting and after corn seeding in 2018 by side dressing. Corn monoculture control was managed using the local farmers' current management practices and rotated with winter wheat. The variety \"Zhengdan 958\" was planted on the same day as corn seeding in AC with a plant density of 75,000 plants ha\({}^{-1}\). The row spacing was also 60 cm. A total of 112 kg N ha\({}^{-1}\), 112 kg P\({}_{2}\)O\({}_{5}\) ha\({}^{-1}\) and 112 kg K\({}_{2}\)O ha\({}^{-1}\) was broadcasted by hand as NPK compound fertilizer (15:15:15) after corn sowing. Silage corn was harvested between 1 October to 5 October each year with a stubble of 10 cm.