In this study, the increase in crop yield and land productivity with maize-soybean relay intercropping was confirmed. The LER of the maize-soybean relay intercropping varied from 1.85 to 2.36 during the cropping seasons (Table 1). Results were similar for summer soybean-spring maize relay intercropping with an increase in land output and an LER of the relay intercropping that varied from 1.38 to 1.59 . In the U.S., the total grain yield is higher in winter wheat-spring soybean relay intercropping than that with monoculture , and in China, the LER of winter wheat-spring cotton relay intercropping ranged from 1.20 to 1.53 . Interspecific competition for nutrient resources is well known to affect crop growth and grain yield in intercropping systems [7, 17, 25, 26]. Numerous studies show that belowground interactions and competition for nutrients play a key role in intercropping and relay intercropping [6, 13, 22, 30]. Lv et al. demonstrated that competition for nutrients is more important than aboveground competition for light in maize-soybean intercropping . By contrast, Yang et al. found no difference in yield between treatments in which roots were separated or not in maize-soybean relay intercropping . The different conclusions may be the result of the difference in coexistence periods, because the component crops in intercropping have a longer coexistence period than that in relay intercropping; therefore, the following crop in relay intercropping can benefit from the longer recovery period. In this study, the complementary ecological niches of crop roots were advantageous to aboveground growth in the maize-soybean relay intercropping system (Figs 4 and 5; Tables 1 and 2, S1 and S2 Tables). The separation of root ecological niches in intercropping systems avoids interspecific competition for nutrients; for example, the total yield of the maize/fava bean intercropping system was significantly higher than that of the wheat/fava bean intercropping system . During the coexistence period, maize was at the grain-filling stage, whereas soybean seedlings were at the stage with 3 fully developed trifoliate leaves. Maize roots rapidly proliferated underneath the maize plants in the soil top layer (0–40 cm) in relay intercropping compared with that in monoculture. The roots of soybean seedlings were insufficiently developed and primarily distributed underneath the soybean plants. However, after maize harvest (at the full-bloom stage of soybean), the soil volume occupied by soybean roots was similar between relay intercropping and monoculture, likely caused by the changes in root distribution and morphologies in space and time in relay intercropping systems . In previous studies, crop roots show plasticity in response to soil nutrients and the distribution of water. With maize growth, the roots of maize extended to the soybean strip and proliferated underneath soybean . When roots of component crops intermingle with one another, the preceding crop suppresses the growth of roots and decreases the shoot biomass of the following crop . However, with the regrowth of roots of the following crop after harvest of the preceding crop, and fertilizer use efficiency increases, ultimately increasing the grain yield of the following crop [6, 13]. Thus, an optimized root system is advantageous in the acquisition of soil nutrients and provides sufficient nutrition for plant shoot growth.