Strip-width determines competitive strengths and grain yields of intercrop species in relay intercropping system

Maize/soybean relay intercropping system (MSR) is a popular cultivation method to obtain high yields of both crops with reduced inputs. However, in MSR, the effects of different strip widths on competitive strengths and grain yields of intercrop species are still unclear. Therefore, in a two-year field experiment, soybean was relay-intercropped with maize in three different strip-width arrangements (narrow-strips, 180 cm; medium-strips, 200 cm; and wide-strips, 220 cm), and all intercropping results were compared with sole maize (SM) and sole soybean (SS). Results showed that the optimum strip-width for obtaining high grain yields of maize and soybean was 200 cm (medium-strips), which improved the competitive-ability of soybean by maintaining the competitive-ability of maize in MSR. On average, maize and soybean produced 98% and 77% of SM and SS yield, respectively, in medium-strips. The improved grain yields of intercrop species in medium-strips increased the total grain yield of MSR by 15% and land equivalent ratio by 22%, which enhanced the net-income of medium-strips (by 99%, from 620 US $ ha−1 in wide-strips to 1233 US $ ha−1 in medium-strips). Overall, these findings imply that following the optimum strip-width in MSR, i. e., strip-width of 200 cm, grain yields, and competitive interactions of intercrop species can be improved.

Intercropping or mixed cropping systems are mostly practiced with a low degree of mechanization, especially in developing countries 1 . Therefore, these cropping systems are under pressure due to the scarcity of rural labor and low labor income from farming activities 2 . Mechanization can increase the total profit of these systems, and it could be a solution to the less availability of rural labor for farming activities. However, for mechanization, we need to change or replace the current intercropping designs, which are in practice by farmers (e.g., Fig. 1). For instance, strip intercropping systems can be used with optimum-strip widths (i.e., wider-strips could be designed that are wide enough for the use of machinery). Nevertheless, the use of wider-strips in intercropping systems will raise the question of whether strip intercropping systems are advantageous over sole cropping systems or not? Therefore, it is important to determine the optimum-strip width, which can increase the crop yields of intercrop species and provide enough space for the use of machines in intercropping systems.
Generally, in intercropping systems, two crops are planted at an appropriate row spacing, allowing positive interactions between different species. These include the benefits of mutual interactions between adjacent allospecific plants, e. g., facilitation in water and nutrient uptake, which are maximized 3,4 . Several studies tested wider-strip widths and revealed that intercropping systems with wider-strips of 3 m 5 , 3.1 m 6 , 3.3 m 7 , 3.4 m 8 , and 6 m 9 achieved the highest LER compared to narrow-strips. Therefore, intercropping of crops with larger operating strips would be easier to manage with existing farm machinery, and it will produce high profits for farmers. In contrast, recent research revealed that the optimum-strip width to obtain the maximum benefits of intercropping is 1 m, and if the strip width increased from 1 m, the benefits of intercropping decreased 10,11 . Similarly, the land equivalent ratio (LER) of maize/common bean intercropping system was decreased from 1.55 to 1.27 when the row ratio was increased from 2:2 (two rows of maize with two rows of common bean) to 5:5 (five rows of maize with five rows of common bean), as strip width increased 12 . These results reinforce the concerns mentioned above Table 1. Effect of different strip-width treatments on photosynthetically active radiation transmittance (PAR-transmittance) of soybean canopy at the fifth trifoliate stage (V5), seventh trifoliate stage (V7), and flower initiation stage (R1) in cropping seasons from 2012 to 2013. Treatment codes represent narrow-strips (T 1 , 180 cm); medium-strips (T 2 , 200 cm); and wide-strips (T 3 , 220 cm) in maize/soybean relay intercropping system. SS is the sole cropping system of soybean. Means are averages over three replicates ± standard error of the mean. Means that do not share the same letters in a column differ significantly at p ≤ 0.05 using least significant differences, calculated separately for each year. Grain yield. Different inter-row spacing treatments (T 1 , T 2 , and T 3 ) significantly (P < 0.05) affected the grain number (plant −1 ), grain weight (mg), and grain yield (kg ha −1 ) of soybean and maize in MSR, and both crops always produced the maximum grain number, grain weight, and grain yield in SS and SM (Table 5). However, among T 1 , T 2 , and T 3 , the average highest grain number (79.9 plant −1 and 522 plant −1 ) of soybean and maize was recorded in T 2 and T 1 , respectively; while the mean maximum (206.8 mg and 230.3 mg) seed weight of soybean and maize was noticed in T 2 treatment. In this study, the average across the years, relay-cropped soybean achieved 52% in T 1 , 77% in T 2 , and 57% in T 3 of sole soybean grain yield, and relay-cropped maize achieved 98% in T 1 , 98% in T 2 , and 87% in T 3 of sole maize grain yield. The grain yield of soybean exhibited the trend SS > T 2 > T 3 > T 1 . The grain yield of maize demonstrated the trend SM > T 1 ≥ T 2 > T 3. Furthermore, the mean maximum (8429.4 kg ha −1 ) and minimum (7306.8 kg ha −1 ) total grain yield (soybean grain yield + maize grain yield) of maize/soybean relay intercropping system were obtained in treatments T 2 and T 3 , respectively. Overall, the total grain yield of maize/soybean relay intercropping system showed the trend T 2 > T 1 > T 3 , suggesting that grain yields of both intercrop species were maximized when both crops complement each other with an optimum inter-row spacing (i. e., T 2 ) between soybean and maize rows in MSR (Table 5). Table 3. Effect of different strip-width treatments on dry matter of soybean at fifth trifoliate stage (V5), seventh trifoliate stage (V7), and flower initiation stage (R1) in cropping seasons from 2012 to 2013. Treatment codes represent narrow-strips (T 1 , 180 cm); medium-strips (T 2 , 200 cm); and wide-strips (T 3 , 220 cm) in maize/soybean relay intercropping system. SS is the sole cropping system of soybean. Means are averages over three replicates ± standard error of the mean. Means that do not share the same letters in a column differ significantly at p ≤ 0.05 using least significant differences, calculated separately for each year.  Table 4. Effect of different strip-width treatments on photosynthetic characteristics of soybean at fifth trifoliate stage (V5), seventh trifoliate stage (V7), and flower initiation stage (R1) in cropping seasons from 2012 to 2013. Treatment codes represent narrow-strips (T 1 , 180 cm); medium-strips (T 2 , 200 cm); and widestrips (T 3 , 220 cm) in maize/soybean relay intercropping system. SS is the sole cropping system of soybean. Means are averages over three replicates ± standard error of the mean. Means that do not share the same letters in a column differ significantly at p ≤ 0.05 using least significant differences, calculated separately for each year. 2012 T 1 6.9 ± 0.1c 8.4 ± 0.1c 11.1 ± 0.1d 3.3 ± 0.0d 3.6 ± 0.0d 5.0 ± 0.0d 0.3 ± 0.0c 0.5 ± 0.0d 0.6 ± 0.0c 285.0 ± 1.0a 309.0 ± 1.3a 321.9 ± 1.9a T 2 11.2 ± 0.1b 14.1 ± 0.2b 17.7 ± 0.3c 4.9 ± 0.1c 6.0 ± 0.1c 6.9 ± 0.1c 0.6 ± 0.0b 0.7 ± 0.0c 0.8 ± 0.0b 246.4 ± 1.7b 264.7 ± 1.6b 274.0 ± 1.5b T 3 11.1 ± 0.1b 13.9 ± 0.2b 16.9 ± 0.3b 4.7 ± 0.0b 5.8 ± 0.0b 6.7 ± 0.1b 0.5 ± 0.0b 0.6 ± 0.0b 0.8 ± 0.0b 243.5 ± 2.6b 261.4 ± 4.0b 271.9 ± 1.5b SS 14.0 ± 0.1a 16.7 ± 0.2a 20.6 ± 0.5a 6.0 ± 0.0a 6.5 ± 0.1a 8.5 ± 0.0a 0.7 ± 0.0a 0.8 ± 0.0a 0.9 ± 0.0a 214. www.nature.com/scientificreports/ Land equivalent ratio and competition ratio. The mean land equivalent ratio values in T 1 , T 2 , and T 3 treatments in maize/soybean relay intercropping system were higher than the one regardless of inter-row spacing treatments, indicating the yield and land advantage over sole maize and sole soybean ( Table 6). Among all inter-row spacing treatments in MSR, the maximum LER was 1.76 in the T 2 , whereas the minimum LER was 1.44 in the T 3 , across two years. Among the three MSR treatments, the LER was highest at the inter-row spacing of 60 cm (T 2 ) (Table 6). Similarly, the competition ratio values of intercrop species followed the same trend with LER values of T 1 , T 2 , and T 3 treatments in MSR (Table 6). Averaged across the years, the competition ratio values of maize (2.01 in T 1 , 1.29 in T 2 , and 1.53 in T 3 ) were found higher than the competition ratio values of soybean (0.55 in T 1 , 0.81 in T 2 , and 0.66 in T 3 ). However, with the medium inter-row spacing (i. e., T 2 ), the competition ratio value of soybean plants significantly increased; for example, the competition ratio values of soybean were improved by 45% and 22% in T 2 treatment compared to T 1 and T 3 , respectively, suggesting the complementarity effect between maize and soybean in medium-strips.
Economic analysis. Economic analysis for soybean and maize production under maize/soybean relay intercropping systems and sole cropping systems is shown in Table 7. The highest total income (1593 US $ ha −1 in 2012 and 873 US $ ha −1 in 2013) was obtained in treatment T 2 under MSR, while the lowest total income (521 Table 5. Effect of different strip-width treatments on grain number, grain weight, grain yields of maize and soybean, and the total grain yield of maize/soybean relay intercropping system in cropping seasons from 2012 to 2013. Treatment codes represent narrow-strips (T 1 , 180 cm); medium-strips (T 2 , 200 cm); and wide-strips (T 3 , 220 cm) in maize/soybean relay intercropping system. SS is the sole cropping system of soybean, and SM is the sole cropping system of maize. Means are averages over three replicates ± standard error of the mean. Means that do not share the same letters in a column differ significantly at p ≤ 0.05 using least significant differences, calculated separately for each year. NS non-significant.

Years Treatments
Grain number (plant −1 ) Grain weight (mg) Grain yield (kg ha −1 )  Table 6. Effect of different strip-width treatments on competition ratios and land equivalent ratios (LER) of maize and soybean in cropping seasons from 2012 to 2013. Treatment codes represent narrow-strips (T 1 , 180 cm); medium-strips (T 2 , 200 cm); and wide-strips (T 3 , 220 cm) in maize/soybean relay intercropping system. Means are averages over three replicates ± standard error of the mean. Means that do not share the same letters in a column differ significantly at p ≤ 0.05 using least significant differences, calculated separately for each year. NS non-significant.

Years Treatments
Competition ratio (%) Land equivalent ratio

Discussion
The main objective of this study was to test three hypotheses: the first hypothesis (soybean produces a lower grain yield when grown in narrow-strips under MSR) was strongly confirmed by our data. Soybean grain yield was significantly lower in narrow-strips (T 1 ) than medium-(T 2 ) and wider-strips (T 3 ) under MSR. The second hypothesis (increasing inter-row spacing in MSR would increase the grain yield of soybean without affecting the maize grain yield) was partially confirmed by the data. Compared to narrow-strips in MSR, the medium-strips had a significantly higher soybean grain yield, and it did not decrease the maize grain yield, while the wider-strips produced significantly lower soybean and maize grain yield in MSR. The third hypothesis (the wider-strips would be more productive and beneficial in increasing the benefits of intercropping systems than narrow-strips) was also partially confirmed by the data. Relative to narrow-strips in MSR, both intercrops showed more complementarity effect in medium-strips, which ultimately enhanced the land productivity (high LER value) and total income of the system, whereas the wider-strips significantly reduced the intercropping benefits by decreasing the LER value and total income of MSR. Overall, these results suggest that wider-strips are not favorable for obtaining maximum benefits of intercropping systems.
Photosynthetically active radiation transmittance. In this study, the leaf area index, photosynthetic rate, and dry matter accumulation of soybean were significantly affected by changing the inter-row spacing in MSR, which might be directly linked with the availability of PAR-transmittance at soybean canopy, because soybean is a C3 crop and sensitive to shade 23 . In all inter-row spacing treatments in MSR, maize intercepted more solar radiation due to its higher leaf area and height compared to soybean during the co-growth phase 26 , which significantly enhanced the competitive ability of maize. However, increasing the inter-row spacing from 50 to 60 cm (T 2 ) significantly improved the leaf area index, photosynthetic rate, and dry matter accumulation of soybean, suggesting that the PAR-transmittance of relay-cropped soybean is dependent on the inter-row spacing in MSR. Another possible reason for this improvement in PAR-transmittance of soybean canopy is that maize foliage in T 2 treatment occupied less row space, leaving a wide-open space for PAR to penetrate at soybean canopy, while in T 1, maize leaves filled the most of the row space, leaving a narrow opening for PAR-transmittance at soybean canopy. Consequently, the soybean plants received more PAR-transmittance in T 2 compared to that of in treatment T 1 . These results are in agreement with the previous findings in which researchers have revealed that the spacing of 60 cm between the rows of intercrop species significantly reduced the maize shade by allowing more sunlight to penetrate to the soil surface 22 . Overall, these results exhibit that the selection of appropriate inter-row spacing is critical in improving the PAR-transmittance of soybean in MSR.
Land use advantages. In relay intercropping systems, component crops have a comparatively short cogrowth phase than in intercropping systems 32 . In these systems, interspecific-interactions during the co-growth phase determine the recovery growth and yield of late-maturing crops 33 . The medium inter-row spacing in MSR reduced the maize shade on the soybean canopy. It improved the initial growth and development of relaycropped soybean in MSR, demonstrating the enhanced competitive ability of soybean by maintaining the competitive ability of maize in T 2 than T 1 and T 3 treatments. This improved ability could help soybean to reduce the adverse impacts of interspecific competition for light 23 , water 4 , and nutrients 19 in MSR. For instance, Raza et al. (2019) estimated that soybean accumulated 26% higher total major-nutrients in the medium inter-row spacing system than the narrow inter-row spacing system of MSR, explaining the reason for the soybean yield gain of the T 2 system over T 1 system 18 . Furthermore, compared to narrow-strips (T 1 ), the extra growing space of 10 cm on both sides of the soybean rows with the optimum plant to plant spacing leads to a temporal niche differentiation, which relaxes competitive interactions, especially during the co-growth phase in MSR. However, in wider-strips (T 3 ), the intra-specific competition for available resources increased due to the reduced plant to plant spacing among soybean and maize plants, which resulted in a disadvantage of yield and land equivalent  T 1  2820  2903  3402  3592  583  689  636   T 2  2820  2903  3971  4015  1152  1112  1132   T 3  2820  2903  3509  3667  690  764  727   SS  1725  1776  2396  2249  671  472  572   SM  1696  1747  2296  2316  599  569  584 Scientific Reports | (2020) 10:21910 | https://doi.org/10.1038/s41598-020-78719-y www.nature.com/scientificreports/ ratio in MSR. Additionally, a reduced distance between soybean plants in wider-strips increased mutual shading within soybean plants, which in turn increased the lodging rate and decreased the seed yield of soybean plants, especially under the intercropping systems. Another possible reason for lower grain yield and competitive ability of intercrop species in wider strips was related to an apparent lack of complementarity between soybean and maize in MSR, partially caused by the complete temporal overlap of intercrop species, which results in intense intra-specific competition between soybean and maize and limited opportunity for complimentary resource capture in time. These results are in line with the results of wheat/chickpea intercropping 34 , maize/soybean intercropping 35 , and maize/common bean intercropping systems 12 , where the yields of intercrop species and intercropping advantages decreased as the strips become wider 11 . Interspecific interactions (above-or below-ground) played a significant role in increasing or decreasing the resource use efficiency of intercrop species, e. g., increasing the inter-row spacing from 50 to 60 cm enhanced the radiation use efficiency of soybean by 15% and maize by 4% 26 . Although, in this study, we did not measure the effect of intercropping on water use of intercrop species in MSR; however, in a previous study (Rahman et al., 2017), it has been confirmed that maize and soybean utilized water more efficiently in medium-strips compared to the maize and soybean plants in narrow-strips in MSR 4 . Similarly, the inter-row spacing of 60 cm in MSR improved the uptake of nitrogen (by 25%), phosphorus (by 33%), and potassium (by 24%) in soybean compared to the inter-row spacing of 40 cm in MSR through the efficient exploitation of the biological potential for nutrient acquisition 22 . In wheat-fababean intercropping system, wheat roots uptake more nitrogen than faba bean from the rhizosphere and decrease the availability of nitrogen for fababean, which increased the percentage of nitrogen fixation in fababean 36 . All these findings revealed that the intercrop species achieved higher values of LER when they planted at an appropriate (e. g., a strip width of two meters) inter-row spacing in intercropping systems, where both crops can facilitate and complement each other in a positive way 23,32 . Moreover, the present results indicate that the higher contributions of soybean yield to MSR yield in T 2 can be attributed to below-ground (nutrients and water) and above-ground (sunlight) complementary resource use between intercropped species in MSR; because T 2 compared to T 1 and T 3 substantially enhanced the competitive ability and yield of soybean without negatively affecting the competitive ability and yield of maize 23 . In previous studies, researchers have tested the strip width of two meters or less than two meters, and they concluded that the intercropping systems achieved the highest LER values in two meters or less than two meters strip 8,13,21,[37][38][39] . Consistent with all these reports, the results of our findings indicate that the strips of two meters (T 2 ) in MSR have an advantage in utilizing the resources (i. e., light and land) more efficiently than narrow-strips (T 1 ) and wider-strips (T 3 ). Nevertheless, the strips of two meters wide in intercropping systems are still narrow compared with that of machinery operated by farmers in large scale mechanized agriculture. Consequently, with the current large machinery, it is not easy to obtain the claimed advantages and benefits of intercropping in strips of two meters or less. Taken together, these results emphasize the previously specified issues that intercropping systems will become less attractive to farmers, especially in developing countries, because they want to replace the labor with machinery. Therefore, we need to bring significant changes in the current farm machinery, which can be operated in strips of two meters in intercropping and relay intercropping systems.

Economic feasibility.
A recent case study on the effects of strip width management in relay intercropping systems revealed that the inter-row spacing in relay intercropping systems contributed substantially to produce high crop yields and LER, especially in systems combining C4 and C3 species 11 . Their simulations showed that the relay intercropping systems with narrow-strips (strips of two meters or less) achieved high LER, and the benefits of relay intercropping systems decreased with wider-strips. Similarly, in our study, the highest LER and net income were obtained in treatment T 2 compared to T 1 and T 3 treatments. This improvement in LER and net income were mainly attributed to higher soybean yield with maintained maize yield, which ultimately increased the total LER and net income of MSR. Furthermore, increasing the distance between the rows of soybean and maize from 50 to 70 cm resulted in a significant decline in LER of MSR, indicating that as the strips become wider, the plant to plant distance within maize and soybean plants reduced, which increased the intra-specific competition for resources 35 . Besides, wider strips in MSR progressively resemble with narrow parcel alternations of sole maize and sole soybean. Therefore, the intercropping advantages and benefits start to diminish with the increase in strip widths 12 , and the complementarity in using the resources between maize and soybean in MSR becomes less likely to occur 11 .
Unfavorable environmental conditions during the life period of crops threatened the yield stability of crops, and yield stability is the main index to consider when judging the value of planting pattern 40 . Relay intercropping systems have greater yield stability compared to sole cropping systems 13 , especially in those regions where the growing seasons are too short for double cropping (e. g., Chongqing, Gansu, and Sichuan in China). Similarly, in this study, the average values of LER in T 1 , T 2 , and T 3 are 1.53, 1.76, and 1.44, respectively, which indicates that 44% to 76% more land will be needed by sole soybean and sole maize to equal the yield of MSR. Besides, compared to SM and SS, treatments T 1 , T 2 , and T 3 increased the net income of MSR by 11% and 9%, 98% and 94%, and 27% and 24%, respectively. These results of LER and net income clearly shows the higher yield stability, land advantages, and net income of maize/soybean relay intercropping systems over sole cropping systems under the prevailing conditions. Overall, intercropping systems remains an interesting and better option to obtain high intercrop yields with high utilization of available resources (light and land). However, for the sustainable production of cereals and legumes, we need to select the optimum inter-row spacing in MSR. These results also provide an example for obtaining high crop yields, intercropping advantages, and net income in other countries of the world, especially in developing countries (China, and Pakistan).

Conclusion
Advantages of maize/soybean relay intercropping system in terms of the competitive ability of intercrop species and land equivalent ratio are maximum with the strip width of two meters. Economic benefits of an increased soybean grain yield with maintained maize yield are likely to be worthwhile only with the use of mediumstrips in maize/soybean relay intercropping system. Wider strips significantly decreased the grain yield and net income of the maize/soybean relay intercropping system, which means that the use of wider strips in maize/ soybean relay intercropping system will reduce the advantages and benefits of the intercropping system over sole cropping systems. Furthermore, small farm machinery is required to attain the maximum benefits of relay intercropping systems; without resolving the machine issue, we cannot achieve the advantages and benefits of intercropping systems.

Materials and methods
Experiment site. This field study was carried out at the Research Farm of the Sichuan Agricultural University in Ya'an (29°59′ N, 103°00′ E), Sichuan of southwest China from 2012 to 2013. The climate of this region is subtropical humid, with an average temperature of 16.2 °C. The frost-free period lasts approximately 300 days, with an average rainfall of 1200 mm. Weather data during the experimental seasons are shown in Table 8. The soil is purple clay loam, with a pH of 6.7, soil organic matter of 30.6 g/kg, available N of 65.5 mg/kg, available P of 18.9 mg/kg, available K of 97.6 mg/kg in the top 30 cm soil layer.
Experimental design. The soybean variety (Gongxuan-1) and the maize variety (Chuandan-418) were used for this study. This study consisted of five different treatments with three replications (Fig. 2). The different cropping systems included SM (sole-maize with a row spacing of 70 cm), SS (sole soybean with a row spacing of 70 cm), and MSR (two rows of soybean were relay-intercropped with two rows of maize after the 60 ± 5 days of maize sowing). In this relay-intercropping system, three different inter-row spacing treatments in MSR are described as follows: T 1 (narrow-strips, row spacing for soybean and maize rows was 40 cm, and the inter-row spacing between soybean and maize was 50 cm with a total strip width of 180 cm), T 2 (medium-strips, row spacing for soybean and maize rows was 40 cm, and the inter-row spacing between soybean and maize was 60 cm with a total strip width of 200 cm), and T 3 (wide-strips, row spacing for soybean and maize rows was 40 cm, and the inter-row spacing between soybean and maize was 70 cm with a total strip width of 220 cm). Every experimental plot consisted of four strips of soybean and maize in MSR. The size of each plot in T 1 , T 2 , and T 3 was 43. In the current study, the total growth period of maize and soybean in MSR was 210 ± 5 days, and the vegetative period of soybean and the reproductive period of maize overlap with a phase of 50 ± 5 days between the maize harvesting and soybean sowing (Fig. 3). Before sowing, for maize, basal N at 135 kg ha −1 as urea, P at 40 kg ha −1 as calcium superphosphate, and K at 10 kg ha −1 as potassium sulfate was used in all treatments. For soybean, basal N at 75 kg ha −1 as urea, P at 40 kg ha −1 as calcium superphosphate, and K at 4 kg ha −1 as potassium sulfate were applied in all treatments. At the V 6 stage of maize and R 1 stage of soybean, basal N at 135 and 75 kg ha −1 as urea was applied to soybean and maize in all treatments, respectively. Weeds were controlled manually.
where PARs and PARm are the PAR at the top of soybean and maize top, respectively.
Leaf area index and dry matter. The leaf area index of soybean was measured at V5, V7, and R1. For this purpose, ten soybean plants were collected from every treatment. The leaf area of every single leaf was determined by multiplying the leaf length by the greatest leaf width by the crop-specific co-efficient factors of 0.75 for soybean 4 . Then, the leaf area index of soybean was determined using the previously published methods 42 . After the measurement of leaf area index, all harvested soybean samples were kept in an oven for one h at 80 °C to destroy the fresh organs of soybean plants and then dried at 65 °C until constant weight achieved for dry matter (g plant −1 ) analysis.
Photosynthesis. The photosynthetic characteristics, i. e., photosynthetic-rate (Pn), transpiration-rate (Tr), stomatal conductance (Gs), and intercellular CO 2 concentration (Ci) of soybean leaves were determined using a portable photosynthesis system (Li-6400, LI-COR Inc., Lincoln, NE, USA). We measured the photosynthetic characteristics of soybean leaves at V5, V7, and R1. In all plots, three fully developed trifoliate leaves were selected to determine the photosynthetic characteristics of soybean plants. All photosynthetic measurements were taken from 11:00 to 12:00 h under the constant carbon dioxide concentration of 400 µmol mol −143 .
Grain yield and competition parameters. At soybean and maize maturity, 40 soybean plants and 24 maize ears were collected from each plot of every replication. After that, all obtained samples were sun-dried for the next ten days. After drying, soybean and maize samples were manually threshed and determined the grain number (plant −1 ), grain weight (mg), and grain yield (kg ha −1 ) of soybean and maize. Furthermore, the total grain yield (kg ha −1 ) of maize/soybean relay intercropping system was calculated by the summation of maize and soybean grain yields in T 1 , T 2 , T 3 under MSR. The land equivalent ratio (LER) was used to determine the land use advantage of soybean and maize provided relay intercropping systems. LER was calculated as follows 44 : where SY im and SY sm are maize grain yields in MSR and SM, respectively, and SY is and SY ss are soybean grain yields under MSR and SS, respectively. The competition ratio (CR) was determined to measure the competitive ability of soybean and maize in MSR. CR was calculated as follows: where Asr and Amr are the sown proportion area of soybean and maize in MSR, and LERs and LERm are the partial LER values of soybean and maize, respectively 45 .
Economic analysis. An economic analysis was done using partial budgeting to assess the economic viability of different treatments for soybean and maize production in MSR. Total expenses for the production of maize included land rent, seedbed preparation, cost of maize seeds, cost of applied fertilizer (N, P, and K), thinning and weeding, harvesting, and threshing of soybean and maize crops were estimated based on local rates. Gross income was calculated by multiplying the measured yields with the local market prices of soybean and maize in 2012 and 2013. Net income (NI) was determined by subtracting all expenses from the gross income 46 .
Statistical analysis. The effects of different inter-row spacing treatments on the PAR-transmittance, leaf area index, dry matter, photosynthesis, yield and yield components, land equivalent ratios, and competition ratios of soybean and maize were analyzed using Statistix 8.1. Mean values were expressed as the least significant difference. All the means were compared at a 5% probability level.

Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.