Temporal Differentiation of Crop Growth as One of the Drivers of Intercropping Yield Advantage

Intercropping studies usually focus on yield advantage and interspecific interactions but few quantify temporal niche differentiation and its relationship with intercropping yield advantage. A field experiment conducted in northwest China in 2013 and 2014 examined four intercropping systems (oilseed rape/maize, oilseed rape/soybean, potato/maize, and soybean/potato) and the corresponding monocultures. Total dry matter data collected every 20 d after maize emergence were fitted to logistic models to investigate the temporal dynamics of crop growth and interspecific interactions. All four intercropping systems showed significant yield advantages. Temporal niche complementarity between intercropped species was due to differences in sowing and harvesting dates or the time taken to reach maximum daily growth rate or both. Interspecific interactions between intercropped species amplified temporal niche differentiation as indicated by postponement of the time taken to reach maximum daily growth rate of late-maturing crops (i.e. 21 to 41 days in maize associated with oilseed rape or potato). Growth trajectories of intercropped maize or soybean recovered after the oilseed rape harvest to the same values as in their monoculture on a per plant basis. Amplified niche differentiation between crop species depends on the identity of neighboring species whose relative growth rate is crucial in determining the differentiation.

Nature has introduced great biodiversity into the world but humans have displayed a passion for simplifying it. Monoculture does not take advantage of the principles by which natural systems function, but instead represents agriculture from the perspective of an engineer 1 . Although farming systems have succeeded in supplying enough food for the majority of the global population, it is widely recognized that many of the systems based on sole cropping with substantial inputs of chemical fertilizers, pesticides, and antibiotics may have led to negative outcomes and vulnerabilities of agricultural ecosystems 2,3 . In contrast, intercropping, the simultaneous growth of two (or more) crop species in the same field area for all or part of their growing period (co-growth) 4,5 , has certain advantages over sole cropping. It is part of nature-based solutions in land management for enhancing ecosystem services 6 . Intercropping has been widely adopted by farmers in developing countries [7][8][9][10][11] , especially in the single-season cropping areas because of the annual thermal limitation in most areas of northwestern China 12,13 .
The main advantage of intercropping is the increase in productivity 14,15 by exploiting the full duration of solar radiation [16][17][18] , thermal energy 19 , water 7,20,21 and nutrient resources 4,22 in resource-limited ecosystems. Moreover, intercropping can maintain or enhance soil quality 13,23 , promote biodiversity 3,24 , control weed growth 25 , minimize the incidence of pests and diseases 26 , reduce soil erosion and runoff discharge 6 , and increase farming incomes 5,8 . To design an intercropping system with advantages in terms of efficient resource utilization it is necessary to identify the relationship between the intercropping advantages and the growth traits and resource requirements of the component crop species 3 . Previous studies show that intercropping advantages depend greatly on niche differentiation in time 12,13 and space 18,22,27,28 , or on positive interspecific interactions (facilitation) 17,23 between intercropped species, thereby moderating competition 29 .
Plant competition has been studied for many decades but it is usually evaluated as a difference in biomass at a single, arbitrary, stage of growth 30 . The determination of the end-point harvest of biomass production can lead to inaccurate interpretations 31 . Furthermore, the same final patterns often result from different processes of

Results
Intercropping advantages in grain yield and aboveground dry weight. Land equivalent ratios were 1.09-1.95 based on grain yields and were 1.02-1.63 based on aboveground dry weight in all four intercropping systems across the two years of the study ( Table 1). The grain yields of oilseed rape/maize, oilseed rape/soybean, potato/maize and soybean/potato intercropping averaged over the two years increased dramatically by 12.6, 78.5, 15.1, and 21.7%, respectively. The above-ground dry weights increased by 15.8, 47.1, 21.6 and 40.8% compared with the corresponding expected values (Table 1). Dynamic trajectories of above-ground dry weight in oilseed rape/maize intercropping. The cumulative dry matter of intercropped oilseed rape was higher than that of the monoculture and the maximum above-ground dry weight (Y max ) of intercropped oilseed rape was close to that of sole oilseed rape in 2013 (Table 2, Fig. 1a) and significantly higher (by 57.0%) than that of sole cropping in 2014 ( Table 2, Fig. 1b). In contrast, the above-ground dry weight of intercropped maize was significantly lower than that of sole maize before the oilseed rape harvest, but the maximum above-ground dry weight (Y max ) of intercropped maize was significantly (52.6%) higher than that of sole maize in 2013 ( Table 2, Fig. 1a).
Sole maize and oilseed rape attained their maximum daily growth rates at 87 and 29 days, respectively, after maize emergence. Intercropped maize took significantly more days (an extra 28-33 days) to achieve its maximum daily growth rate than did monocultured maize. There was no significant delay in the above-ground dry weight of intercropped oilseed rape (Table 2; Fig. 2a,b).
Cropping system did not significantly affect the relative growth rate (k) of maize but intercropped maize had a higher maximum daily growth rate (I max ; 540 kg ha −1 d −1 ) than sole maize (435 kg ha −1 d −1 ) in 2014 (Table 2). Intercropped oilseed rape was higher in both relative growth rate (k) and maximum daily growth rate (I max ) compared to the corresponding monocultures in 2013, by 87.0 and 130.5%, respectively (  Table 1. Observed or expected total grain yields, above-ground dry weight and land equivalent ratios (LER) in different intercropping systems in 2013 and 2014. NB: values (mean ± SE, n = 3) followed by the same lowercase letters for one crop combination are not significantly different between expected and observed grain yields or aboveground dry weight (horizontal comparison) within each year at the 5% level by LSD; values (mean ± SE, n = 6) with the same capital letter within each row within one crop combination are not significantly different between average expected and observed grain or aboveground dry weight across two years (one-way ANOVA, P < 0.05).
ScIentIFIc RepoRts | (2018) 8:3110 | DOI:10.1038/s41598-018-21414-w Dynamic trajectories of above-ground dry weight in oilseed rape/soybean intercropping. The growth dynamic trajectories of all components were similar in different treatments in both years (Fig. 1). The maximum above-ground dry weight (Y max ) of intercropped oilseed rape was close to that of sole oilseed rape ( Table 2). In contrast, the above-ground dry matter of intercropped soybean was significantly lower than that of sole soybean during the co-growth stages. After the oilseed rape harvest the above-ground dry matter increased sharply and the maximum above-ground dry weight (Y max ) of intercropped soybean increased significantly by 32.5 and 49.3% compared with sole soybean in 2013 and 2014, respectively ( Table 2). The times of maximum daily growth rate in sole soybean and oilseed rape were at 80 and 29 days after maize emergence, respectively. Intercropped soybean delayed the time taken to attain maximum daily growth rate (by 17-41 days) compared with sole soybean ( Table 2; Fig. 2c,d). In contrast, there was no significant effect on the growth of oilseed rape.
Taking the whole cropping system into consideration, the relative growth rate (k) of intercropping was similar to that of sole cropping, but oilseed rape behaved differently in 2013 (Table 2; Fig. 2c,d). Again, intercropping enhanced the maximum daily growth rates (I max ) by 158.5% compared to sole oilseed rape in 2013 ( Dynamic trajectories of above-ground dry weight in potato/maize intercropping. In both years the trajectories of all intercropped components were initially similar to those of the corresponding sole cropped species (Fig. 1e,f). However, the maximum above-ground dry weight (Y max ) of both component species in intercropping systems increased by 15.7-116.3% compared with sole cropping ( Table 2; Fig. 1e,f).
The time taken to reach the maximum daily growth rate (t max ) of intercropped maize occurred 21-41 days (significantly) later than in sole maize ( Table 2; Fig. 2e,f). Intercropping potato significantly postponed (by 10

Intercropping pattern
Year Treatment Oilseed rape/maize   Fig. 2e). Averaged over 2013 and 2014, there was no difference in relative growth rate (k) between intercropped and sole crops (Table 2). Subsequently, the maximum daily growth rate (I max ) of intercropped potato was 77.2 and 81.3% higher than that of sole potato in 2013 and 2014, respectively ( Table 2; Fig. 2e,f) but there was no significant effect on that of maize in either year. Dynamic trajectories of above-ground dry weight in soybean/potato intercropping. The growth dynamic trajectories of sole and intercropped soybean and potato were different in both years (Fig. 1g,h). In 2013 the growth trajectory of intercropped potato was greater than that of sole potato over the whole growing season but there was no significant difference between sole and intercropped soybean in above-ground dry weight (Fig. 1g). The maximum above-ground dry weight (Y max ) of intercropped potato was 118.0% higher than that of sole potato, but there was no significant effect on that of soybean ( Table 2, Fig. 1g). In 2014 the divergences of the above-ground dry weight curves of sole-cropped and intercropped soybean were significant over the whole growing season. However, the presence of a neighbor had no effect on the growth trajectories of potato (Fig. 1h). Subsequently, the maximum above-ground dry weight (Y max ) of intercropped soybean was 122.1% higher than sole soybean, but there was no significant difference between sole-cropped and intercropped potato in maximum above-ground dry weight (Y max ) ( Table 2, Fig. 1h).
Cropping system had no significant effect on either the relative growth rate (k) or the time taken to reach the maximum daily growth rate (t max ) of the plants ( Table 2; Fig. 2g,h) except for the t max of intercropped soybean which was 5 days shorter than that of sole soybean in 2014 (Table 2, Fig. 2h).

Discussion
Our study provides evidence that grain yields, above-ground dry weight and the maximum above-ground dry weights (Y max ) of all intercropped species were approximately equal to or significantly higher than those of the corresponding monocultures (Tables 1, 2). Furthermore, we found that land use efficiency, measured as LER, was >1 in all four intercropping systems during the two years (Table 1). Similar yield advantages have long been recognized in other intercropping systems 5,24 and a meta-analysis found that the average value of LERs was 1.22 ± 0.02 43 . Some previous studies have also demonstrated significant yield increases in oilseed rape/maize in the same area as our experiment 38,40 , and in oilseed rape/soybean in North America 9 , potato/maize in West Asia 10 and common bean/potato in Africa 11 .
In early/late-maturing species mixtures, e.g. oilseed rape/maize, oilseed rape/soybean and potato/maize, sowing and harvesting date were different from component crops (Table 3). These findings suggest the separation of growth periods between intercropped components and this may induce yield advantage in intercropping 25,43 . In addition, our study indicates that the time taken to attain maximum daily growth rate (t max ) was also different between intercropped species in the three intercropping systems (Table 2; Fig. 2). Therefore, intercropped species obtained the resources at different times (as indicated by dashed lines in the conceptual model of Fig. 3). Niche differentiation refers to the process by which competitive species use the resources differently in time or space, which reduces interspecific competition and maintains species coexistence and complementarity in resource use by the various species 44 . Thus, our results suggest that 'temporal niche differentiation' indicated by the maximum daily growth rates (I max ) by neighboring plant species is a key ecological mechanism in overyielding. More specifically, intercropping allowed plants to exploit the length of the growing season adequately 5,15 and utilize available resources efficiently at separate times 17,18 .
Our study therefore highlights significant postponement of the time taken to reach the maximum daily above-ground dry weight rate (t max ) by 20-40 days by the later maturing intercropped species, e.g. maize in oilseed rape/maize and potato/maize or soybean in oilseed rape/soybean, compared with the corresponding monocultures ( Table 2, Fig. 2). In the present study we find that intercropping strengthened temporal niche differentiation as indicated by the conceptual model in Fig. 3. The results of this study are in agreement with previous studies on the dynamic processes of above-ground dry weight accumulation 33,35-37 and nutrient uptake 13 . Previous research suggests that crops reach their maximum daily growth rate at the stages of canopy closure and maximum leaf area 45 . Intense competition from neighboring plants usually decreases the survival, growth or reproduction of weak competitors 46 . It is therefore possible that prolonging the root lifespan and slowing down shoot senescence of intercropped maize or soybean may partly explain the delayed time of maximum growth rate 40,47 .
We also found that the dynamic trajectories of cumulative dry weight in oilseed rape/maize and oilseed rape/ soybean intercropping systems can be explained in terms of the "competition-recovery production principle" of  intercropping 22,29 . The trajectories of cumulative dry weight by intercropped oilseed rape clearly diverged from those of the monocultures at the early stages of the experiment, but the growth of intercropped maize or soybean was impaired before the oilseed rape harvest (Fig. 1a-d). In previous studies, intense competition occurred in early/late-maturing mixtures, and only early-maturing crops benefited from intercropping during the co-growth period 13,22,29,33 . This is the most likely explanation for the yield advantage of early-maturing crops in intercropping. After the oilseed rape harvest the trajectories of cumulative dry weight by intercropped maize or soybean increased sharply, and thereby the maximum above-ground dry weights (Y max ) of intercropped soybean or maize were approximately equal to or significantly higher than those of the corresponding monocultures at maturity ( Table 2, Fig. 1). The biomass production of late-maturing crops (soybean or maize) can effectively recover after the harvest of early-maturing crops (oilseed rape). Numerous studies have attributed such recovery or overyielding of growth by late-maturing crops to both the longer growing season 13,22,29,33 and also the greater above-and below-ground space 15,39,47,48 . Yield advantages were obtained in potato/soybean intercropping (Tables 1, 2), and the component species even shared a similar temporal niche by the absence of a significant difference in sowing dates, harvesting dates and the time taken to reach the maximum daily growth rate (t max ) between both species (Tables 2, 3; Fig. 2g,h). In this experimental field, intercropped potato was planted in ridges and companion soybean was in furrows, thus the component species were inherently different in rooting pattern 41,42 and shoot architecture 11 . The combination may improve their rhizosphere and canopy micro-environments due to the different spatial distributions of species relative to each other 18,27,39 . Previous studies show that the yield advantage of combinations containing legume species may be attributable to interspecific facilitation by processes such as N 2 fixation 34,49 , N transfer 50 and increased resource availability 23,24 .
The present study found that crop species can respond differently to various neighboring species. Soybean postponed the time taken to reach the maximum daily growth rate (t max ) by 17-41 days when growing with neighboring oilseed rape, a fast growing species with 136 × 10 −3 d −1 of average k, and did not delay the time when associated with potato, a species with a relatively slow growth rate with 63 × 10 −3 d −1 of average k (Table 2, Fig. 2). Similarly, previous studies show that crop species had a substantially different growth pattern in two intercropping systems 28,49 . Interspecific facilitation between faba bean and maize enhanced nutrient uptake by maize, and the roots of intercropped maize spread underneath the faba bean plants 28,40 . However, competition from wheat resulted in a decrease in nutrient uptake by maize and limited the lateral spread of the roots of intercropped maize 28,48 . This highlights the importance of plasticity of crop response to different neighboring species in the design of new intercropping combinations.
Our experiment indicates higher recovery of maize intercropped with oilseed rape in 2013 than in 2014 ( Table 2; Fig. 1a,b), and in the soybean/potato intercropping system divergences in the dry weight trajectories between intercropped and sole plants were detectable in only one species at later growth stages in both years ( Table 2; Fig. 1g,h). This may be due to the different row arrangements (Table 3, Fig. S1) in 2013 and 2014. Intercropping experiments on plant spacing have shown that the density of the component crops influences the interception of light 16,17 and the total yield 7,45 . Furthermore, seasonal weather conditions, e.g. temperatures (Fig. 4), partially account for the differences in the results between years 19,51 .  Plot size was 3.6 × 6.0 m (4.2 × 6.0 m for potato/maize in 2014) and a total of 24 plots were established in an east-west row orientation. In oilseed rape/maize intercropping, 2 rows of maize alternating with 5 or 4 rows of oilseed rape were planted in each strip (Table 3; Fig. S1e,i). In oilseed rape/soybean intercropping, one strip was planted comprising 3 soybean rows and 5 oilseed rape rows in 2013, and 2 soybean rows and 4 oilseed rape rows in 2014 (Table 3; Fig. S1f,j). In potato/maize intercropping, one strip included 2 potato rows and 1 maize row in 2013, and 2 potato rows and 2 maize rows in 2014 (Table 3; Fig. S1g,k). Potato/soybean intercropping had 2 rows of potato alternating with 2 rows of soybean in each strip, but the width of each strip was different in 2013 and 2014 (Table 3; Fig. S1h,l). The sowing ratios of the cropping systems are shown in Table 3. The central strip of each plot remained free of damage until maturity in order to calculate grain yields. The remaining strips were used to collect samples continually during the growing season (the rows adjacent to the two ridges being discarded).

Materials
The inter-row and inter-plant distances of the cropping systems were the same in both sole and intercropped plots (Fig. S1). Soybean had two seeds in bunch planting. Oilseed rape was planted by broadcast sowing in each row. Maize and potato were planted mulched with white plastic film (0.90 m width). Potatoes were in ridges, and each ridge was 0.50 m high × 0.60 m wide.
Oilseed rape were sown in late March and harvested in late June or early July each year. Maize and potato were sown in late April with harvest dates in mid-October (maize) and late August to early September (potato) each year. Sole soybean and soybean intercropped with potato were harvested in late September or early October each year, but the harvest date of soybean intercropped with oilseed rape was almost one month later than that of sole soybean in 2014 ( Table 3).
The same rate of fertilizer nitrogen (165 kg N ha −1 as urea) was applied to potato, soybean and oilseed rape with double this rate applied to maize in both sole and intercropping systems. Before sowing, all the fertilizer P (120 kg P ha −1 , applied as triple superphosphate) and 165 kg ha −1 of the fertilizer N were evenly broadcast into the top 20 cm of the soil profile, with two topdressings of the fertilizer N (82.5 kg ha −1 each) for intercropped and sole maize at the maize stem elongation stage and the pre-tasseling stage, respectively. No potassium (K), organic manure or fungicide was applied to any crop. All plots were weeded by hand.
All plots were adequately irrigated seven times throughout all growth stages to prevent water stress (Table 4). Each irrigation was 75 mm (750 m 3 ha −1 ), and the irrigation practice was applied at the same times according to conventional local farming practice each year. Plant sampling and analysis. The first samples of crops were taken 15 days after maize emergence. Ten plants of maize, soybean and potato were cut at ground level randomly due to the smaller straw at this time. Subsequently, four plants were sampled at 20-day intervals. When the tubers emerged, the shoots and tubers of potato were measured for calculation of the whole dry matter yields. Because oilseed rape is broadcast-sown and has a short growth period, each sample was taken once every 10 days. The sampling areas were 20 cm × 5 rows (2013) or 20 cm × 4 rows (2014).
At maturity, the sampling areas were 6 m × 2 rows for maize and potato, 6 m × 5 rows (2013) or 6 m × 4 rows (2014) for oilseed rape, and 6 m × 3 rows or 6 m × 2 rows for soybean. Maize, soybean and oilseed rape were divided into seeds and straw for calculation of grain yields and above-ground dry matter yields. The shoot and tuber dry weights of potato were determined.
Plant samples were oven dried at 105 °C for 30 min and then at 65 °C for 72 h to constant weight. Dry matter values determined during the cropping seasons were used to calculate the dynamic trajectories of crop growth.
Calculations. The comparison between observed and expected yields 53 was used to evaluate the overyielding of intercropping systems in grain yield and above-ground dry weight. The total grain yield in intercropping was calculated as: where M a and M b are the grain yields (per unit of total area of the intercrop) of crops 'a' and 'b' in the sole cropping system. P a and P b are the proportions of the area occupied by the individual crop species in the intercropping system (Table 3). This expectation is based on the null hypothesis that the grain yield per individual plant is the same in intercropped and sole crops. If observed grain yields are greater than expected the grain yield per plant is greater in intercropping than in the sole crop. The above equations were also used to calculate the aboveground dry weight (per unit of total area of the intercrop). The grain yield of potato refers to tuber dry matter and the above-ground dry matter yield of potato includes shoots and tubers. In all analyses the land equivalent ratio (LER) is generally used to evaluate the land use advantage of intercropping 2 and is defined as follows: Where Y a and Y b are the above-ground dry weights or grain yields (per unit of total area of the intercrop) of intercropped species a and b. An intercropping system exhibits a land use advantage if LER >1.0 and conversely no yield advantage if LER <1.0 2 . The logistic growth function using least squares has been used increasingly to fit above-ground dry weight yield data (at least six harvests) from emergence until death or harvest 30,37 . The logistic growth equation comprises: Where M t (kg ha −1 ) is the above-ground dry weight per unit ground area of each crop component grown in a given treatment at (t) days after maize emergence during the growing season. Y max (kg ha −1 ) is a parameter determining the asymptotic maximum above-ground dry weight, k (d −1 ) is the relative growth rate (dM t /dt × 1/M t ), and t max (d) is the time taken to reach maximum daily growth rate (dM t /dt). These parameters were determined using the Slogistic1 procedure of the OriginPro8 software (OriginLab Corporation, Northampton, MA). The daily growth rate 13,33 is: = −  The daily growth rate attains a maximum at M t = Y max /2, therefore the maximum daily growth rate, I max = k Y max /4, occurs at time t max . Statistical analysis. The main effects of the cropping treatments on the four parameters (k, Y max , t max and I max ) were determined using analysis of variance (ANOVA). One-way ANOVA was used to compare the significance of differences among all treatments and pairs of treatment mean values were compared using least significance difference (LSD) at the 5% level. All statistical analysis was carried out using the SAS version 8.2 software package (SAS Institute, 2003).