Effects of strip width on yields in relay-strip intercropping: A simulation study

European Journal of Agronomy 112 (2020) 125936

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Effects of strip width on yields in relay-strip intercropping: A simulation study

T

P.A.J. van Oorta,*, F. Goub, T.J. Stomphc, W. van der Werfc a

Agrosystems Research, Wageningen Plant Research, P.O. Box 16, 6700 AA Wageningen, the Netherlands Bragato Research Institute, PO Box 845, Blenheim 7240, New Zealand c Centre for Crop Systems Analysis, Wageningen University, P.O. Box 430, Wageningen, AK 6700, the Netherlands b

ARTICLE INFO

ABSTRACT

Keywords: Strip intercropping Strip width Wheat Maize Land Equivalent Ratio (LER) Gross Margin Ratio (GMR)

Intercropping is the cultivation of multiple crop species on the same land. Relay strip intercropping is an intercropping system in which the component species are grown in strips, while the growing periods of the crop species overlap only partially. The effects of strip width on yields in relay-strip intercropping are still poorly understood. Here in a case study on wheat-maize relay intercropping a simple strip intercropping model was applied to quantify intercropping performance as a function of a wide range of strip widths. Simulations showed that (1) the optimum strip width is less than 1 meter and (2) benefits of intercropping rapidly drop as strips become wider. Most previous experimental work was also done at narrow configurations, with strips less than 3 meters wide. Benefits of intercropping may therefore be less than what would be expected from experiments if narrow configurations are not attainable because of lack of mechanisation. All optimised strip configurations showed a Land Equivalent Ratio (LER) larger than 1 indicating benefits of intercropping, irrespective of assumptions that were made on radiation use efficiency in intercropped species as compared to sole crops. At current prices of wheat and maize, however, intercropping gross margin exceeded sole cropping gross margin only if the intercrop RUE was larger than sole crop RUE for both species. This study shows that strip crop growth models can be used to specify needs for future machinery, that will enable farmers to attain benefits from intercropping.

1. Introduction Intercropping systems in the world today are mostly found in countries with a low degree of mechanisation (Brooker et al., 2015). These systems are under pressure due to growing rural labour scarcity and low labour income from agricultural activities (Feike et al., 2012; Brooker et al., 2015). Mechanisation can be a solution to the labour income problem in agriculture, but intimately integrated intercropping designs that are currently used by farmers (e.g. Fig. 1) may then have to be changed into strip cropping designs with strips that are wide enough to be compatible with currently available machinery. This then raises the question whether strip cropping will still offer advantages over sole cropping, given that currently mechanisation almost inevitably implies wider machines, while it remains to be tested if intercropping still outperforms sole cropping with wider strips. Western mechanised agriculture has evolved towards the use of ever larger machinery operating on ever bigger parcels. This development raises concerns about monotonous landscapes, reduced environmental

⁎

services and soil compaction (Brooker et al., 2015). Intercropping can to some extent mitigate these problems (Martin-Guay et al., 2018) but classical intercropping with species integrated at a fine spatial grain may be hard to exploit, and only feasible if crops can be managed and harvested as a whole (e.g. maize/legume silage), or for crops for which grains can be simultaneously harvested and separated after harvest (Bedoussac et al., 2015). In intercropping with strips, as is the rule in Chinese intercropping (Li et al., 2013), strip width is of prime concern. Mechanisation will be a much greater challenge with narrow strips than with wide strips. It is therefore necessary to clarify how intercropping advantages in strip intercropping change with strip width. As strips become wider, the strip intercropping system increasingly resembles an alternation of narrow parcels of two sole crops. Logically, benefits of intercropping diminish as strips become wider and complementarity in resource capture between species becomes less likely to occur. With this theory in mind one may easily be locked in on a frame in which one thinks that with current (large) machinery, intercropping will simply not be able to deliver the claimed benefits. What is missing

Corresponding author. E-mail address: [email protected] (P.A.J. van Oort).

https://doi.org/10.1016/j.eja.2019.125936 Received 8 January 2019; Received in revised form 7 June 2019; Accepted 21 August 2019 Available online 06 November 2019 1161-0301/ © 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/).

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Fig. 1. Example of typical narrow configuration strip intercrops. (a) wheat-maize intercrop (Photo: Zhang Fusuo); (b) wheat- soybean intercrop (Photo: Wopke van der Werf). Location: Gansu province, northwest China.

here is a quantitative understanding of the trade-off between strip width and intercropping benefits. Machinery may well undergo great changes in the decades to come, towards autonomously navigating swarms of machinery operating narrow strips (Slaughter et al., 2008). In this context it is relevant to know, as design criteria, the optimum strip widths (of two crops), and the maximum strip widths at which intercropping still outperforms sole cropping. The number of possible strip width combinations is infinite. Practical impediments make it impossible to test in practice a wide range of configurations. Consequentially, this has not happened. The number of configurations tested experimentally is generally between 1 and 4 (e.g. Wang et al., 2017). From such a limited number of strip configurations tested one cannot tell if these were the best configurations possible. And one cannot make inferences on intercropping performance on other configurations than those tested, for example much wider configurations. Crop growth models in theory would allow for simulating a large number of strip width configurations. A few crop growth models can simulate intercropping, but most of these have been developed for fully mixed stands without horizontal heterogeneity in the form of crop strips (e.g. Keating and Carberry, 1993; Baumann et al., 2002; Brisson et al., 2004; Knörzer et al., 2011; Chimonyo et al., 2016). Light distribution in a strip intercropping system is completely different from the mixed stand system and requires a different approach for simulating light distribution among the crops (Goudriaan, 1977; Pronk et al., 2003; Gou et al., 2017b). A few models were explicitly designed for simulating strip intercropping. Published studies with these models have so far been limited to model development and testing (Munz et al., 2014; Wang et al., 2015; Gou et al., 2017b; Liu et al., 2017). Here we apply to our best knowledge for the first time a strip intercropping model to identify optimum strip intercropping configurations. Previous studies attributed differences between sole cropping and intercropping performance to differences in light interception, harvest index (HI) and radiation use efficiency (RUE) (Marshall and Willey, 1983; Keating and Carberry, 1993; Tsubo et al., 2001). Light interception and HI are in the current study model outcomes that follow from simulations of crop growth at a given set of sowing dates and crop configuration and weather conditions, based on the linked processes of growth of canopy cover, light interception and dry matter accumulation. Previous studies showed different effects of intercropping on RUE. Comparing the same species, researchers have reported RUE being lower, the same, or higher in intercropping compared with sole cropping. It is still unclear if reported RUE differences always represent true radiation conversion differences or in fact partly represent differences in light interception. In some reported cases, there are sound explanations for why RUE would be higher. For instance, when maize is intercropped with legumes at low soil fertility, a difference in RUE between sole maize and intercropped maize is expected because the intercropped maize has better access to soil N than sole maize. On the

other hand, the situation is less clear when two cereals are intercropped, e.g. maize and wheat (Gou et al., 2017a). The implications of this uncertainty about intercrop RUE for intercropping performance are still poorly understood. A literature review of RUE comparisons is presented and used as the basis for a sensitivity analysis. Intercropping performance can be measured with different performance indicators, reflecting different societal and farmers’ objectives. In this paper two performance indicators were used, the Land Equivalent Ratio (LER) and the Gross Margin Ratio (GMR). This paper has three objectives: 1 To identify in a case-study the optimal strip configuration. Optimal here means maximising either of two performance indicators (LER and GMR) 2 To quantify the trade-off between strip widths and LER or GMR 3 To quantify implications of uncertainty in RUE for LER, GMR and optimum strip width 2. Materials and methods 2.1. Intercrop performance indicators The land equivalent ratio (LER) is one of the most widely used indicators for comparing intercropping system performance with sole cropping (Mead and Willey, 1980). LER is calculated as the sum of the relative yields obtained in an intercrop as compared to sole crops: LER=Yinter1/Ysole1 + Yinter2/Ysole2

(1)

Where Yinter,n and Ysole,n are intercrop yield and maximum sole crop yield, for crops n = 1,2, wheat and maize, respectively, in the current study. LER is an indicator of land use efficiency. An LER of 1.5 means 50% more land would be needed to produce the quantity of two crops when grown as sole crops compared with intercrops. This indicator is a relevant indicator in the context of land scarcity. While LER is a measure for land use efficiency, farmers would consider in their decision making also the profitability per unit land. To assess optimal intercropping designs we therefore also used a measure for profitability, the Gross Margin Ratio, taking into account the product prices as follows: GMR = (Yinter1*Price1 Ysole2*Price2)

+

Yinter2*Price2)

/

max(Ysole1*Price1, (2)

Where Price1 and Price2 are the prices per unit product. A GMR value greater than 1 indicates intercropping outperforms the best sole crop, in terms of gross margin. A ratio greater than 1 is possible under certain scenarios. Consider as an example a maize crop with potential yield 20 t/ha and a wheat crop with 10 t/ha potential yield. At first sight, if grain prices of the two crops do not differ by a factor 2, maize would simply be the more profitable crop, because as soon as wheat is mixed 2

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in, total profit would drop. Two factors may tip the balance in favour of intercropping. Firstly, the yield penalty of maize resulting from mixing in wheat might be less than expected, due to advantages of intercropping in system light interception (Goudriaan, 1977; Pronk et al., 2003; Yu et al., 2015; Gou et al., 2017b), or increased RUE (Gou et al., 2017b). Secondly, following basic laws of economics, scarce products tend to be more valuable. Wheat prices are higher than maize prices, internationally and also in the study area, where farmers receive higher prices for wheat (2.38 Yuan/kg) than for maize (1.72 Yuan/kg), according to the China’s statistical yearbook, 2018 (National Development and Reform Commission, 2018). The crop growth model (§2.3) simulates yields expressed in dry matter (DM) per hectare. Prices in Yuan per kilogram dry matter were calculated as Price1 = 2.38 / (10.135) = 2.751 Yuan/kg DM and Price2 = 1.72 / (1-0.155) = 2.036 Yuan/kg DM, accounting for moisture content of wheat grain (13.5%) and maize grain (15.5%). The GMR indicator only considers gross income and not the production costs. Intercropping is generally considered more labour intensive than sole cropping. An advantage of the GMR indicator is that it decouples costs and gains, allowing for backwards calculations on maximum production costs of intercropping. Another advantage of GMR is that it avoids speculation on uncertain future prices of labour and machinery. If the two performance indicators pointed in exactly the same direction there would be no need for two indicators; one indicator would suffice. The following example illustrates how using LER or GMR one could come to different conclusions on intercropping performance. Let intercropping and sole cropping yields be Yinter1 = 6 ton/ha, Yinter2 = 12 ton/ha, Ysole1 = 10 ton/ha and Ysole2 = 20 ton/ha. From these LER and GMR are calculated as LER = 6/10 + 12/20 = 1.2 and GMR = (6*2.751 + 12*2.036) / max(10*2.751, 20*2.036) ≈ 1.0. In this example LER suggests sole cropping claims 20% more land than intercropping, making intercropping advantageous. On the contrary, the GMR performance indicator shows no benefits of intercropping over sole maize cropping.

149 days. The period from earliest sowing to latest harvest was 26080 = 180 days. The overlap period of the two crops was 91 days. Wheat was growing alone for 32 days, while maize was growing alone for 57 days. Supplementary irrigation and fertiliser were given to meet demands of both crops. The simulations were done assuming potential growing conditions, i.e. water and soil fertility were provided and not limiting growth. 2.3. Model We used the relay strip intercrop model of Gou et al. (2017b) which was calibrated for the study site by Gou et al. (2017c). This model can simulate light distribution as a function of strip widths (W1 and W2) and crop heights (H1(t) and H2(t)) for two crops, labelled 1 and 2, in which height changes dynamically over time t. The model is based on unit area processes (not modelling individual plants). The model uses row number and row spacing to calculate strip width, using the method outlined below. The model was calibrated for the study site by Gou et al. (2017c), who reported the following accuracies. The model simulated LAI in the range of 0–5 with RMSE values ranging between 0.39 and 0.64 for sole wheat, sole maize, intercropped wheat and intercropped maize. The model simulated aboveground biomass in the range of 0–30000 kg dry matter per hectare with RMSE values ranging between 101 and 236 kg dry matter per hectare. These accuracies were considered sufficient for subsequently studying strip width effects as in the current paper. 2.3.1. Strip definition To analyse the relationship between strip width and yield calculation in a relay strip intercropping model, possible border row effects on radiation use efficiency need to be taken into account. This section presents equations for the relationship between strip width, row distance, and number of border and inner rows per strip of each species. Fig. 2 illustrates an intercrop configuration with two species strips. Each strip consists of n1 and n2 rows with row distances r1 and r2. iW1 and iW2 are the inner (i) widths (W) of the part of the strip which are respectively just wheat (crop 1) or maize (crop 2). Between the wheat border row and the maize border row there is a boundary space of width Wb. How much of Wb belongs to W1 and how much belongs to W2 is a matter of definition but matters for the light interception by the strip crop radiation interception model (Gou et al., 2017b). Wb was partitioned over W1 and W2 based on row widths r1 and r2 (Eqs. 5 and 6). Let crop 2 be the taller crop, which normally has a wider inner row width (r2 > r1), in such case Eqs. 5 and 6 partition a greater part of Wb to the taller crop 2, as is also illustrated in Fig. 3. Strip widths W1 and W2 are used as parameters in the Gou et al. strip (2017b) intercrop model. Eqs. 3 to 7 show how these widths are calculated from the number of rows (n), row spacing (r) and boundary width Wb:

2.2. Study site The model calculations are based on a case study using environmental data in Wuwei City, a historically important area for wheat/ maize relay-strip intercropping (Li et al., 2001; Gou et al., 2017c). Wuwei City is located at 37°96′N, 102°64′E in Gansu province in northwest China. Fig. 2 shows monthly average temperatures and radiation for the years 2010-2014. It is a temperate climate with a growing season longer than necessary for growing one crop, but too short for growing two consecutive crops as in double cropping, which is common on the North China plain. The intercropping experiments on which the crop model was calibrated were conducted in 2010, 2011 and 2012 (Gou et al., 2017c). In 2010, Crop 1 (wheat) was sown on day 80 (21 March 2010) and was mature on day 203 (21 July 2010); total duration was 124 days. Crop 2 (maize) was sown on day 112 (21 April 2010) and was mature on day 260 (16 September 2010); total duration

iW1 = (n1-1)r1

(3)

iW2 = (n2 -1)r2

(4)

Fig. 2. Monthly average temperature and solar radiation over 2010–2014 at the study site. Wuwei, 37°96′N, 102°64′E. Data from http://data.cma.cn/. 3

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Fig. 4. Narrowest possible strip configuration considered in the current analysis. With alternating wheat (n1 = 1) and maize (n2 = 1) rows and space Wb between wheat and maize set to 30 cm.

Fig. 3. Definition of row widths and strip widths. WTOT is the total width, which consists of the widths of strips 1 and 2 (W1 and W2). Both species strips consist of an inner width iW and a part of the boundary space Wb between the outer rows of the strips of the different species. This boundary space Wb is partitioned over W1 and W2 proportionally to the inner row spacings r1 and r2: crop 1 has a smaller spacing (r1 < r2), therefore W1 takes a smaller share of Wb and W2 expands further into Wb.

W1 = iW1+2

r1 Wb r1 + r2

(5)

W2 = iW2+2

r2 Wb r1 + r2

(6)

2.3.3. Wheat tillering A sensitivity analysis was conducted on allocation of the boundary space Wb to wheat and maize. In the approach presented above, wheat occupies 12/(12 + 40) = 23% of Wb and maize occupies 40/ (12 + 40) = 77%. The justification for this approach is that maize, being taller and having longer leaves would occupy a greater share of Wb. However, wheat produces tillers and maize does not. It has been shown that wheat plants in border rows produce significantly more tillers than wheat plants in inner rows (Zhu et al., 2016a,b). For sensitivity analysis a second set of simulations was conducted in which 80% of Wb was allocated to wheat. The objective here was not to judge which of these allocation assumptions is most realistic – we lacked data on this. Rather, the aim was find out is if simulated optimum strip configurations are sensitive to how Wb is allocated to the two species.

(7)

WTOT = iW1 + iW2 + 2Wb = W1 + W2

The fraction border rows fb1 and fb2 are calculated from the number of rows:

fb1 = 2/max(n1,2)

(8)

fb2 = 2/max(n2,2)

(9)

2.3.4. Model parameters Crop model parameters (Table 2) were taken from Gou et al. (2017c) who calibrated the model for the study site (Gou et al., 2017b). We assumed that biomass growth starts after emergence with an initial leaf area index LAIinit of 0.01 in sole crops while in intercrops, the LAI per species was set equal to 0.01 times the land proportion (Table 2). If for example wheat strips occupy one quarter of the field, initial LAI expressed as m2 wheat leaf per unit area of the whole field is 0.01*0.25 = 0.0025 m2 wheat leaf / m2 whole intercrop area. Thus, in intercrops the initial LAI is still 0.01 within the cropped strip.

In Eq. 8 if n1 = 1 then fb1 = 2/max(2,1) = 2/2 = 1, i.e. all rows are border rows. If n1 = 2 still all rows are border rows (fb1 = 2/max (2,2) = 2/2 = 1). If n1 is 3 or larger then no longer all rows are border rows (e.g. fb1 = 2/max(2,3) = 2/3 = 0.67). Table 1 illustrates the above calculations.

2.3.5. Extra rules We added two extra rules to the Gou et al. (2017b) strip intercrop model to enable simulations for extreme sowing dates that could result in crop failure. These extra rules did not change model performance for normal sowing date and normal strip configurations:

2.3.2. Strip configurations Row spacings were set to values common for the study site (Table 1, Gou et al., 2017c): r1 = 12 cm (wheat), r2 = 40 cm (maize) and Wb = 30 cm. Total width in the narrowest possible configuration (n1=n2 = 1) can be calculated as: WTOT = iW1 + iW2 + 2Wb = (1 1) × 12 + (1 1) × 40 + 2 × 30 = 2 × 30 = 60 cm, with wheat 12 width W1 = (1 1)12 + 2 12 + 40 30 = 13.8 cm and maize width

1 If 40 days after sowing the crop had still not emerged we assumed it had died and we set the yield to zero. The number of 40 days was derived from the APSIM model for wheat and maize. This rule serves to avoid artefacts of getting high yields with very early sowing dates. 2 If the crop had not yet matured by 1 November (day 305) we set the

40 2 12 + 40 30

W2 = (1 1)40 + = 46.2 cm. For illustration Fig. 4 shows this narrowest possible configuration. We simulated all possible wheat:maize configurations composed of wheat strips consisting of 1–100 rows (13.8–1202 cm wide) and maize strips consisting of 1–30 maize rows (46.2–1206 cm).

Table 1 Example strip width (in cm) as calculated from strip configuration in two experiments used for model parameterization. Study

Name

n1

r1

n2

r2

Wb

iW1

iW2

W1

W2

WTOT

fb1

fb2

Gou et al. (2016)

6:2 8:2 6:3 6:2

6 8 6 6

12.5 12.5 12.5 12

2 2 3 2

75 75 37.5 40

43.75 31.25 43.75 30

62.5 87.5 62.5 60

75 75 75 40

75 96.4 84.4 73.8

150 128.6 140.6 86.2

225 225 225 160

0.33 0.25 0.33 0.33

1 1 0.67 1

Gou et al. (2017c)

W:M W:M W:M W:M

All widths are in centimetres. 4

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Fig. 5. Above ground assimilate partitioning fractions (Gou et al., 2017c). Note the model does not simulate root mass and thus there is no parameter for partitioning to the roots.

Table 2 Model parameters used in this study as derived from Gou et al. (2017b). Parameter

Wheat

Maize

DOYSOW: sowing day Tbase: base temperature (°C) Temergence: thermal time sowing to emergence (°Cd) Ttiller: thermal time from sowing to phase when LAI growth becomes radiation dependent (°Cd), which is normally around tillering Tsen: thermal time from sowing to stage at which leaf death accelerates (°Cd) Tmature: thermal time sowing to maturity (°Cd) LAIinit: initial leaf area index (m2 leaf / m2 crop) RGRL: relative growth rate of leaves in the initial exponential, temperature driven growth stage (°Cd−1) SLA: specific leaf area (m2 leaf / g DM leaf) RDL1: relative death rate of leaves from Ttiller to Tsen RDL2: relative death rate of leaves from Tsen to Tmature Assimilate partitioning fractions k: light extinction coefficient H0: plant height at emergence (cm) Hmax: maximum plant height (cm) GRH: growth rate height (°Cd−1) Fgrain: grain weight / storage organ weight RUE: Radiation Use Efficiency

80 0 90 430 1600 2000 0.01 0.013 0.025 0.0008 0.002 See Fig. 5 0.7 5 80 0.005 0.82 See section 2.4

112 8 50 430 1500 1900 0.01 0.013 0.025 0.0005 0.001 See Fig. 5 0.48 5 280 0.005 0.77 See section 2.4

yield to zero. This is because after 1 November temperatures are so low (Fig. 1) that hardly any development takes place while at the same time the grains risk to be damaged by frost. This empirical rule could in a later stage be replaced by a more mechanistic rule.

previous meta-analysis by Slattery et al. (2013). The causes of these divergent findings on RUE of intercrops are not fully understood. The 4 cases in which intercropping had lower RUE were all for a taller C4 crop (maize or sorghum), but not all tall C4 crops had a lower RUE in the intercrop than in the sole crop.

2.4. Radiation use efficiency

2.4.2. Sensitivity analysis To quantify implications of uncertainty in RUE for simulated LER, GMR and optimum strip width, we optimised strip configuration under 4 different RUE assumptions (Table 4, Fig. 6). First of all, we recognize variability in measured values of RUE in different contexts. We use quantifications of RUE based on wheat-maize strip intercropping in Wuwei, Gansu province, northwest China (Gou et al., 2017c) and also alternative quantifications based on wheat-maize strip intercropping in Wageningen in the Netherlands (Gou et al., 2017a, b). The value of RUE was for both crop species higher in Gansu than in the Netherlands. Then, for data from each geographic origin, we considered a scenario in which intercropping did not affect RUE and a scenario in which intercropping did affect RUE. These scenarios were developed to account for the variability in intercropping effects on RUE reported in the literature. The actual experimental data from the two sites support an increased RUE of wheat in intercropping, and an increased RUE of maize in intercropping in Gansu, China but a lower RUE of maize in intercropping in Wageningen, The Netherlands. The four scenarios are:

2.4.1. Literature review Differences in radiation use efficiency (RUE) of the same crops grown either as a sole crop or as an intercrop are still poorly understood. RUE is calculated as biomass growth divided by light interception, usually by regressing biomass at periodic harvests versus cumulative radiation interception by the canopy (Monteith, 1977). If radiation interception is underestimated this can be compensated by overestimation of RUE to obtain the same biomass growth. If previous studies were inaccurate in their modelling of strip row radiation interception, which can be hard to measure, this may have led to erroneous conclusions on RUE. We show in Appendix A (in Supplementary material) that due to cancelling out of errors, this would not have an impact on the outcomes presented in this paper. We discuss this issue in more detail in the general discussion section, in section 4.3.1. Table 3 shows the results of a review on experiments in which comparisons were made of RUE in sole crops and intercrops. Most previous studies (58%) found that crop species grown in intercropping have a higher RUE than crop species grown as sole crops. However, many also found no differences in RUE (33%) and a few (10%) found lower RUE for crop species grown in an intercrop than for the same species grown as a sole crop. These findings are consistent with a

1 Gansu, China RUE quantification, no effect of intercropping on RUE 2 Gansu, China RUE quantification, intercropping increases both wheat RUE and maize RUE 5

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The 4 developed scenarios cover the full range of different RUE findings in Table 3 with same, lower and higher RUE for intercrops compared with sole crops.

Table 3 Effects of intercropping on crop species RUE in intercropping. Intercropping effect on RUEa,b,c Reference

Crop1

Crop2

Crop names (Crop1, Crop2)

Chimonyo et al. (2018)

+

NA

Liu et al. (2018) Gou et al. (2017a) Liu et al. (2017) Gou et al. (2017b) Gou et al. (2017c) Wang et al. (2015) Du et al. (2015) Nassiri Mahallati et al. (2015) Barker and Dennett (2013) Rezig et al. (2013) Coll et al. (2012) Gao et al. (2010) Jahansooz et al. (2007) Awal et al. (2006) Tsubo and Walker (2004) Tsubo and Walker (2002) Friday and Fownes (2001)

+ + + + + 0 + + 0 + + 0 0 0 0 0 0

+ – + – + – NA + 0 + NA + 0 + + + NA

Rodrigo et al. (2001) Cruz and Sinoquet (1994)

+ 0

+ 0

Marshall and Willey (1983) Harris et al. (1987) Zhang et al. (2008)

0 – 0

+ + 0

Sorghum, cowpea or bottle gourd Maize, soybean Wheat, maize Maize, soybean Wheat, maize Wheat, maize Wheat, maize Cotton, wheat Maize, common bean Wheat, faba bean Potato, sulla Soybean, maize Maize, soybean Wheat, chickpea Maize, peanut Maize, common bean Maize, common bean Flemingia macrophylla, maize banana, rubber Arachis pintoi, Digitaria decumbens millet, groundnut sorghum, groundnut Wheat, cotton

2.4.3. Border row effects Previous experimental work by Nassiri Mahallati et al. (2015) and Gou et al. (2016) strongly suggests that differences in RUE between sole crops and intercrops are largely due to plants in the border of each strip, while growth of plants in the inner rows of intercrop strips is substantially similar to that of sole crops. Possible reason for superior performance in border rows is the better access to growth resources. For instance, plants in border rows of a tall crop have a better insolation of the lower leaves than plants in a homogeneous canopy. The ratio of crop photosynthesis to total radiation intercepted in border rows may be higher than in the inner rows as a result of the more even distribution of radiation over the leaf layers. This finding implies that differences in RUE can essentially be attributed to the fraction border rows of the intercrop strip configuration. Here we develop a simple descriptive approach for modelling this relationship. For assumptions 1 and 3 (no border row effect), the same RUE value was used for intercrop and sole crop. In simulations for assumptions 1 and 3 the observed RUEs of the sole crops were used for both species (eq 10a, b).

RUE inter1 = RUEsole1,obs

(10a)

RUE inter2 = RUEsole2,obs

(10b)

For the assumptions 2 and 4, we set the intercrop RUE of the inner = non-border rows equal to the RUE of the sole-crop (RUEinner1 = RUEsole1,obs). Intercrop border rows are allowed to have a different RUE (RUEborder1). To derive a radiation use efficiency for border rows, we reasoned that the overall radiation use efficiency of a whole strip of the intercrop (RUEinter1) can be expressed as a weighted average of the RUE in the inner and border rows, using as a weight the fraction border rows (fb1, eq 8):

a + means measured RUE for a species is higher when grown as an intercrop than when grown as a sole crop; 0 means no difference in species RUE between intercrop and sole crop; - means a species had a RUE lower in the intercrop than in the sole crop. b in some cases, RUE was only compared for the main crop. For example Chimonyo et al., 2018 compared sole sorghum with a sorghum-cowpea intercrop and a sorghum-bottle gourd intercrop, but they did not grow sole cowpea. Hence an NA (not available) is given for crop 2. c a number of studies lumped together grains of two crops and calculated intercrop RUE as total biomass (of two species) divided by total light interception (of two species). For example see Watiki et al. (1993); Keating and Carberry (1993); Ong et al. (1991); Caviglia et al. (2004). These are not included here because they did not differentiate between the component crop species.

(11)

RUE inter1 = (1-fb1)RUEinner1 + fb1RUEborder1

Where RUEinter1 is measured in the intercrop while RUEinner1 is equal to RUEsole1, measured in the sole crop 1. RUEborder1 is unknown, and fb1 is calculated using Eq. 8. The RUE specifically for border rows is then found by solving RUEborder1 from Eq. 11:

RUEborder1 = =

3 Netherlands RUE quantification, no effect of intercropping on RUE 4 Netherlands RUE quantification, intercropping increases wheat RUE but decreases maize RUE

RUEinter1 RUE inter1

(1 fb1)RUE inner1 fb1 (1 fb1)RUEsole1 fb1

(12)

Table 4 and Fig. 6 show the border row RUEs of wheat and maize calculated using Eq. 12 using as inputs the data reported in Gou et al. (2017a, b,c). On average over the experiments wheat RUEborder1 was

Table 4 RUE assumptions and the ensuing different RUE values for sole crop, inner and border rows (RUE in gram dry matter per MegaJoule photosynthetically active radiation). Site, source

Radiation Use Efficiency (g DM / MJ PAR) RUE assumption

Wheat

Maize

China, Gou et al., 2017c

1. RUEsole = RUEinter

Netherlands, Gou et al. 2017a,Gou et al. 2017bb

3. RUEsole = RUEinter, but lower than in assumption 1

RUEsole1 = 2.377 RUEinter1 = 2.377 RUEsole1 = 2.377 RUEinner1 = 2.377 RUEborder1 = 4.457 RUEsole1 = 2.215 RUEinter1 = 2.215 RUEsole1 = 2.215 RUEinner1 = 2.215 RUEborder1 = 3.380

RUEsole2 = 3.210 RUEinter2 = 3.210 RUEsole2 = 3.210 RUEinner2 = 3.210 RUEborder2 = 3.557 RUEsole2 = 3.180 RUEinter2 = 3.180 RUEsole2 = 3.180 RUEinner2 = 3.180 RUEborder2 = 2.751

2. RUEinter > RUEsole (positive border row effect on RUE in wheat and in maize)

4. RUEinter1 > RUEsole1 & RUEinter2 < RUEsole2 (positive border row effect in wheat, negative in maize)

6

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Fig. 6. Relationship between species RUE in an intercrop, for 4 different assumptions on RUE in inner and border rows. Panel a shows wheat RUE (4 RUE assumptions) while panel b shows maize RUE (4 RUE assumptions). The four RUE assumptions are detailed in the text (section 2.4.2) and summarized in Table 4.

64% higher than RUEinner1. This is very close to wheat border rows reportedly having 62% higher yield than inner rows as reported in Austin and Blackwell (1980). The calculated RUEs for the border rows and inner rows in the experimental intercrops were then used to calculate for different strip widths in the scenarios the aggregate RUE over the whole strip as a weighted average of inner and border row RUE (eq. 11). Simulations were then run using the strip light interception and strip RUE, without making distinction between border rows and inner rows. As strips become increasingly wide fb1 approaches zero in which case RUEinter1 approaches RUEsole1, which is what would logically be expected. Growth of the border and inner rows was thus not separately simulated. Doing so would have required an altogether different light interception

model, the development of which is beyond the scope of the current study. 3. Results 3.1. Sole crops Fig. 7 shows simulated crop duration and simulated yields for the sole cropping case, simulated with RUE assumption 1. Other RUE assumptions lead to different yields but exactly the same simulated safe sowing windows which depend only on phenological parameters and temperature. Safe earliest possible sowing dates can be read from the top panes, where dashed lines intersect with the horizontal red line Fig. 7. Simulated phenology and yield. Top panes show simulated duration from sowing to emergence (dashed lines) and emergence to maturity (solid lines), results were independent of RUE assumption. Crops were assumed to die if not emerged after 40 days (horizontal red line). Wheat risks such crop failure when sown before day 60, maize risks such failure when sown before day 80. Crops were assumed to die without yield in winter if not yet mature before 1 November (day 305). Solid lines are shown only for sowing dates in which crops did not die. Bottom panes show simulated yields for RUE assumption 1. Similar patterns are found for the other RUE assumptions.

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Fig. 8. Intercropping performance indicators LER (left panes) and GMR (right panes) as a function of wheat (x-axis) and maize (4 lines) strip widths for four contrasting assumption on the response of RUE to intercropping (panels from top to bottom). Each graph shows LER or GMR averaged over 5 simulations (2010–2014 weather data from Wuwei, China) for each configuration and for one RUE assumption in each panel. When lines are above the red horizontal line the intercrop configuration outperforms sole cropping (LER > 1; GMR > 1). The filled squares in panes c and d represent actual observed LER and GMR values for intercrops grown in Wuwei, China in 3 individual years (2010, 2011 and 2012). For this set of simulations, 23% of the boundary space between wheat and maize was allocated to wheat.

(maximum 40 days from sowing to emergence). Wheat can safely be sown in the study area in Gansu after day 60, while maize can safely be sown after day 80. To ensure maturity before 1 November in all 5 years, wheat must not be sown later than day 160 and maize no later than day

110. The safe sowing windows are therefore from day 60 to 160 for wheat and from day 80 to 110 for maize. Optimum wheat sowing dates over the 5 years were day 70, 70, 70, 60 and 60 respectively. For maize without safe sowing window restrictions optimum sowing dates would 8

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be day 110 (2011), 120 (2010, 2012 and 2014) and 130 (2013). However, results showed that in 2011, maize sown on day 120 or later would not mature before 1 November. Given this risk we considered for the current analysis day 110 the latest safe maize sowing date. In the scenarios, we used the identified optimal sowing dates for wheat (70, 70, 70, 60, 60) and maize (day 110 in all years) to calculate the yields for sole crops and intercrops with different strips widths. Interestingly, the set of sowing dates tested by Gou et al. (2017c), day 80 and 112, appears to be quite close to simulated optimal safe sowing dates (70, 110). This suggests that local experience with wheat and maize cropping, used in the design of the experiments of Gou et al. (2017c), has already converged close to the simulated optimum. Simulated yields at optimum sowing dates, averaged over the 5 years, were around 7.8 t/ha wheat and 15.0 t/ha maize (note: ton dry matter (DM)/ha). With farm gate prices of 2.751 Yuan/kg DM for wheat and 2.036 Yuan/kg DM for maize gross margins are 31 thousand Yuan/ha for maize and 20 thousand Yuan/ha for wheat. Thus, maize is the more profitable crop.

indicates that for LER and GMR (and the value of intercropping) it is not so much the absolute values of RUE that matter, but rather the difference in RUE of a species grown as sole crop or intercrop. LER drops when wheat strips are made too narrow, due to wheat yields suffering from severe shading by maize during grain filling. For RUE assumptions 1 and 3, without a positive border row effect on RUE, this leads to optimum configurations of 5:1 for both RUE assumptions. For RUE assumptions 2 and 4, the border row effect on wheat and maize RUE plays a key role, leading to a narrower optimum of 2:1 for both RUE assumptions. In comparison with LER, GMR is more sensitive to maize yields and less sensitive to wheat yields. For GMR the positive maize border row effect in RUE2 (Fig. 7b) leads to a GMR substantially larger than 1, with an optimum configuration of 2:1 (Fig. 8d). In RUE4 the negative maize border row effect (Fig. 7b) leads to a GMR below 1 for most configurations (Fig. 8h). Not surprisingly, highest values of LER and GMR are achieved if both the wheat and maize intercrop have an RUE higher than the sole crops. What is new here is that for the first time the consequences of this RUE effect on LER and GMR are quantified using realistic RUE values and over a wide range of strip configurations. This quantitative comparison indicates that differences between intercrop and sole crop RUE do matter a great deal and must be better understood in order to make realistic estimates of intercrop performance.

3.2. Intercropping Fig. 8 shows the response of the two intercropping performance indicators, LER (left panes) and GMR (right panes) (benchmark 1 = red horizontal line), for a wide range of strip configurations and for the 4 RUE assumptions. In addition, Figs. 8c and 8d include observations from the study area, which are discussed in section 3.2.4. Variation between years was limited, therefore averages over the four years of simulations are shown in Fig. 8. Between the years, maximum LER for the RUE assumptions ranged from 1.17 to 1.25 (RUE1), 1.62 to 1.79 (RUE2), 1.16 to 1.23 (RUE3), and 1.17 to 1.25 (RUE4). Maximum GMR ranged between the years from 1.05 to 1.09 (RUE1), 1.41 to 1.49 (RUE2), 1.04 to 1.08 (RUE3) and 1.02 to 1.06 (RUE4).

3.2.3. Trade-off between strip width and intercrop performance For the GMR performance indicator only RUE assumption 2 showed benefits of intercropping (GMR > 1, Fig. 8d). In this case, the lower yield potential of wheat calls for wheat strips not wider than 3 metres. The reason why wheat is included is not so much for the wheat, but rather because including wheat introduces a positive maize border row effect (maize border row RUE higher than sole maize RUE). This effect, and therefore also GMR, is maximised when the number of maize border rows is maximised. This is achieved with maize strips of 1 or 2 rows (to maximise the fraction border rows in the maize strips) and with wheat strips as narrow as possible (to maximise the area under maize per unit total area). As strips become wider, GMR and LER both drop. Remarkably, even at the widest tested configuration of 12:12 meters, LER remains around 1.03 (fat tail), where intuitively we would expect a value of 1. This finding raises questions about accuracy of the light interception model at wide configurations. From the practical perspective such LER values are probably too low for intercropping to offer meaningful benefits. The finding does however call for further scientific research on the validity of the light interception model, which is widely used in various versions in intercropping research (Munz et al., 2014; Wang et al., 2015; Gou et al., 2017b; Liu et al., 2017).

3.2.1. Optimal strip configurations Both LER and GMR are maximised when wheat strips are narrow (low values for the x variable) and when maize strips are narrow (compare solid with dashed lines). Optimum configurations with which maximum LER was obtained were 5:1, 2:1, 5:1 and 2:1 (wheat:maize rows) for RUE assumptions 1 to 4. Expressed in centimetres, optimum configurations range from 26:46 to 62:46 (cm wheat : cm maize). The optimum configuration for maximising GMR in RUE assumption 2 (GMR range 1.24 to 1.31) was for all four RUE assumptions 2:1 W:M (26:46 cm). For both indicators and in all RUE assumptions, the optima appear to occur with strips of less than 1 meter wide for both crops together. 3.2.2. RUE, LER and GMR All systems have an LER larger than 1 indicating intercropping outperforms sole cropping systems. Maximum LER is larger in RUE assumption 2 (Gansu condition with higher RUE in border rows; maximum LER = 1.7) than in the other RUE assumptions (maximum LER = 1.2). GMR was markedly higher than 1 only in RUE assumption 2 (maximum GMR = 1.45). In the other RUE assumptions maximum GMR was only marginally higher than 1: 1.06, 1.05 and 1.04 for RUE assumptions 1, 3 and 4 respectively. If farmers followed GMR they would only practice intercropping if both species had an increased RUE in border rows. These results show that both LER and GMR are substantially higher for RUE assumption 2 than for the other RUE assumptions. RUE assumptions 1 and 3 represent cases in which intercrop RUE equals sole crop RUE, with RUE assumption 1 having consistently higher RUE values. This difference in the absolute values of RUE has very little effect on LER (compare Fig. 8a with 8e and compare 8b with 8f: they are almost identical). On the other hand, whether or not RUE differs between sole crop and intercrop has a strong effect on LER and GMR (compare 8a with 8c, 8b with 8d, 8e with 8 g, 8f with 8 h). This

3.2.4. Observed data We compared simulation results with empirically based values of LER and GMR, calculated from observed yields from the study area for a 6:2 (73.8 : 86.2 cm) wheat:maize configuration in the year 2010–2012 with same spacing as in the simulations and with previously shown RUEinter > RUEsole for both crops Gou et al (2017c). These data are shown as points in Fig. 8c and 8d and must be compared with the top dashed line for 2 maize rows. Overall, the comparison shows that observed LER (˜1.55) was similar to simulated LER (˜1.45). Observed GMR (˜1.6) was, however, higher than simulated GMR (˜1.3). The larger discrepancy between simulations and observations for GMR occurs because the GMR indicator is more sensitive to the yield of maize, while accuracy of simulations was less for maize than for wheat (Gou et al., 2017c). Interestingly, the configuration tested by Gou et al. (2017c), which was defined based on farmers’ common practice, appears to be quite close to simulated optimal configuration. This suggests that local experience with intercropping, has converged to an optimum. If model simulations are correct, they imply that benefits of relay strip 9

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intercropping will be lost if mechanisation leads to use of machines with wider operating widths. These findings align with previously expressed concerns about the slow death of intercropping in the North China Plain (Feike et al., 2012).

considered. Thus, empirical evidence indicates that intercropping is under specific conditions overall advantageous and is therefore adopted by farmers (Hong et al., 2017).

3.2.5. Wheat tillering Appendix B (in Supplementary material) shows the sensitivity of model outcomes to the allocation of the boundary space Wb to wheat and maize. Effects of wheat occupying a greater share of Wb were analysed, thus mimicking the effects of enhanced wheat tillering in the boundary space. Findings confirm those reported above, i.e. optimum LER and GMR at narrow strip width, rapid drop in LER and GMR as strips become wider and a strong sensitivity of model results to the RUE assumption.

4.2.2. Water and nitrogen There are many regions in the world where water and nitrogen are non-limiting, for example in the case study area in Gansu where most farmers have ample access to irrigation and fertilisers. The model applied here is valid for such environments. There are also many regions in the world where water and nitrogen are strongly limiting production. These limitations were not considered in the current study. Plants can be competing for water and nitrogen when rooting in the same soil compartment. Plants can also be complementary, e.g. when rooting in different soil compartments, when one of the mixed species is nitrogen fixing or when cropped strips create a microclimate with reduced soil evaporation. Further development of the model is needed to also deal with this complexity, which will make the model more widely applicable. An interesting question is whether including effects of water and nitrogen would alter the main findings of this paper. Farmers in intercropping systems will select for mixtures that are mainly complementary, or in any case not too strongly competitive for the same resources at the same time and place (Brooker et al., 2008, 2015). Most mixtures of annual species have lateral roots less than 1 m wide. Lateral flows of water and nitrogen in the soil solution will also occur mostly in this shorter range (exceptions are rainfall events causing run-off). We therefore expect that complementarity effects under water and N limited conditions will also occur in the close range of 1 m: more effectively exploiting different soil layers, nitrogen transfer and reduced competition for mineral nitrogen. If so, optimum configurations will also be narrow under water and N limitation. This conjecture will require further testing.

4. Discussion 4.1. Main findings The following outcomes are obtained regardless of uncertainty in RUE and regardless of assumptions regarding boundary space allocation: 1 The optimum strip configuration in wheat maize intercropping is one with very narrow strips of just a few rows per crop and less than 1 meter wide; 2 Performance indicators LER and GMR rapidly drop as strips become wider. 3 Both performance indicators are strongly sensitive to uncertainty in the RUE of border plants. LER and GMR are highest when both intercrop species have an elevated RUE in border plants compared with plants in sole crops of the same species. The current study also presents a proof of concept, showing that a strip intercrop model can be used to quantify the trade-off between strip width and performance indicators. Such a model can be used to answer a practically relevant questions for future design of machinery for intercropping, namely what should be the maximum strip widths (of two species) at which intercropping offers meaningful benefits over sole cropping.

4.3. Radiation use efficiency

4.2. Limitations of the study

This paper showed that attainable LER and GMR were sensitive to uncertainty about radiation use efficiency (RUE). A sensitivity analysis was presented and an approach for attributing differences in RUE to the fraction of border rows in an intercrop. To further advance this work, a deeper understanding and more mechanistic modelling of differences in RUE is needed.

4.2.1. Performance indicators We used two indicators for intercropping performance: LER and GMR. Both are calculated from crop yields, but the latter also takes into account the product prices. Clearly production is important for farmers and for society as a whole from the food security perspective. Taking a broader perspective we observe intercropping offers other ecosystem services such as improved pest and disease control, better nutrient cycling and increased organic matter input in the soil due to higher root mass, which are not included in the LER and GMR indicators (Feike et al., 2012; Boudreau, 2013; Bedoussac et al., 2015; Brooker et al., 2015; Cong et al., 2015; Martin-Guay et al., 2018). What is also important for farmers is labour use efficiency, which is considered a limitation in intercropping practice (Huang et al., 2015; Qian et al., 2018). These too are not included in the LER and GMR performance indicators used here. These additional advantages and disadvantages of intercropping are all important considerations. Quantifying these advantages and disadvantages is possible but requires substantial further work, for instance to quantify the effects of intercropping with various strip widths on pest and disease suppression and quantify the associated economic benefits. Hong et al. (2019) found that the use of intercropping contributed positively to the overall technical efficiency of agriculture in the case study area in Gansu when the use of all inputs (including land, seed, fertilizer, water and labour) and output was

4.3.1. Radiation use efficiency or light interception? Many previous studies have reported border rows showing different growth than inner rows (Zhu et al., 2016a,b; Gou et al., 2016). Often in intercropping research the same light interception has been calculated for the whole strip of border plus inner rows, because light interception by individual rows is hard to measure. Such was also the case in the current study – the model does not, and cannot, differentiate between light interception of border and inner rows. Yet if a cropped strip is bordered by an empty strip, it is evident that, in comparison with inner rows, border rows will intercept more light. With a model that cannot separately model light interception of border and inner rows, the simplest and effective way to model greater growth in the border rows is through modification of the RUE. What is treated for simplicity as elevated RUE might in reality be a (partial) correction for underestimation of light interception of the border rows. For the main results reported here, narrow optimum strip widths, one can argue that this conclusion would remain unaltered by the decision whether to model enhanced border row growth through enhanced light interception or enhanced RUE (Appendix A in Supplementary material). Scientifically, it is important to disentangle effects of light interception and RUE. Models of light interception by individual plants (e.g. Zhu et al., 2015; Evers et al., 2018) will be able to shed more light on this. 10

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4.3.2. Elaborating the RUE approach The current RUE approach could be further enhanced, e.g. by multiplying a potential RUE (parameter RUEpot) by biophysical factors (0–1). For example in APSIM-Wheat, for daily average temperatures (Tavg) in the range of 0–10 °C, RUE is calculated as RUE = Tavg/ 10*RUEpot, thus decreasing RUE to account for low temperatures. Two relevant factors in the context of intercropping are nitrogen (N) and crop height. RUE would be strongly reduced when insufficient N is available for the two intercropped species. This stress would be less for an N-fixing legume. In a cereal-legume intercrop the legume can acquire Nitrogen from air, thus reducing competition for N with and potentially increasing RUE. Especially in low fertility environments, cereal-legume systems can benefit from N-fixation by the legume (Yu et al., 2016). But also in cereal-cereal systems effects of nitrogen require further study. Differences in RUE may be shaped by nitrogen profiles in the border plants but the relationship between nitrogen content and leaf photosynthesis rate in intercropped maize is not self-evident and requires further study (Gou et al., 2018). Light scattering increases in strip canopies, leading to more diffuse radiation for the shorter crop, which generally tends to increase crop radiation use efficiency (Spitters, 1986a,b, Sinclair et al., 1992). In line with this, Table 3 shows more often an elevated intercrop RUE for the shortest of two intercrops and more often no differences in RUE are found when crops are of similar height. A descriptive approach for modelling intercrop performance could use the RUE, assuming a statistical relationship between species heights of species and their RUE, based on empirical data.

wheat:maize, or 74:86 cm (Gou et al., 2017c), were similar to similar to model based optimum configurations (Fig. 8c and d). The study by Gou et al. (2017c) is not unique in the sense of experimenting with quite narrow configurations. Jahansooz et al. (2007) tested 2:2 wheat:chickpea configurations. Gao et al. (2010) tested maize:soybean configurations of 1:3 and 2:3. Nassiri Mahallati et al. (2015) experimented with maize: common bean configurations of 2:2, 3:3, 4:4 and 5:5 and found LER dropping from 1.55 to 1.39, 1.28 and 1.27, a similar pattern as in our simulations with LER rapidly dropping as strips become wider. There are but a few studies that tested wider configurations. Wang et al. (2015) compared wheat:maize configurations of 6:2 and 12:4 (90:80 cm and 180:160 cm), finding LER of 1.24 and 1.13. Even in this study, strips of less than 2 meters wide are still quite narrow compared with that of machinery operated by farmers in large scale mechanised agriculture. Studies cited in Table 3 have two things in common (1) they invariably tested strip configurations with strips less than 2 meters wide and (2) where 2 or more configurations were compared, comparisons showed highest LER attained at narrowest configurations. This finding reinforces previously stated concerns that intercropping will become less attractive as farmers in developing countries replace labour with machinery with larger operating widths. We can also conclude that, unless the machine issue is resolved, or systems with simultaneous sowing and harvesting are developed, farmers in large scale mechanised agriculture should not hold overly optimistic views on possible benefits of a transition to intercropping. A co-evolution of intercropping and swarms of autonomously operating small machines will be needed to attain maximum benefits of relay strip intercropping while maintaining a high labour productivity.

4.3.3. Photosynthesis and respiration It would be theoretically appealing to replace the RUE approach in the current model by a more mechanistic approach of modelling photosynthesis. It is well known that the assumption of a constant RUE is not valid at low light intensities (Goudriaan and van Laar, 1994), which are typically encountered in narrow strip configurations. A more mechanistic approach could also explicitly model the fraction diffuse radiation and its interception. More mechanistic models also require more parameters to be measured. While this helps in better understanding it remains to be tested if ultimately this leads to better predictions. More sophisticated photosynthesis models will not necessarily give better predictions – not if these too do not capture possibly relevant factors such as more favourable micro climates or pest and diseases suppression in intercrops (Boudreau, 2013). A better understanding of photosynthesis in relation to light and N profiles in intercropping is relevant for the design of strip intercropping systems.

5. Conclusions Benefits of intercropping in terms of gross margin and land use efficiency are highest with strips not more than 1 meter wide. Economic benefits of an improved radiation capture and use efficiency of intercropping are not likely to be worthwhile with strip width beyond 3 m. The study results present a proof-of-concept showing that responses can be simulated for high input systems where light is the dominant limiting factor, which is relevant in the context of future machinery design. Major uncertainties were identified and discussed. Appendices A and B. Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.eja.2019.125936. References

4.4. Light interception

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The light interception model used here, originally based on Goudriaan (1977) and Pronk et al. (2003), was applied in extreme conditions, including extremely narrow strip configurations and extremely wide configurations. The model was previously shown to accurately simulate light distribution in “normal” strip configurations (Pronk et al., 2003; Gou et al., 2017a, b). Whether it also does so in extremely narrow/wide strip configurations remains to be further tested. So far though, our outcomes of highest LER at extremely narrow configurations seem to be consistent with previous studies, which are discussed in the following subsection. An alternative approach would be to assess the same using a 3D representation of the canopies with a functional structural plant model (e.g. Zhu et al., 2015; Evers et al., 2018) as this approach explicitly captures detailed aspects of the leaf placement and light distribution. 4.5. Have previous studies been too optimistic about intercropping? Previously tested strip configurations in the study area, 6:2 11

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