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- Materials and methods
The principal reason cited for intercropping multiple species is to increase efficiency of natural resource use, in particular solar radiation (Keating & Carberry 1993). As a consequence, intercropping has been credited with an increase in total biological productivity per unit area of land, generally known as an intercrop advantage (Willey 1979a). However, there is much debate as to the statistical validity of many claims of an intercrop advantage (Trenbath 1974). The main issues centre on the statistical analysis of productivity data and two questions in particular.
While the most commonly used design in intercrop studies is the replacement series (Willey 1979a; Gibson et al. 1999), this design is criticized on the grounds that the density of one component is confounded with that of the other component species (Snaydon 1991, 1994). Consequently estimation of the effects of intra- and interspecific competition cannot be distinguished (Watkinson & Freckleton 1997). Alternatively, with an additive or additive series design, the use of appropriate regression statistics allows the effects of both intra- and interspecific competition on yield to be analysed (Freckleton & Watkinson 2000).
The land equivalent ratio (LER) is the index most frequently used to compare intercrop and monocrop yields (Willey 1979a). The LER provides a comparative measure of the biological efficiency of pure and mixed species cropping systems calculated in units of land area, and can be interpreted as the relative land area required under monocropping to produce the harvested yields achieved in an intercrop. The LER is calculated thus:
- (eqn 1)
where yi and yj are the yields of species i and j in monoculture and yij and yji the yields in mixtures of species i and j, respectively. LER values greater, and less than, unity identify intercrop combinations that are more, or less, biologically productive per unit area, respectively, than monocrops.
Many of the indices used to measure the net competitive effect of neighbours or the overall yield advantage, in a similar manner to the LER, have been criticized for the failure of their values to remain constant over a range of densities (Connolly 1986; Law & Watkinson 1987). In addition, Freckleton & Watkinson (1997) note that indices fail to give any indication of the changing form of the yield–density relationship under varying environmental and competitive conditions. They further argue that the inability to dissociate intra- and interspecific competition using an index limits the description of competition to merely the net effect on a per capita basis (Freckleton & Watkinson 1999).
Given that the comparison of intercrop and monocrop yields is regularly based on data obtained from experiments using a substitutive design and calculated using the LER, there appears to be demand for an unequivocal and unified approach to the assessment of the biological productivity of intercropping. This would necessitate the identification of optimal crop density combinations that maximize yield, but research into the methodology of determining such combinations has been limited (Mead 1979; Willey & Rao 1980; Vandermeer 1989).
The objectives of this study were to draw upon research methodologies from the field of population ecology to (i) identify the optimum density combinations of the two species in an intercrop design, and (ii) compare the relative advantages of intercropping with monocropping. This was done by using a yield–density model (Watkinson 1981) and an additive experimental design to quantify the intra- and interspecific competition in maize and bean grown in both monocrop and intercrop. Maize and bean were chosen for this study as they are a widely practised cereal and legume intercrop combination and are regularly found to produce a LER value > 1 (Santalla, Deron & Escribano 1994; Siame, Willey & Morse 1998).
Materials and methods
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- Materials and methods
The experiment was conducted at Horticulture Research International, Wellesbourne, UK, 52·12° N and 1·35° W (National Grid reference SP271570). The soil type was a sandy loam of the Wick Series. The site required the removal of barley stubble from a crop planted in autumn 1996. This was done by applying Paraquat on 30 April 1997 and then spading in the debris on 13 May 1997 to a depth of approximately 30 cm using a Tomlin spader.
The experiment consisted of crops of fodder maize Zea mays var. Loft L. and dwarf french bean Phaseolus vulgaris var. Newton L. grown both in monoculture and a variety of mixtures. Maize seed was supplied by Huntseeds (Lydney, UK) and treated with Thiram and Methiocarb, while the bean seed was supplied by Elson Seeds (Spalding, UK) and treated with Aatifon, Thiram and Dichlofenthion. Bean plants were inoculated with Rhizobium (strain 3622) after 75% of seedlings had emerged (20 June 1997).
The experiment was a split-split-plot design that allowed for 20 treatment combinations (Table 1). The site was 87·8 × 26·8 m and divided into three replicate blocks (Fig. 1). Each block was split into two main plots: a main crop of maize and a main crop of bean was randomly allocated to the main plots within each block. Each main plot was split into 10 subplots, five of which contained monocrop treatments and five of which contained intercrop treatments. The 10 subplots were randomly allocated within the main plots. Each subplot allowed for six harvest areas. There was a total of 60 subplots in the experiment.
Table 1. The density of maize and beans (plants m−2) used in the 20 monoculture and intercrop treatment combinations, together with the plot length (m) of each treatment, mean LER (± SE) value for the three replicates calculated using equation 1, and total plant dry weight at 105 DAPM
|Monoculture/main crop*||Density (plants m−2)||Component crop†||Density (plants m−2)||Plot length (m)||LER (2 d.f.)|
|Maize|| 9·8||–||–|| 9·44||–|
|Bean|| 9·8||–||–|| 9·44||–|
|Maize||13·1||Bean|| 5·5|| 8·20||0·96 (0·085)|
|Maize||13·1||Bean|| 6·6|| 7·08||0·85 (0·133)|
|Maize||13·1||Bean|| 8·7|| 7·08||1·01 (0·114)|
|Maize||13·1||Bean||13·1|| 7·08||0·89 (0·033)|
|Maize||13·1||Bean||26·2|| 7·08||0·89 (0·127)|
|Bean||13·1||Maize|| 5·5|| 8·20||0·95 (0·033)|
|Bean||13·1||Maize|| 6·6|| 7·08||0·73 (0·121)|
|Bean||13·1||Maize|| 8·7|| 7·08||0·89 (0·120)|
|Bean||13·1||Maize||13·1|| 7·08||1·08 (0·080)|
|Bean||13·1||Maize||26·2|| 7·08||1·09 (0·083)|
Figure 1. The layout of the experiment in the field (not to scale). An example is shown of a subplot containing a main and component crop.
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Each block was surrounded by a 2-m guard area of bare ground. Within each block, a tractor width of 1·83 m was left bare between the two main plots. There was a 0·5-m guard area at the side of each subplot and a 1-m guard area at the end. All subplots were 1·83 m wide and varied in length according to the treatment they contained. Monocrop stands contained three rows. Intercrop stands were of an additive nature and contained a total of five rows (two rows of component crop sown between the three rows of main crop).
The site was tine harrowed and sown with maize on 14 May and beans on 30 May 1997, both dates being within the recommended sowing periods for the UK. To aid harvesting and the statistical analysis of final dry weight, the sowing dates of the crops were staggered in an attempt to ensure that both species reached maturity at a similar time. Both crops were sown using an Oyjord drill (an experimental cone drill for drilling small areas) set at a between-row spacing of 0·75 m. Although the Oyjord drill does not sow at a constant density, care was taken to sow an initial density of seed equivalent to approximately 60 plants m−2. Intercropped treatments were produced by drilling a component crop between the main crop rows, producing an additive design of alternative crop rows with a between-row spacing of 0·38 m for the middle three rows within each subplot.
After emergence, the treatments were produced by thinning the seedlings to an approximate between-plant distance of 20, 16, 12, 8 and 4 cm. The density of plants m−2 was then calculated by multiplying the number of plants in 1 m of row by the number of rows in a subplot, divided by plot width. This equated to a density of 8·2, 9·8, 13·1, 19·7 and 39·3 plants m−2, respectively, in monocrop stands. The three rows of main crop in an intercrop stand equated to a density of 13·1 plants m−2, and the two rows of component crop to a density of 5·5, 6·6, 8·7, 13·1 and 26·2 plants m−2. The density ranges used in the experiment were chosen so as to incorporate the recommended density of 11 plants m−2 for maize (Huntseeds 1995) and the recommended inter-row spacing of 6–7 cm for bean (PGRO 1999) when sown in monocrop stands.
Nitram (ammonium nitrate) granules (34·5% N) were applied on 24 April 1997 at a rate of 174 kg ha−1 using an agrimono napsac. A delay in sowing and high rainfall resulted in considerable nitrogen leaching; this necessitated a further application of Nitram on 6 May at a rate of 100 kg ha−1. A soil sample taken on 1 July showed the C : N ratio to be high and the level of nitrogen to be below that recommended for maize. An additional top dressing of 50 kg ha−1 was applied by hand on 4 July 1997.
The soil moisture on the site was kept sufficient for crop growth throughout the duration of the experiment by using a sprinkler irrigation system on a daily basis after an absence of rain for a period of 2–3 days. Guard areas were kept weed-free and treatment plots were hand-weeded at monthly intervals. Aphids were controlled using applications of Aphox (Plant Protection) and grey mould was controlled on beans by spraying with Folio 575sc (Ciba Agricultural).
A total of six harvests was taken from each subplot at 36, 51, 69, 85, 105 and 128 days after the maize was sown. Plots were harvested sequentially along their length. At each harvest six individuals of the main crop were removed from the middle row of each subplot, and in intercrop treatments the three closest individuals from each of the neighbouring component crop rows were also removed. At least four guard plants were left growing at each end of the middle row and a minimum of three guard plants were left growing between each harvest area. The single guard row of plants along the long side of the plots was considered sufficient to eliminate most of the confounding influence of edge effect. The between-row spacing in this experiment was at least 0·38 cm, and edge effects typically only penetrate about 20 cm into crop plots (Peach, Benjamin & Mead 2000).
Dry weight measurements were taken after the plants had been oven-dried for a period of 48 h at 80 °C.
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The bean crop was ready to harvest at 105 days after planting maize (DAPM). It was assumed that in mechanized systems the two crops would generally be harvested simultaneously and particular attention was therefore focused on the data from this harvest.
Analysis of variance (anova) was used to analyse the logarithm of monocrop and main crop yield m−2 at 105 DAPM. The anova model was a randomized complete block with treatments of main crop species and main crop and component crop density nested in the treatment structure. Using an F-test, no significant difference was found between the within-block and between-block variances.
The LER was calculated for each block using equation 1. The denominator values of yi and yj were taken as the maximum yield of maize produced in monoculture stands and the maximum yield of bean produced in monoculture stands, respectively, within each block (Huxley & Maingu 1978; Mead & Willey 1980). A t-test was used to assess if the LER values were significantly different from unity.
A transform-both-sides approach (TBS) with a log-transformation (Rudemo, Ruppert & Streibig 1989) was used to stabilize the variance in the maize and bean data. The relation between the mean plant dry weight, w̄, and density, N, of species i and j in a mixed stand at 105 DAPM was explored using the following two-species generalized linear reciprocal model (Watkinson 1981; Wright 1981):
- w̄i = wmi(1 + aiNi + aijNj)−1(eqn 2)
where wmi is a parameter representing the mean dry weight of an isolated plant of species i at a given time, and a is a density-dependent feedback parameter. The competition coefficients ai and aij measure the effect of increasing intraspecific densities (Ni) and interspecific densities (Nj), respectively, on species i. As the per capita competition coefficient ai has been shown to co-vary with wmi, i.e. intraspecific competition increases with plant weight (Li, Watkinson & Hara 1996; Freckleton & Watkinson 1997), the per individual equivalence coefficient ɛij was also calculated:
The equivalence coefficient measures how many individuals of species i have an equivalent competitive effect to one individual of species j (Watkinson 1981). A value of ɛij < 1 indicates that the effect of intraspecific competition is greater than that of interspecific competition, and the converse is the case for a value ɛij > 1. The measure of variance of the equivalence coefficient, ɛij (σɛ2), can be calculated using the following formula (Haefner 1996):
- (eqn 4)
A Levenberg–Marquardt estimation method was used to obtain a least-squares estimate of the parameters log wmi, ai and aij using equation 2. The equivalence coefficient was calculated using equation 3.
An F-test was used to compare the two-species version of the generalized linear reciprocal model (equation 2) with the one-species version of the model, i.e. excluding the interspecific competition coefficient, aij (equation 5).
- w̄i = wmi(1 + aiNi)−1(.eqn 5)
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Yields in monoculture of both maize and bean at 105 DAPM increased with density to a maximum of 1142 and 469 g m−2, respectively (Fig. 2a,c). Where maize was grown at a range of densities with a constant density of beans (Fig. 2a), there was no effect of the presence of bean on the yield of maize. However, where maize was grown at a single density with an increasing density of beans (Fig. 2b), there was some decrease in the yield of maize. In contrast, whenever bean was grown in the presence of maize, either with bean at a range of densities with a constant density of maize (Fig. 2c), or with bean grown at a single density with an increasing density of maize (Fig. 2d), the mean yield of bean was considerably lower than when bean was grown in monoculture. At 105 DAPM the mean height of maize in mixed stands was 160·1 cm (±1·7 SE) and the mean height of bean was 39·5 cm (±1·6 SE).
Figure 2. The relationship at 105 DAPM between the mean yield (g m−2) and the density of (a) maize in monoculture (○) and maize as the component crop in an intercrop (•), (b) maize as the main crop in an intercrop (•), (c) bean in monoculture (○) and bean as the component crop in an intercrop (•), and (d) bean as the main crop in an intercrop (•), displayed on a log-transformed scale. Note that the main crop yields of maize (b) and bean (d) are plotted against the density of the component crop in the intercrop. Maize SED = 152·0, bean SED = 65·7 (d.f. 26).
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Averaging over densities, the yield of maize in monoculture was 917 g m−2 and the yield of beans in monoculture was 324 g m−2, whereas in mixed stands the yield of maize was 912 g m−2 but the yield of beans was reduced to only 75 g m−2 (P < 0·01).
The LER values ranged from 0·73 to 1·09 (Table 1). Less than a third of the LER values suggested an intercrop advantage and the highest values were obtained from those plots sown with a high density of maize. None of the LER values was significantly different from unity.
When the two-species reciprocal model was fitted to the logarithm of the mean dry weight of maize and bean in intercrop, this revealed a simultaneous increase in the parameter values for log wm and ai over time (Fig. 3). There was no marked difference in the effect of intraspecific competition, as measured by parameter ai, between the species. In contrast, estimates of the effect of interspecific competition, as measured by parameter aij, showed a different pattern and value for the two species. Estimates of aij for the effect of bean on maize fluctuated at a low value over time, while the values for the effect of maize on bean were generally higher and increased with time, although the interspecific competition coefficient was not significantly different to zero for either species. These patterns were similarly reflected in the values of the equivalence coefficients (ɛ).
Figure 3. Parameter estimates for the two-species reciprocal model (equation 2), where log wm, ai and aij are estimated parameters for maize and bean at each harvest up to 105 DAPM. Standard error bars are shown for each time period (d.f. 12). Equivalence coefficients, ɛ, calculated using equation 3.
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Assuming a final harvest of both crops at 105 DAPM, the two-species yield version of the reciprocal model (equation 2) when fitted to the data could account for 94% and 90% of the variation in the mean dry weight of maize and bean grown in intercropped stands. Intraspecific competition had a greater effect on maize yield than interspecific competition, while interspecific competition had a greater effect on bean yield on a per capita basis. The equivalence coefficient estimated the intensity of maize interspecific competition to have increased over time to approximately four times that of bean on an individual plant basis.
In order to assess the importance of the interspecific competition coefficient, the one-species version of the model (equation 5) was fitted to the data for maize and bean. The two-species version of the model provided a significantly better fit to the data for bean (F0·01(1),13,12 = 9·01), although the inclusion of the interspecific competition coefficient did not improve the fit of the model to the mean dry weight of maize. However, given the biological significance of interspecific competition in the growth of two species in an intercrop, the two-species version of the generalized linear reciprocal model (equation 2) was used for all further analysis. When an F-test was used to compare the fit of the two-species regression model to that provided by the anova model, no significant difference was found for either beans or maize data.
The parameter estimates for maize and bean at 105 DAPM were used to estimate the response surface of the yields of the two crops in an intercrop at the full complement of density combinations used in the experiment using equation 2. The response surfaces for the logarithm of the yield of maize (Fig. 4a) showed there to be little effect of increasing bean density on the yield of maize. The asymptotic yield–density response in Fig. 4a indicated that the maize crop was close to a constant final yield at the higher maize densities.
Figure 4. Estimated individual yields of (a) maize and (b) bean (logarithmic scale) over a range of densities of the two species at 105 DAPM. The estimated yields were derived using equation 2 with the following parameter values: (a) wmi = 226·99 (± 19·975, d.f. 12), ai = 0·156 (± 0·044, d.f. 12), aij = 0·002 (± 0·01, d.f. 12); (b) wmi = 69·34 (± 20·386, d.f. 12), ai = 0·161 (± 0·154, d.f. 12), aij = 0·659 (± 0·465, d.f. 12).
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The response surfaces for the logarithm of the yield of bean (Fig. 4b) showed that bean yield continued to increase with an increase in bean density, although at higher densities the yield of bean tended towards an asymptote. Increasing densities of maize produced significant decreases in the yield of bean.
An estimate of the response surface of the combined yield of the two species was produced by summing the individual maize and bean yields (Fig. 5). The shape of the response surface for total yield was similar to the response surface for maize by itself, although total yield was slightly higher, thus reflecting the domination of the mixtures by maize and its greater contribution to total yield over all density combinations. The close correspondence of predicted intercrop yields to those observed suggested that the estimated competition coefficients did not vary with density.
Figure 5. Logarithm of the estimated total yield of maize and bean at 105 DAPM over a combination of densities of the two species.
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The estimated LER across a range of densities (Fig. 6) was calculated from the predicted yields in mixtures (Fig. 4). At low densities of either species the LER suggested a disadvantage to intercropping. The advantage of intercropping appeared, however, to increase with density; the LER index increased more with bean than maize density such that, at high densities of bean, the density of maize had only a limited impact on the LER. An inspection of the surface for the LER indicated that the minimum density combination required to produce the maximum yield advantage within the density range considered, comprised maize being planted at a density of 11 plants m−2 and bean being planted at a density of 39 plants m−2.
Figure 6. Response surface for the LER calculated over a range of densities of maize and bean grown in an intercrop at 105 DAPM. The response surface was calculated using equation 1 on the predicted yields obtained from the two-species reciprocal model (equation 2).
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The yield–density relationship for maize when grown in monoculture was found to be asymptotic and similar in form to the response curves obtained from a series of fodder maize density trials conducted in England by Bunting (1971). Bean similarly displayed an asymptotic yield–density response curve in agreement with other studies (Andrews & Hardwick 1981; Vandermeer 1986). When bean was planted at a constant density in intercropped stands with an increasing density of maize, the yield of bean was reduced by up to 50%. In contrast, when maize was planted at a constant density with an increasing density of bean, the yield of maize was only marginally reduced. The significantly greater effect of maize on the yield of bean, than the effect of bean on the yield of maize, is a common response found in intercropping experiments including these two species (Willey 1979b; Siame, Willey & Morse 1997; Carruthers et al. 2000)
When comparing the yield of maize in monoculture to the total yield of maize and bean in an intercrop, neither cropping system produced a consistently greater biological productivity per unit area over the range of densities considered, although the intercrop yield was generally higher. However, when considering the total biological productivity per unit area for bean, all intercrop treatments produced a total yield that was considerably larger than the yield of bean grown in monoculture at a range of densities. Willey & Osiru (1972) similarly found that maize grown in monoculture regularly produced yields equal to, or greater than, the total yield obtained in an intercrop, while the yield of bean grown in monoculture was consistently lower than the total yield obtained in an intercrop. This is perhaps to be expected given the higher yield potential of maize compared with bean.
The maximum monocrop yields of maize and bean per block were used in the calculation of the LER. These yields were chosen in order to standardize the comparison of biological productivity in the two cropping systems across the range of intercrop treatments, and provide a measure of dispersal around the LER. However, the choice of monocrop yield to be used in the calculation of a LER is not without dispute. While some researchers (Huxley & Maingu 1978; Mead & Willey 1980) specify how the standardizing monocrop yield should be selected, others (Francis 1989) consider that the choice of monocrop yield depends on experimental objectives, the interpretation of which are at the discretion of the researcher.
While only three of the intercrop treatments produced a LER value greater than one, many maize and bean intercrop experiments report a LER value greater than one. It is regularly found that maize has a higher yielding potential and is more competitive than bean. Willey & Osiru (1972) noted that when the most competitive species in an intercrop is also the species with the highest yielding potential, the LER will be biased in favour of a value greater than one. In the case of a maize and bean intercrop, maize provides a greater proportion of the total yield harvested from an intercrop than the total yield harvested when the two crops are grown in monoculture, if the sowing densities of maize and bean are the same in both monoculture and intercropping. Consequently, when the yield from the intercrop is compared with the total yield from maize and bean in monoculture, the LER will tend towards a value greater than one. The LER calculation has also been found to tend towards a value greater than one where the intercrops differ in the timing of their maturity periods (Odulaja 1996).
In order to answer the question of whether it is more biologically productive to intercrop maize and bean or to cultivate a proportion of land with each crop grown in monoculture, further clarification of the biological productivity requirements from the intercrop are required. Willey (1979a) distinguishes three alternative intercrop requirements for a given area of land: (i) intercropping must provide a minimum yield of a main crop and some yield of a component crop; (ii) the combined intercrop yield must exceed the higher monocrop yield; and (iii) the combined intercrop yield must exceed a combined monocrop yield. Clearly, the composite nature of the LER fails to provide any indication of the individual yields and thus cannot measure the biological productivity where the intercrop requirements are options (i) and (ii) above. The LER is limited to comparing the biological productivity in option (iii) only, where the total yield from an intercrop is compared with the total yield in monoculture. The broad range of LER values calculated in this study highlights the failure of the index to provide a quantitative assessment of yield loss or gain for an individual species grown in an intercrop (Banik 1996).
In addition to the assessment of biological productivity, the LER has previously been used to consider the economic productivity of a cropping system (Mead & Willey 1980). However, a lack of solid economic foundations and empirical support for the incorporation of supposed farmer behaviour has hindered attempts to apply an economic interpretation to the index (Ranganathan, Fafchamps & Walker 1991).
The LER is not dissimilar from a number of other indices that claim to state something about competition; they all essentially compare yields in monoculture and mixture. While some of these indices have been used to make statements about competition intensity, e.g. aggressivity index (McGilchrist & Trenbath 1971), and about niche differentiation, e.g. relative yield total (de Wit & van den Bergh 1965), they all essentially attempt to make statements about the nature of interspecific competition from measures of the net effect of competition, which includes not only interspecific competition but also intraspecific competition. This has led to the frequent misinterpretation of index values, with the net competitive effect in a mixed stand being attributed entirely to interspecific competition, thus generating criticism (Connolly 1986; Law & Watkinson 1987; Austin et al. 1988).
Alternatively, we have used a non-linear regression technique to dissociate intra- and interspecific competition and predict the yield response surface of maize and bean over a range of densities of the two crops when grown as an intercrop. The response surfaces for the individual species indicate that the yield of maize increases with density to an asymptote and that an increase in the density of bean has little effect on the yield of maize. The response surface for bean indicates that even at low densities of maize, the yield of bean is reduced substantially in the presence of maize. Consequently, the optimum yield of bean obtainable from the range of densities considered is achieved when bean is planted in a monoculture at the highest density of 39 plants m−2.
The response surface for the total maize and bean yield indicates that a greater yield per unit area can be obtained from intercropping maize and bean at any of the density combinations considered, than can be obtained from either maize or bean grown as a monocrop. These data allow the farmer to identify the optimal density combination for an intercrop of maize and bean. The response surface approach may also be used when the farmer’s objectives extend beyond the simple maximization of biological productivity per unit area. For example, a farmer may wish to achieve a target marketable yield per crop, maximize the protein content contained within total yield, or specify the proportional contribution of each crop to total yield. Allometric relations between the yield of a plant part and total plant weight (Watkinson 1981) allow the same modelling approach to be used to predict the yield of a plant part. Perhaps of more importance is the identification of optimal density combinations in terms of maximizing gross economic margin. Given the substantial reduction in the individual plant yield of bean when grown in the presence maize, this would suggest that the maximum gross economic margin obtainable from these two species is likely to be different to the density combination that would provide maximum biological productivity per unit area. Clearly, the response surface approach can offer a valuable contribution to the identification of optimum density combinations to achieve a broad range of objectives.
The production of the response surfaces depends initially upon estimating three parameters for each species from data obtained from an experiment using an additive experimental design and containing a range of monocrop and intercrop densities. The use of an additive design in the intercrop treatments is necessary for the dissociation of intra- and interspecific competition (Snaydon 1991, 1994; Watkinson & Freckleton 1997). The three parameters estimated from the data are the yield of an isolated plant (wm), the per capita effect of intraspecific competition (ai) and the per capita effect of interspecific competition (aij).
The estimation of the parameter values for the two-species reciprocal model elucidates the competitive relationship between maize and bean at the observed densities. A comparison of the parameter values estimated for maize and bean shows that, while an isolated maize plant has a greater weight than an isolated bean plant (wmi), the estimated effect of intraspecific competition (ai) is similar for the two species. The parameter estimates for interspecific competition (aij) show that the growth of the bean plants was significantly reduced by the increasing interspecific competition from the larger maize plants, but that beans had little impact on the yield of maize.
Although the interspecific competition coefficients for maize and bean are not statistically significant, the significantly better fit provided by the two-species version of the model to the mean plant weight of bean, indicates the importance of interspecific competition from maize in determining the growth of bean in an intercrop. In addition, the inclusion of the interspecific term in the model enables calculation of the equivalence coefficient (ɛ), which provides further clarification of the competitive interactions between the two species. In estimating how many maize plants are equivalent to a single bean plant and vice versa, the equivalence coefficient indicates the relative importance of both intra- and interspecific interactions in determining the individual yields of maize and bean in an intercrop. The increasing value of the equivalence coefficient for maize with bean over time indicates the increasing importance of interspecific competition from the maize crop, relative to intraspecific competition from neighbouring bean plants, on the yield of bean. At the final harvest, the effect of one maize plant on the yield of a bean plant was equivalent to that of more than four bean plants. In contrast, the effect of a bean plant on the yield of maize was equivalent to approximately one-twentieth of a maize plant. The progressive increase in the value of the equivalence coefficient would suggest an increasing asymmetry in the level of competition between the species over time. This may reflect the increasing relative difference in the height, and consequentially interception of solar radiation, of the two crops over the growing season. Indeed, Weiner, Griepentrog & Kristensen (2001) found the initial difference in the individual size of a crop and weed plant resulted in an increase in asymmetric competition with time.
While the above discussion has focused on the comparative analysis of the yields obtained from maize and bean in monoculture and intercropping, there still remains the challenge of designing optimal intercrop systems to satisfy the objectives of the farmer. It has long been recognized that one of the primary issues to be addressed when designing intercrop systems is the relative densities of the component crops (Francis, Flor & Pragner 1978; Mead 1979; Willey & Rao 1981). Manipulating the relative densities of two species, either in an intercrop or a weed–crop scenario, facilitates the management of asymmetric competition (Weiner, Griepentrog & Kristensen 2001). The first stage in identifying the optimal density combination requires an understanding of the effect of density on the yield of the two species in the intercrop. Here we have shown that a single additive design coupled with regression analysis can be used to determine the optimal planting densities of crops in an intercrop. The experimental design incorporates the three basic requirements of (i) both species being grown at a range of densities, (ii) both species being grown in monoculture and mixed stands, and (iii) mixed stands being additive in design. Moreover, the experimental design satisfies these requirements using a relatively restricted range of plant densities and is thus economical in nature. The reciprocal model has then been used to interpolate within the observed density range to estimate the yield of both species at the full complement of density combinations.
The dissociation of intra- and interspecific competition and the subsequent computation of the equivalence coefficient, illuminates the relative importance of intra- to interspecific competition on the individual crop yields in an intercrop. A further benefit of the use of equivalence coefficients in the design of optimal intercropping systems is that the coefficient standardizes the measure of per individual competition across pairwise combinations of species. This will be particularly important for intercrop systems that involve more than two crops.
A major limitation to the regression analysis used in this study is that no account has been taken of the spatial arrangement of the component crops in the mixture. Spatial arrangement is known to affect both the total yield and the variance of individual plant yield in monoculture (Bleasdale 1966) and intercrops (Willey & Rao 1981). However, the reciprocal model has shown some robustness to spatial arrangement in providing a good fit to data from the row arrangement in this experiment, as well as to the neighbourhood designs used by Li (1995). Clearly, given the vast number of spatial arrangements that are possible between multispecies within an intercrop, a spatially explicit model, such as that developed by Pacala & Silander (1987, 1990), may prove advantageous in the optimal design of intercrop systems.