Introduction

As human activities cause widespread threats to biodiversity, investigation of the potential effect of declining species diversity on ecosystem functions has emerged as an important scientific question (Costanza et al. 1997; Loreau et al. 2001; Hooper et al. 2005). Investigations of the relationship between diversity and ecosystem functioning have mostly used extensively managed grassland communities as a model system, and generally demonstrate that biomass production is reduced when plant species diversity declines (Tilman et al. 1996; Hector et al. 1999; Tilman et al. 2001; Hooper & Dukes 2004; Hooper et al. 2005; Roscher et al. 2005). Explanations of such patterns centre around hypotheses that more diverse communities better utilize available resources due to their greater occupation of niche space, and that they have a greater probability of containing positive inter-specific interactions (Trenbath 1974; Harper 1977; Vandermeer 1989; Hector et al. 1999). Selection effects (Huston 1997; Tilman et al. 1997; Loreau 2000) can also contribute, and these different explanations need not be mutually exclusive (Loreau 2000; Hooper et al. 2005).

Intensive grassland systems cover large land areas, perform important ecosystem functions such as biomass production and nutrient cycling and are often associated with high input of nutrients and the widespread use of monocultures in research and practice (but see Sanderson et al. 2004). Diversity-function research suggests that increased diversity in such systems could improve the provision of ecosystem services (Hooper et al. 2005). Such general predictions are largely untested due to the rarity of multi-species agronomic experiments (Vandermeer 1989; Federer 1999; Gibson et al. 1999). Whether ecological principles from diversity-function research in extensive semi-natural grassland communities (Hector et al. 1999; Tilman et al. 2001; Hooper et al. 2005) translate to intensively managed grasslands (Tilman 1999) requires investigation.

Diversity-function studies have generally manipulated the number (richness) or composition of species or functional groups in the community. However, relative abundance is also expected to be an important determinant of diversity-function relationships (Nijs & Roy 2000; Wilsey & Potvin 2000; Hooper et al. 2005). In diversity-function experiments the relative abundance of species has been almost universally used as a passive descriptor of a community (Stirling & Wilsey 2001; Mulder et al. 2004) but has rarely been investigated as an active determinant of ecosystem function (Schmid et al. 2002). The few results from experimental manipulations of relative abundance are ambiguous, sometimes indicating an effect on selected ecosystem functions (Wilsey & Potvin 2000; Smith & Knapp 2003; Smith et al. 2004), and sometimes not (Wilsey & Polley 2004). Where the effect of diversity depends on inter-specific interactions (Trenbath 1974; Harper 1977; Loreau 2000), their total contribution depends on the number and the contribution of individual interactions. The number of interactions depends on species richness. The contribution of a particular interaction depends on the strength of the interaction and the relative abundances of the species involved (Sheehan et al. 2006). One would not expect a large contribution from two species that interact strongly but for which one or both have a very low relative abundance. At low evenness (e.g. close to a monoculture) all interactions will involve at least one species with very low relative abundance and hence the total contribution of interactions (the effect of diversity) will be low. The net effect of interactions may lead to overyielding (or underyielding), where the performance in mixture exceeds that expected from performance in monocultures and interactions may be so strong as to lead to transgressive overyielding (Trenbath 1974), where mixture performance exceeds that of the highest-yielding monoculture. To assess the contribution of inter-specific interaction to ecosystem function requires an experimental and modelling framework within which the contributions of interactions can be separately estimated. To date such a framework has been lacking. We develop it in this paper.

We manipulated relative abundance to investigate the contribution of inter-specific interaction to diversity–function relationships in an experiment using four-species plant mixtures, repeated at 28 sites in Europe. We developed novel methods of design and analysis to address issues in diversity-function research. We address the following questions and discuss how our methods contribute to resolving issues in diversity-function research.

• 1Can functional responses in mixed-species communities be decomposed into the sum of identity effects, and the effects of inter-specific interaction, and how does this relate to the richness and evenness of the community?
• 2Are there patterns among the interaction effects that lead to a simplified description of the effect of diversity on a functional response?
• 3Is there evidence of overyielding or transgressive overyielding in our four-species communities?
• 4Are diversity effects consistent across large spatial scales?

Materials and methods

experiment design

A common experiment with 30 plots was established at 28 sites in 17 countries in Europe (see Fig. 1 and Table S1 in Supplementary Material) in 2002 or 2003, giving 840 plots in total. At each site two legume and two grass species were sown. One of the grass and one of the legume species was fast establishing and the other was slow establishing. Five species-groups were used: north European (NE), mid-European (ME), dry Mediterranean (DM), moist Mediterranean (MM) (Table 1) and a fifth group (Other) consisted of three sites, each with its own species (Table S1). We used a simplex design (Cornell 2002; Ramseier et al. 2005) to define four monocultures and 11 mixtures of the four species (Fig. 2a). The 11 mixtures consisted of four mixtures dominated in turn by each species (sown proportions of 70% of dominant and 10% of each of the other species), six mixtures dominated in turn by pairs of species (40% of each of two species and 10% of the other two) and the centroid community (25% of each species). The monocultures and mixtures were sown at two levels of overall sown abundance (Connolly et al. 2001) (low being 60% of high). Species proportions at sowing were based on proportions of seed mass considered appropriate for monocultures for each species at a site.

Table 1.  Composition of species-groups in the different geographical areas ME, NE, MM and DM

Species	Functional group	Mid-European (ME)	Northern European (NE)	Moist Mediterranean (MM)	Dry Mediterranean (DM)
Five species-groups were used: north European (NE), mid-European (ME), dry Mediterranean (DM), moist Mediterranean (MM) (Table 1) and a fifth group (Other) consisted of three sites, each with its own species (see Table S1).
1	Grass – Fast	Lolium perenne	Phleum pratense	Lolium perenne	Lolium rigidum
2	Grass – Slow	Dactylis glomerata	Poa pratensis	Dactylis glomerata	Dactylis glomerata
3	Legume – Fast	Trifolium pratense	Trifolium pratense	Trifolium pratense	Medicago polymorpha
4	Legume – Slow	Trifolium repens	Trifolium repens	Medicago sativa	Medicago sativa
Number of sites		15	5	3	2

A common protocol was established for plot management. Experimental communities were randomly assigned to plots and managed by cutting (two to five cuts per annum as appropriate for local conditions). Annual application of nitrogen fertiliser ranged from 0 to 200 kg ha⁻¹. Minimum plot size was 2 × 3 m. For estimation of yield (total annual above-ground biomass including unsown species) a subplot (≥ 3 m²) was cut to a height of 5 cm at each harvest. See Table S1 for other site information and management details.

diversity model

We propose a diversity model for the analysis of yield that includes the effects of species identity, interactions based on species relative abundance and overall sown abundance. We define the diversity effect (D) as the difference between mixture performance and that expected from proportional combination of monocultures (Polley et al. 2003; Spehn et al. 2005). D is zero for a monoculture and must be close to zero for a community that is almost a monoculture. We first define a simple model based on a measure of sown community evenness that captures the effect of all pairwise interactions; this generalizes naturally to a wide range of models that describe alternative patterns of inter-specific interaction.

Evenness is a measure of the distribution of the relative abundance of species in a community. Where there are up to s species in a community and P_i is the sown relative abundance of the ith species, we define the sown evenness (E) of the community as E =, which lies between 0 for monocultures and 1 for a community in which all s species are equally represented (Fig. 2). The multiplier 2s/(s − 1) is introduced to ensure that the values of E lie between 0 and 1. For a community strongly dominated by one species, at least one of the P_i values in each P_iP_j pair will be small and so its evenness will be close to zero. As D and E are zero for monocultures the relationship between D and E must intercept the origin. Overall sown abundance (M) was coded −1 and 1 for low and high, respectively, with a mean of zero for the design. Applying the evenness formula to the species proportions in our experimental design gives sown evenness values of 0, 0.64, 0.88 and 1 (Fig. 2a). We related yield (y) to species’ sown relative abundance, total sown community abundance and evenness. The basic model for yield at a site was

( (eqn 1))

where β_i is the expected monoculture performance of the ith species at the average overall sown abundance, α is the effect of sown overall abundance, δ is the linear effect of evenness and ɛ is normally distributed with zero mean and constant variance. The coefficient β_i reflects the effect of species identity. (For a monoculture of the ith species P_i = 1, P_j = 0 for j ≠ i and E = 0. Its response is predicted as β_i1 + αM which, at the mean value of M (i.e. zero), gives predicted monoculture yield for the ith species as β_i.) As the performance expected solely from monocultures is , the diversity effect in model 1 is D = δE. For this model the diversity effect changes linearly with evenness and its maximum is δ when E = 1. From the definition of evenness all pairwise interactions among species in this model have the same coefficient (δ(2s/(s − 1))).

Results

combined analysis

In the combined analysis across sites the diversity effect differed between species-groups. D was positively linearly related to evenness for NE (P = 0.002, five sites) and MM (but not significantly, P = 0.108, three sites) and the maximum diversity effect was 2.26 and 1.38 t ha⁻¹, respectively, at E = 1 (Table 3). For ME (15 sites), the relationship between the diversity effect and evenness was quadratic (D = δE + δ₁E²). The estimated maximum diversity effect for ME was 3.09 t ha⁻¹ (P < 0.001) at E = 0.97 (Fig. 3). For ME the effect on yield in multi-species agronomic mixtures seemed less sensitive to modest changes across higher evenness levels (Table 3, Fig. 3), although to intercept the origin the diversity effect must decrease at lower evenness levels. There was a significant difference among identity effects (β_i) for each of the three species-groups, indicating that estimated performance in monoculture differed among species (Table 3).

Table 3.  Estimates of the coefficients in the diversity model for three species-groups from the combined analysis of yield across sites, for the linear model where D = δE and for the quadratic model where D = δE + δ₁E². The coefficient β_i is the expected monoculture performance of the ith species at the average overall sown abundance, α is the effect of sown overall abundance, δ is the linear effect of evenness and δ₁ is the quadratic effect of evenness

Species-group	Coefficient	Coefficient estimate (t ha−1)	Standard error	Approximate d.f.*	Approx t	P > t
* The approximate degrees of freedom (d.f.) are based on the Kenward-Roger approximation (Kenward & Roger 1997) and used in approximate t-tests for coefficients.
ME	β1	7.78	0.709	26	10.98	< 0.001
	β2	8.25	0.709	26	11.65	< 0.001
	β3	10.21	0.792	29	12.89	< 0.001
	β4	7.55	0.792	29	9.54	< 0.001
	α	0.30	0.136	23	2.20	0.039
	δ	6.32	0.783	308	8.07	< 0.001
	δ1	−3.26	0.777	550	−4.20	< 0.001
NE	β1	6.42	1.226	26	5.24	< 0.001
	β2	4.74	1.227	26	3.87	0.01
	β3	6.92	1.376	29	5.03	< 0.001
	β4	4.72	1.371	29	3.44	0.002
	α	0.19	0.237	24	0.78	0.441
	δ	2.26	0.640	23	3.53	0.002
MM	β1	5.13	1.583	26	3.24	0.003
	β2	4.24	1.583	26	2.68	0.013
	β3	8.06	1.770	29	4.55	< 0.001
	β4	7.43	1.770	29	4.20	< 0.001
	α	0.08	0.304	23	0.27	0.792
	δ	1.38	0.825	23	1.67	0.108

Across sites, the annual use of nitrogen (N) fertiliser ranged between 0 and 200 kg ha⁻¹ (Table S1). High N application was not incompatible with producing diversity effects, which were significant for sites (n = 6) with annual N application ≥ 150 kg ha⁻¹ (Table 2, Table S2). To check the robustness of the models based on sown evenness, we fitted the models in Table 3 using established evenness at harvest 1 and obtained similar coefficient estimates (Table S4).

transgressive overyielding

For ME, NE and DM (Fig. 4, Table S3) virtually all the mean yields of mixtures exceeded the mean yield of the highest-yielding monoculture, providing very strong evidence for transgressive overyielding. Estimates of average transgressive overyielding of 12%, 12% and 16% for ME, NE and DM, respectively, were computed by comparing the average mixture yield with the highest yielding monoculture; but the true overyielding effects are likely to be even larger (Appendix S2). Each of the ‘Other’ sites demonstrated transgressive overyielding (P < 0.05) but the MM species-group did not.

Discussion

In our study, the yield of four-species mixtures exceeded that expected from monoculture performances. This diversity effect was consistent across a wide geographical scale, adding generality to our finding. Our methodology partitions functional responses into the sum of the effects of species identity and the effects of inter-specific interactions. We demonstrate that even a modest increase in the diversity of intensive grassland systems can produce diversity benefits leading to transgressive overyielding. The data were best described by a model in which all two-species interactions contributed equally to the diversity effect; a simple model based on the evenness of the community captured the effects of these interactions. The experimental design based on the simplex allows for discrimination among alternative descriptions of the effects of species interactions, which may be more complex than those found here. Moreover, our methodology contributes to resolving issues in diversity-function research and is relevant for both agronomic and ecological investigations of diversity-function relationships.

In our combined analysis we found no evidence for a more complex diversity effect than one based on evenness, despite some evidence for alternatives at individual sites. The models presented in Tables 2 and 3 assume that all pairwise interactions between species contribute equally to the diversity effect; thus, the positive interaction between two grass species or two legume species was as strong as that between a grass and a legume. There is considerable evidence for positive interactions between grasses and legumes (Vandermeer 1989; Zanetti et al. 1997; Hector et al. 1999; Spehn et al. 2005). The mechanism for a mixing effect among grass or legume species is less clear but synergistic effects can occur in mixtures without legumes (Trenbath 1974; van Ruijven & Berendse 2003; Hooper & Dukes 2004). If these grass-grass and legume-legume effects in our study are due to temporal partitioning between fast- and slow-establishing species (Ofori & Stern 1987; Chesson et al. 2002), it is somewhat surprising that the strength of interaction between species that share both functional group differences (e.g. slow grass × fast legume) does not show an even greater positive effect (Table S2). To provide mechanistic explanations of observed responses and model terms will require information on site environments, the contribution of individual species to total yields, and temporal dynamics.

A positive diversity effect implies overyielding; but does it lead to transgressive overyielding? Our data show that on average within each species group, transgressive overyielding occurred in three of the four species-groups (Fig. 4) and at each of the ‘Other’ sites. The magnitude and generality of transgressive overyielding observed in our study strongly suggests that modest increases in agronomic species diversity can contribute to agricultural production in intensive grassland systems.

This study suggests that to obtain the practical benefit of the diversity effect in intensively managed agricultural grasslands, sowing rates and adaptive management can be used to maintain evenness at levels suggested by Fig. 3. Results for ME indicate that this range of evenness may be quite broad for this species-group (Fig. 3). Of course, yield is one of several important functional responses that are of practical relevance in intensive systems. Mixtures contained much lower proportions and biomass of unsown species than monocultures for all species-groups (Table 4), suggesting reduced invasibility of mixtures. Indeed, as our yield analysis includes unsown species, the diversity effect would be even greater if analysed in terms of sown species only. Other important functional responses will include the nutritional quality of the produced yield as well as the seasonal and multi-annual stability of yield production. Given that the diversity effect in these agricultural mixtures was related to evenness, the temporal persistence of the species in mixtures (to realize the diversity effect) is a significant issue, as are the effects of vegetation dynamics and abiotic factors in affecting persistence.

Designs based on the simplex allow us to estimate interaction effects, to discriminate between a range of possible models and to describe the diversity effect over the widest range of relative abundance and species richness. Models of the diversity effect that are based on our evenness index assume that the effect of diversity is due to pairwise interspecific interactions, all of which are equally strong. However, a model based on evenness may not best describe the diversity effect in other communities. Species may not interact equally, i.e. the strength of inter-specific interaction may differ (Sheehan et al. 2006). Patterns of species interaction may be associated with environmental conditions, with particular species traits (Hooper & Vitousek 1997; Hooper & Dukes 2004), and may involve more than two species.

Our methodology can be used to quantitatively disentangle the separate contributions of species richness and relative abundance to the diversity effect. In the broadest sense, the contribution of species richness to the diversity effect can be discerned by comparing mean or maximum diversity effects at different levels of richness. At each level of richness the community with the maximum diversity effect will depend on the relative strength of inter-specific interactions and may not occur at maximum evenness (the centroid). The effect of variation in relative abundance can be isolated by exploring the diversity effect in communities that have the same level of richness but vary in relative abundance. This broad approach simplifies greatly when the diversity effect is a function of evenness (E) only. The relative effect of changing richness and evenness can be calculated from model 1 or the quadratic model in evenness. For model 1, increasing richness from two to four species increased maximum diversity effects from 0.67δ to δ. Within each level of richness, the effect of varying relative abundance ranges from 0 to 0.67δ for two species and 0 to δ for four-species mixtures. For the quadratic model fitted for ME sites, the effect of changing species richness was weak; the maximum estimated diversity effect for two and three species was only 9.7% and 0.6% lower, respectively, than that for the four-species community. By comparison, changing relative abundance had a far greater effect within two- and three-species mixtures. For two species the range of diversity effects associated with different patterns of relative abundance ranged from 0% to 90.3% of the maximum diversity effect achievable for four species. For three species the range was 0% to 99.4%. In both models the effect of changing relative abundance for a given level of richness was greater than the effect of changing richness (except from a monoculture to two species). The responses to richness in the quadratic model for ME sites suggests saturation (Hooper et al. 2005) of the diversity effect at four species, while model 1 suggests that diversity benefits increase with richness but at a diminishing rate.

Multi-site experiments increase statistical power to detect general relationships that may not be obvious from individual site analyses. Three of the individual site analyses did not show significant diversity effects (Table 2) and seven sites provided evidence of a more complex diversity effect than model 1. The combined analysis identifies effects that are generally consistent, despite variation across individual sites. This analysis generalizes interpretation (Verbeke & Molenberghs 2000); the average diversity effect coefficient(s) is the most reliable predictor of the magnitude of the diversity effect at any location in the absence of additional location-specific information. The formulation of general predictions from diversity-function research for large areas of intensive or natural systems therefore requires experiments to be conducted across multiple sites (Hector et al. 1999). Experiments with perennial species should be conducted over several years to check the persistence or evolution of effects (Hooper et al. 2005; Tilman et al. 2006). Our currently available data (Table 2) highlight the persistence of the effect of diversity over at least 2 years.

Acknowledgements

We wish to thank Tom Bolger, David Gibson, Kristina Stinson, Paul Struik and Brian Wilsey for very helpful comments. Many colleagues, too numerous to list, have assisted with this work. We were supported by the EU Commission through COST Action 852. L.K. was supported by the Irish Environmental Protection Agency. It is with great regret that we note the tragic death of one of our authors, Chiara Coran. Chiara was a young and energetic member of the COST852 team. We wish to express our deep sympathy to her family and colleagues.