Summary1 Ecological and agronomic research suggests that increased crop diversity in speciespoor intensive systems may improve their provision of ecosystem services. Such general predictions can have critical importance for worldwide food production and agricultural practice but are largely untested at higher levels of diversity. 2 We propose new methodology for the design and analysis of experiments to quantify diversity-function relationships. Our methodology can quantify the relative strength of inter-specific interactions that contribute to a functional response, and can disentangle the separate contributions of species richness and relative abundance. 3 Applying our methodology to data from a common experiment at 28 European sites, we show that the above-ground biomass of four-species mixtures (two legumes and two grasses) in intensive grassland systems was consistently greater than that expected from monoculture performance, even at high productivity levels. The magnitude of this effect generally resulted in transgressive overyielding. 4 A combined analysis of first-year results across sites showed that the additional performance of mixtures was driven by the number and strength of pairwise inter-specific interactions and the evenness of the community. In general, all pairwise interactions contributed equally to the additional performance of mixtures; the grass-grass and legume-legume interactions were as strong as those between grasses and legumes. 5 The combined analysis across geographical and temporal scales in our study provides a generality of interpretation of our results that would not have been possible from individual site analyses or experimentation at a single site. 6 Our four-species agricultural grassland communities have proved a simple yet relevant model system for experimentation and development of methodology in diversity-function research. Our study establishes that principles derived from biodiversity research in extensive, semi-natural grassland systems are applicable in intensively managed grasslands with agricultural plant species.

Summary 1.A coordinated continental-scale field experiment across 31 sites was used to compare the biomass yield of monocultures and four species mixtures associated with intensively managed agricultural grassland systems. To increase complementarity in resource use, each of the four species in the experimental design represented a distinct functional type derived from two levels of each of two functional traits, nitrogen acquisition (N 2 -fixing legume or nonfixing grass) crossed with temporal development (fast-establishing or temporally persistent). Relative abundances of the four functional types in mixtures were systematically varied at sowing to vary the evenness of the same four species in mixture communities at each site and sown at two levels of seed density. 2. Across multiple years, the total yield (including weed biomass) of the mixtures exceeded that of the average monoculture in >97% of comparisons. It also exceeded that of the best monoculture (transgressive overyielding) in about 60% of sites, with a mean yield ratio of mixture to best-performing monoculture of 1Á07 across all sites. Analyses based on yield of sown species only (excluding weed biomass) demonstrated considerably greater transgressive overyielding (significant at about 70% of sites, ratio of mixture to best-performing monoculture = 1Á18).3. Mixtures maintained a resistance to weed invasion over at least 3 years. In mixtures, median values indicate <4% of weed biomass in total yield, whereas the median percentage of weeds in monocultures increased from 15% in year 1 to 32% in year 3. 4. Within each year, there was a highly significant relationship (P < 0Á0001) between sward evenness and the diversity effect (excess of mixture performance over that predicted from the monoculture performances of component species). At lower evenness values, increases in community evenness resulted in an increased diversity effect, but the diversity effect was not significantly different from the maximum diversity effect across a wide range of higher evenness values. The latter indicates the robustness of the diversity effect to changes in species' relative abundances. 5. Across sites with three complete years of data (24 of the 31 sites), the effect of interactions between the fast-establishing and temporal persistent trait levels of temporal development was highly significant and comparable in magnitude to effects of interactions between N 2 -fixing and nonfixing trait levels of nitrogen acquisition. 6. Synthesis and applications. The design of grassland mixtures is relevant to farm-level strategies to achieve sustainable intensification. Experimental evidence indicated significant yield benefits of four species agronomic mixtures which yielded more than the highest-yielding monoculture at most sites. The results are relevant for agricultural practice and show how grassland mixtures can be designed to improve resource complementarity, increase yields and reduce weed invasion. The yield benefits were robust to considerable changes in the relative propo...

Abstract. We develop a modeling framework that estimates the effects of species identity and diversity on ecosystem function and permits prediction of the diversity-function relationship across different types of community composition. Rather than just measure an overall effect of diversity, we separately estimate the contributions of different species interactions. This is especially important when both positive and negative interactions occur or where there are patterns in the interactions. Based on different biological assumptions, we can test for different patterns of interaction that correspond to the roles of evenness, functional groups, and functional redundancy. These more parsimonious descriptions can be especially useful in identifying general diversity-function relationships in communities with large numbers of species. We provide an example of the application of the modeling framework. These models describe community-level performance and thus do not require separate measurement of the performance of individual species. This flexible modeling approach can be tailored to test many hypotheses in biodiversity research and can suggest the interaction mechanisms that may be acting.

Current challenges to global food security require sustainable intensification of agriculture through initiatives that include more efficient use of nitrogen (N), increased protein self‐sufficiency through homegrown crops, and reduced N losses to the environment. Such challenges were addressed in a continental‐scale field experiment conducted over 3 years, in which the amount of total nitrogen yield (Ntot) and the gain of N yield in mixtures as compared to grass monocultures (Ngainmix) was quantified from four‐species grass–legume stands with greatly varying legume proportions. Stands consisted of monocultures and mixtures of two N2‐fixing legumes and two nonfixing grasses. The amount of Ntot of mixtures was significantly greater (P ≤ 0.05) than that of grass monocultures at the majority of evaluated sites in all 3 years. Ntot and thus Ngainmix increased with increasing legume proportion up to one‐third of legumes. With higher legume percentages, Ntot and Ngainmix did not continue to increase. Thus, across sites and years, mixtures with one‐third proportion of legumes attained ~95% of the maximum Ntot acquired by any stand and had 57% higher Ntot than grass monocultures. Realized legume proportion in stands and the relative N gain in mixture (Ngainmix/Ntot in mixture) were most severely impaired by minimum site temperature (R = 0.70, P = 0.003 for legume proportion; R = 0.64, P = 0.010 for Ngainmix/Ntot in mixture). Nevertheless, the relative N gain in mixture was not correlated to site productivity (P = 0.500), suggesting that, within climatic restrictions, balanced grass–legume mixtures can benefit from comparable relative gains in N yield across largely differing productivity levels. We conclude that the use of grass–legume mixtures can substantially contribute to resource‐efficient agricultural grassland systems over a wide range of productivity levels, implying important savings in N fertilizers and thus greenhouse gas emissions and a considerable potential for climate change mitigation.