1 Ecological and agronomic research suggests that increased crop diversity in species‐poor 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.

Grassland diversity can support sustainable intensification of grassland production through increased yields, reduced inputs and limited weed invasion. We report the effects of diversity on weed suppression from 3 years of a 31‐site continental‐scale field experiment. At each site, 15 grassland communities comprising four monocultures and 11 four‐species mixtures based on a wide range of species' proportions were sown at two densities and managed by cutting. Forage species were selected according to two crossed functional traits, “method of nitrogen acquisition” and “pattern of temporal development”. Across sites, years and sown densities, annual weed biomass in mixtures and monocultures was 0.5 and 2.0 t DM ha⁻¹(7% and 33% of total biomass respectively). Over 95% of mixtures had weed biomass lower than the average of monocultures, and in two‐thirds of cases, lower than in the most suppressive monoculture (transgressive suppression). Suppression was significantly transgressive for 58% of site‐years. Transgressive suppression by mixtures was maintained across years, independent of site productivity. Based on models, average weed biomass in mixture over the whole experiment was 52% less (95% confidence interval: 30%–75%) than in the most suppressive monoculture. Transgressive suppression of weed biomass was significant at each year across all mixtures and for each mixture. Weed biomass was consistently low across all mixtures and years and was in some cases significantly but not largely different from that in the equiproportional mixture. The average variability (standard deviation) of annual weed biomass within a site was much lower for mixtures (0.42) than for monocultures (1.77). Synthesis and applications. Weed invasion can be diminished through a combination of forage species selected for complementarity and persistence traits in systems designed to reduce reliance on fertiliser nitrogen. In this study, effects of diversity on weed suppression were consistently strong across mixtures varying widely in species' proportions and over time. The level of weed biomass did not vary greatly across mixtures varying widely in proportions of sown species. These diversity benefits in intensively managed grasslands are relevant for the sustainable intensification of agriculture and, importantly, are achievable through practical farm‐scale actions.