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.

Questions: Trait differentiation among species occurs at different spatial scales within a region. How does the partitioning of functional diversity help to identify different community assembly mechanisms?Location: Northeastern Spain.Methods: Functional diversity can be partitioned into within‐community (α) and among‐communities (β) components, in analogy to Whittaker's classical α and β species diversity concept. In light of ecological null models, we test and discuss two algorithms as a framework to measure α and β functional diversity (the Rao quadratic entropy index and the variance of trait values). Species and trait (specific leaf area) data from pastures under different climatic conditions in NE Spain are used as a case study.Results: The proposed indices show different mathematical properties but similarly account for the spatial components of functional diversity. For all vegetation types along the climatic gradient, the observed α functional diversity was lower than expected at random, an observation consistent with the hypothesis of trait convergence resulting from habitat filtering. On the other hand, our data exhibited a remarkably higher functional diversity within communities compared to among communities (α≫β). In contrast to the high species turnover, there was a limited functional diversity turnover among communities, and a large part of the trait divergence occurred among coexisting species.Conclusions: Partitioning functional diversity within and among communities revealed that both trait convergence and divergence occur in the formation of assemblages from the local species pool. A considerable trait convergence exists at the regional scale in spite of changes in species composition, suggesting the existence of ecological redundancy among communities.