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.Increasing plant species richness often increases biomass production in nutrient-poor seminatural grasslands. If such positive diversity-productivity effects also apply to nutrient-rich agricultural grasslands, mixtures could improve resource-use efficiency in the vast area used for forage production. We therefore quantified the diversity-productivity effects in nutrient-rich agricultural grasslands using four-species grass-legume mixtures. 2. The sown overall density and species proportions of Lolium perenne , Dactylis glomerata , Trifolium pratense and Trifolium repens were varied in a 3-year field experiment to investigate the effects of species richness (1, 2, 4 species) and species proportion (0, 3, 10, 25, 40, 50, 70, 90, 100% sowing proportion) on productivity under a nitrogen fertilization of 50, 150 or 450 kg N ha − 1 year − 1 . 3. The four-species mixtures reached up to twice the yield of the average of the four species' monocultures (overyielding up to 106%), predominantly due to combining grass and legume species. Mixtures were up to 57% more productive than the most productive monoculture (transgressive overyielding). Both these diversity-productivity effects appeared across a broad range of species proportions and persisted at the two lower levels of N fertilization for 3 years. Mixtures fertilized with 50 kg N ha− 1 year − 1 produced yields comparable to grass monocultures fertilized with 450 kg N ha − 1 year − 1 , if the legume proportion was about 50 to 70%. Diversityproductivity effects were reduced at the highest level of N fertilization, where they virtually disappeared in the third year. Increased N fertilization also accelerated the observed general trend towards D. glomerata dominated and legume-poor swards. 5. Synthesis and applications . Diversity-productivity effects led to consistent transgressive overyielding in intensively managed grasslands, suggesting a highly increased resource-use efficiency in mixtures. Performance better than monocultures can be achieved with grass-legume mixtures that have a low number of species, across a wide range of species proportions and in nutrient-rich conditions. Processes such as niche complementarity and positive interspecific interactions leading to diversity effects proved to be highly relevant and widely applicable for intensive forage production. Such diversity-productivity effects could allow reduced inputs of N fertilizer without loss of productivity in different grassland production systems.

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