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.

Gene flow from sugar beets to sea beets occurs in the seed propagation areas in southern Europe. Some seed propagation also takes place in Denmark, but here the crop-wild gene flow has not been investigated. Hence, we studied gene flow to sea beet populations from sugar beet lines used in Danish seed propagation areas. A set of 12 Danish, two Swedish, one French, one Italian, one Dutch, and one Irish populations of sea beets, and four lines of sugar beet were analysed. To evaluate the genetic variation and gene flow, eight microsatellite loci were screened. This analysis revealed hybridization with cultivated beet in one of the sea beet populations from the centre of the Danish seed propagation area. Triploid hybrids found in this population were verified with flow cytometry. Possible hybrids or introgressed plants were also found in the French and Italian populations. However, individual assignment test using a Bayesian method provided 100% assignment success of diploid individuals into their correct subspecies of origin, and a Bayesian Markov chain Monte Carlo (MC MC) approach revealed clear distinction of individuals into groups according to their subspecies of origin, with a zero level of genetic admixture among subspecies. This underlines that introgression beyond the first hybridization is not extensive. The overall pattern of genetic distance and structure showed that Danish and Swedish sea beet populations were closely related to each other, and they are both more closely related to the population from Ireland than to the populations from France, the Netherlands, and Italy.