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.

Increased biodiversity may improve ecosystem services, including herbage yield. A mixture experiment was carried out at five sites in Northern Europe and one in Canada to investigate whether mixtures of grasses and legumes would give higher herbage yield than monocultures. Resistance of the mixtures to weed invasion and nutritive value of the herbage were also investigated. The experimental layout followed a simplex design, where four species differing in specific functional traits, timothy (Phleum pratense L.), smooth meadow grass (Poa pratensis L.), red clover (Trifolium pratense L.) and white clover (Trifolium repens L.), were grown in monocultures and eleven different mixtures with systematically varying proportions of the four species. Positive diversity effects (DE) were observed, leading to greater herbage dry‐matter (DM) yield in mixtures than expected from species sown in monocultures. For centroid mixtures, the DE generated on average an additional 32, 25 and 21% of the DM yield than would be expected from the monocultures in the first, second and third year respectively. On average, the mixtures were 9, 15 and 7% more productive than the most productive monoculture (transgressive overyielding) in the first, second and third year respectively. These benefits persisted over the three harvest years of the experiment and were consistent among most sites. This positive effect was not accompanied by a reduction in herbage digestibility and crude protein concentration that is usually observed with increased DM yield. Mixtures also reduced the invasion of weeds to <5% of herbage yield compared to monocultures (10–60% of herbage yield).

Summary 1.The development of models of the relationship between biodiversity and ecosystem function (BEF) has advanced rapidly over the last 20 years, incorporating insights gained through extensive experimental work. We propose Generalised Diversity-Interactions models that include many of the features of existing models and have several novel features. Generalised Diversity-Interactions models characterise the contribution of two species to ecosystem function as being proportional to the product of their relative abundances raised to the power of a coefficient h. 2. A value of h < 1 corresponds to a stronger than expected contribution of species' pairs to ecosystem functioning, particularly at low relative abundance of species. 3. Varying the value of h has profound consequences for community-level properties of BEF relationships, including: (i) saturation properties of the BEF relationship; (ii) the stability of ecosystem function across communities; (iii) the likelihood of transgressive overyielding. 4. For low values of h, loss of species can have a much greater impact on ecosystem functioning than loss of community evenness. 5. Generalised Diversity-Interactions models serve to unify the modelling of BEF relationships as they include several other current models as special cases. 6. Generalised Diversity-Interactions models were applied to seven data sets and three functions: total biomass (five grassland experiments), community respiration (one bacterial experiment) and nitrate leaching (one earthworm experiment). They described all the nonrandom structure in the data in six experiments, and most of it in the seventh experiment and so fit as well or better than competing BEF models for these data. They were significantly better than Diversity-Interactions models in five experiments. 7. Synthesis. We show that Generalized Diversity-Interactions models quantitatively integrate several methods that separately address effects of species richness, evenness and composition on ecosystem function. They describe empirical data at least as well as alternative models and improve the ability to quantitatively test among several theoretical and practical hypotheses about the effects of Journal of Ecology 2013Ecology , 101, 344-355 doi: 10.1111Ecology /1365Ecology -2745 biodiversity levels on ecosystem function. They improve our understanding of important aspects of the relationship between biodiversity (evenness and richness) and ecosystem function (BEF), which include saturation, effects of species loss, the stability of ecosystem function and the incidence of transgressive overyielding.

Most ecosystems provide multiple services, thus the impact of biodiversity losses on ecosystem functions may be considerably underestimated by studies that only address single functions. We propose a multivariate modelling framework for quantifying the relationship between biodiversity and multiple ecosystem functions (multifunctionality). Our framework consolidates the strengths of previous approaches to analysing ecosystem multifunctionality and contributes several advances. It simultaneously assesses the drivers of multifunctionality, such as species relative abundances, richness, evenness and other manipulated treatments. It also tests the relative importance of these drivers across functions, incorporates correlations among functions and identifies conditions where all functions perform well and where trade‐offs occur among functions. We illustrate our framework using data from three ecosystem functions (sown biomass, weed suppression and nitrogen yield) in a four‐species grassland experiment. We found high variability in performance across the functions in monocultures, but as community diversity increased, performance increased and variability across functions decreased.

Abstract. Biodiversity is an important determinant of primary productivity in experimental ecosystems. We combine two streams of research on understanding the effects of biodiversity on ecosystem function: quantifying phylogenetic diversity as a predictor of biodiversity effects in species-rich systems and the contribution of pairwise interspecific interactions to ecosystem function. We developed a statistical model that partitions the effect of biodiversity into effects due to community phylogenetic diversity and other community properties (e.g., average pairwise interaction, between-and within-functional-group effects, and so forth). The model provides phylogenetically based species-level explanations of differences in ecosystem response for communities with differing species composition. In two well-known grassland experiments, the model approach provides a parsimonious description of the effects of diversity as being due to the joint effect of the average pairwise statistical interaction and to community phylogenetic diversity. Effects associated with functional groupings of species in communities are largely explained by community phylogenetic diversity. The model approach quantifies a direct link between a measure of the evolutionary diversity of species and their interactive contribution to ecosystem function. It proves a useful tool in developing a mechanistic understanding of variation in ecosystem function.

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.