Cropping systems that rely on renewable energy and resources and are based on ecological principles could be more stable and productive into the future than current monoculture systems with serious unintended environmental consequences such as soil erosion and water pollution. In nonagricultural systems, communities with higher species diversity have higher productivity and provide other ecosystem services. However, communities of well-adapted crop species selected for biomass production may respond differently to increasing diversity. Diversity effects may be due to complementarity among species (complementary resource use and facilitative interactions) or positive selection effects (e.g., species with higher productivity dominate the mixture), and these effects may change over time or across environments. Our goal was to identify the ecological mechanisms causing diversity effects in a biodiversity experiment using agriculturally relevant species, and evaluate the implications for the design of sustainable cropping systems. We seeded seven perennial forage species in a replicated field experiment at two locations in Iowa, USA, and evaluated biomass productivity of monocultures and two- to six-species mixtures over 3 years after the establishment year under management systems of contrasting intensity: one or three harvests per year. Productivity increased with seeded species richness in all environments, and the positive relationship did not change over time. Polyculture overyielding was due to complementarity among species in the community rather than to selection effects of individual species. Complementarity increased as a log-linear function of species richness in all environments, and this trend was consistent across years. Legume–grass facilitation may explain much of this complementarity effect. Although individual species with high biomass production had a major effect on productivity of mixtures, the species producing the highest biomass in monoculture changed over the years in most environments. Furthermore, transgressive overyielding was observed and was more prevalent in later years, in some environments. We conclude that choosing a single well-adapted species for maximizing productivity may not be the best alternative over the long term and that high levels of species diversity should be included in the design of productive and ecologically sound agricultural systems.

Summary: 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 proposeGeneralisedDiversity‐Interactions models that include many of the features of existing models and have several novel features.GeneralisedDiversity‐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 θ. A value of θ < 1 corresponds to a stronger than expected contribution of species' pairs to ecosystem functioning, particularly at low relative abundance of species. Varying the value of θ has profound consequences for community‐level properties ofBEFrelationships, including: (i) saturation properties of theBEFrelationship; (ii) the stability of ecosystem function across communities; (iii) the likelihood of transgressive overyielding. For low values of θ, loss of species can have a much greater impact on ecosystem functioning than loss of community evenness. GeneralisedDiversity‐Interactions models serve to unify the modelling ofBEFrelationships as they include several other current models as special cases. GeneralisedDiversity‐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 competingBEFmodels for these data. They were significantly better than Diversity‐Interactions models in five experiments. Synthesis. We show thatGeneralizedDiversity‐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 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.