Summary1. Extensive research shows that more species-rich assemblages are generally more productive and efficient in resource use than comparable assemblages with fewer species. But the question of how diversity simultaneously affects the wide variety of ecological functions that ecosystems perform remains relatively understudied. It presents several analytical and empirical challenges that remain unresolved. In particular, researchers have developed several disparate metrics to quantify multifunctionality, each characterizing different aspects of the concept and each with pros and cons. 2. We compare four approaches to characterizing multifunctionality and its dependence on biodiversity, quantifying (i) magnitudes of multiple individual functions separately, (ii) the extent to which different species promote different functions, (iii) the average level of a suite of functions and (iv) the number of functions that simultaneously exceeds a critical threshold. 3. We illustrate each approach using data from the pan-European BIODEPTH experiment and the R multifunc package developed for this purpose, evaluate the strengths and weaknesses of each approach and implement several methodological improvements. 4. We conclude that an extension of the fourth approach that systematically explores all possible threshold values provides the most comprehensive description of multifunctionality to date. We outline this method and recommend its use in future research.

A rich body of knowledge links biodiversity to ecosystem functioning (BEF), but it is primarily focused on small scales. We review the current theory and identify six expectations for scale dependence in the BEF relationship: (1) a nonlinear change in the slope of the BEF relationship with spatial scale; (2) a scale‐dependent relationship between ecosystem stability and spatial extent; (3) coexistence within and among sites will result in a positive BEF relationship at larger scales; (4) temporal autocorrelation in environmental variability affects species turnover and thus the change in BEF slope with scale; (5) connectivity in metacommunities generates nonlinear BEF and stability relationships by affecting population  synchrony at local and regional scales; (6) spatial scaling in food web structure and diversity will generate scale dependence in ecosystem functioning. We suggest directions for synthesis that combine approaches in metaecosystem and metacommunity ecology and integrate cross‐scale feedbacks. Tests of this theory may combine remote sensing with a generation of networked experiments that assess effects at multiple scales. We also show how anthropogenic land cover change may alter the scaling of the BEF relationship. New research on the role of scale in BEF will guide policy linking the goals of managing biodiversity and ecosystems.

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Biodiversity loss decreases ecosystem functioning at the local scales at which species interact, but it remains unclear how biodiversity loss affects ecosystem functioning at the larger scales of space and time that are most relevant to biodiversity conservation and policy. Theory predicts that additional insurance effects of biodiversity on ecosystem functioning could emerge across time and space if species respond asynchronously to environmental variation and if species become increasingly dominant when and where they are most productive. Even if only a few dominant species maintain ecosystem functioning within a particular time and place, ecosystem functioning may be enhanced by many different species across many times and places (β-diversity). Here, we develop and apply a new approach to estimate these previously unquantified insurance effects of biodiversity on ecosystem functioning that arise due to species turnover across times and places. In a long-term (18-year) grassland plant diversity experiment, we find that total insurance effects are positive in sign and substantial in magnitude, amounting to 19% of the net biodiversity effect, mostly due to temporal insurance effects. Species loss can therefore reduce ecosystem functioning both locally and by eliminating species that would otherwise enhance ecosystem functioning across temporally fluctuating and spatially heterogeneous environments.