Biodiversity-ecosystem functioning (BEF) research has provided strong evidence and mechanistic underpinnings to support positive effects of biodiversity on ecosystem functioning, from single to multiple functions. This research has provided knowledge gained mainly at the local alpha scale (i.e. within ecosystems), but the increasing homogenization of landscapes in the Anthropocene has raised the potential that declining biodiversity at the beta (across ecosystems) and gamma scales is likely to also impact ecosystem functioning. Drawing on biodiversity theory, we propose a new statistical framework based on Hill-Chao numbers. The framework allows decomposition of multifunctionality at gamma scales into alpha and beta components, a critical but hitherto missing tool in BEF research; it also allows weighting of individual ecosystem functions. Through the proposed decomposition, new BEF results for beta and gamma scales are discovered. Our novel approach is applicable across ecosystems and connects local- and landscape-scale BEF assessments from experiments to natural settings.

Bavarian Forest National Park Grafenau Germany

Biological Sciences University of Toronto Scarborough Toronto Ontario Canada

Czech Academy of Sciences Biology Centre Institute of Entomology České Budějovice Czech Republic

Department for Spatial Structures and Digitization of Forests University of Göttingen Göttingen Germany

Department of Agronomy National Taiwan University Taipei Taiwan

Department of Animal Ecology 1 Bayreuth Center of Ecology and Environmental Research University of Bayreuth Bayreuth Germany

Department of Animal Ecology and Tropical Biology Biocenter University of Würzburg Würzburg Germany

Ecology of Fungi Bayreuth Center of Ecology and Environmental Research University of Bayreuth Bayreuth Germany

Epidemiology Biostatistics and Prevention Institute University of Zurich Zurich Switzerland

Faculty of Biological Sciences Institute for Ecology Evolution and Diversity Conservation Biology Goethe University Frankfurt Frankfurt am Main Germany

Field Station Fabrikschleichach Department of Animal Ecology and Tropical Biology Biocenter University of Würzburg Rauhenebrach Germany

Geobotany Faculty of Biology University of Freiburg Freiburg Germany

German Centre for Integrative Biodiversity Research Halle Jena Leipzig Leipzig Germany

Hessian Agency for Nature Conservation Environment and Geology Biodiversity Center Gießen Germany

Institute of Biology Leipzig University Leipzig Germany

Institute of Ecology Leuphana University Lüneburg Lüneburg Germany

Institute of General Ecology and Environmental Protection Technische Universität Dresden Tharandt Germany

Institute of Statistics National Tsing Hua University Hsin Chu Taiwan

Plant Ecology and Nature Conservation Group Wageningen University and Research Wageningen The Netherlands

Research Center for Advanced Science and Technology The University of Tokyo Tokyo Japan

Silviculture and Forest Ecology of the Temperate Zones University of Göttingen Göttingen Germany

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