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Climate change, land-use change, pollution and exploitation are among the main drivers of species' population trends; however, their relative importance is much debated. We used a unique collection of over 1,000 local population time series in 22 communities across terrestrial, freshwater and marine realms within central Europe to compare the impacts of long-term temperature change and other environmental drivers from 1980 onwards. To disentangle different drivers, we related species' population trends to species- and driver-specific attributes, such as temperature and habitat preference or pollution tolerance. We found a consistent impact of temperature change on the local abundances of terrestrial species. Populations of warm-dwelling species increased more than those of cold-dwelling species. In contrast, impacts of temperature change on aquatic species' abundances were variable. Effects of temperature preference were more consistent in terrestrial communities than effects of habitat preference, suggesting that the impacts of temperature change have become widespread for recent changes in abundance within many terrestrial communities of central Europe., Additionally, we appreciate the open access marine data provided by the International Council for the Exploration of the Sea. We thank the following scientists for taxonomic or technical advice: C. Brendel, T. Caprano, R. Claus, K. Desender, A. Flakus, P. R. Flakus, S. Fritz, E.-M. Gerstner, J.-P. Maelfait, E.-L. Neuschulz, S. Pauls, C. Printzen, I. Schmitt and H. Turin, and I. Bartomeus for comments on a previous version of the manuscript. R.A. was supported by the EUproject LIMNOTIP funded under the seventh European Commission Framework Programme (FP7) ERA-Net Scheme (Biodiversa, 01LC1207A) and the long-term ecological research program at the Leibniz-Institute of Freshwater Ecology and Inland Fisheries (IGB). R.W.B. was supported by the Scottish Government Rural and Environment Science and Analytical Services Division (RESAS) through Theme 3 of their Strategic Research Programme. S.D. acknowledges support of the German Research Foundation DFG (grant DO 1880/1-1). S.S. acknowledges the support from the FP7 project EU BON (grant no. 308454). S.K., I.Kü. and O.S. acknowledge funding thorough the Helmholtz Association’s Programme Oriented Funding, Topic ‘Land use, biodiversity, and ecosystem services: Sustaining human livelihoods’. O.S. also acknowledges the support from FP7 via the Integrated Project STEP (grant no. 244090). D.E.B. was funded by a Landes–Offensive zur Entwicklung Wissenschaftlich–ökonomischer Exzellenz (LOEWE) excellence initiative of the Hessian Ministry for Science and the Arts and the German Research Foundation (DFG: Grant no. BO 1221/23-1).

It is urgent in science and society to address climate change and other sustainability challenges such as biodiversity loss, deforestation, depletion of marine fish stocks, global ill-health, land degradation, land use change and water scarcity. Sustainability science (SS) is an attempt to bridge the natural and social sciences for seeking creative solutions to these complex challenges. In this article, we propose a research agenda that advances the methodological and theoretical understanding of what SS can be, how it can be pursued and what it can contribute. The key focus is on knowledge structuring. For that purpose, we designed a generic research platform organised as a three-dimensional matrix comprising three components: core themes (scientific understanding, sustainability goals, sustainability pathways); cross-cutting critical and problem-solving approaches; and any combination of the sustainability challenges above. As an example, we insert four sustainability challenges into the matrix (biodiversity loss, climate change, land use changes, water scarcity). Based on the matrix with the four challenges, we discuss three issues for advancing theory and methodology in SS: how new synergies across natural and social sciences can be created; how integrated theories for understanding and responding to complex sustainability issues can be developed; and how theories and concepts in economics, gender studies, geography, political science and sociology can be applied in SS. The generic research platform serves to structure and create new knowledge in SS and is a tool for exploring any set of sustainability challenges. The combined critical and problem-solving approach is essential.