Towards a universal model for carbon dioxide uptake by plants

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Gross primary production (GPP)—the uptake of carbon dioxide (CO2) by leaves, and its conversion to sugars by photosynthesis—is the basis for life on land. Earth System Models (ESMs) incorporating the interactions of land ecosystems and climate are used to predict the future of the terrestrial sink for anthropogenic CO21. ESMs require accurate representation of GPP. However, current ESMs disagree on how GPP responds to environmental variations1,2, suggesting a need for a more robust theoretical framework for modelling3,4. Here, we focus on a key quantity for GPP, the ratio of leaf internal to external CO2 (χ). χ is tightly regulated and depends on environmental conditions, but is represented empirically and incompletely in today’s models. We show that a simple evolutionary optimality hypothesis5,6 predicts specific quantitative dependencies of χ on temperature, vapour pressure deficit and elevation; and that these same dependencies emerge from an independent analysis of empirical χ values, derived from a worldwide dataset of >3,500 leaf stable carbon isotope measurements. A single global equation embodying these relationships then unifies the empirical light-use efficiency model7 with the standard model of C3 photosynthesis8, and successfully predicts GPP measured at eddy-covariance flux sites. This success is notable given the equation’s simplicity and broad applicability across biomes and plant functional types. It provides a theoretical underpinning for the analysis of plant functional coordination across species and emergent properties of ecosystems, and a potential basis for the reformulation of the controls of GPP in next-generation ESMs.

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We thank Y.-S. Lin, V. Maire, B. Medlyn, B. Stocker and IIASA colleagues for discussions, and R. Keeling for comments on successive drafts. The paper is a contribution to the AXA Chair Programme on Biosphere and Climate Impacts and Imperial College’s initiative on Grand Challenges in Ecosystems and the Environment. Research is supported by a National Basic Research Programme of China (2013CB956602) grant to C.P. and H.W., the National Natural Science Foundation of China (Grant no. 31600388) to H.W., an Australian Research Council Discovery grant (‘Next-generation vegetation model based on functional traits’) to I.C.P. and I.J.W., an Australian National Data Service (ANDS) grant (‘Ecosystem production in space and time’) to I.C.P. and Terrestrial Ecosystem Research Council (TERN) grants (‘Ecosystem Modelling and Scaling Infrastructure’) to I.C.P. and B.J.E. TERN and ANDS are supported by the Australian Government National Collaborative Infrastructure Strategy. T.F.K. acknowledges financial support from the Laboratory Directed Research and Development fund under the auspices of DOE, BER Office of Science at Lawrence Berkeley National Laboratory and a Macquarie University Research Fellowship. In addition to the authors of this paper, data were provided by M. Barbour, L. Cernusak, T. Dawson, D. Ellsworth, G. Farquhar, H. Griffiths, C. Keitel, A. Knohl, P. Reich, D. Williams, R. Bhaskar, H. Cornelissen, A. Richards, S. Schmidt, F. Valladares, C. Körner, E.-D. Schulze, N. Buchmann and L. Santiago. We used ‘free and fair use’ eddy-covariance data acquired by the FLUXNET community and, in particular, by the following networks: AmeriFlux (US Department of Energy, Biological and Environmental Research, Terrestrial Carbon Program), AsiaFlux, CarboEuropeIP, Fluxnet-Canada (supported by CFCAS, NSERC, BIOCAP, Environment Canada and NRCan), OzFlux and TCOS-Siberia. We acknowledge the financial support to the eddy-covariance data harmonization provided by CarboEuropeIP, FAO- GTOS-TCO, iLEAPS, Max Planck Institute for Biogeochemistry, National Science Foundation, University of Tuscia, Université Laval and Environment Canada and US Department of Energy, and the database development and technical support from Berkeley Water Center, Lawrence Berkeley National Laboratory, Microsoft Research eScience, Oak Ridge National Laboratory, University of California–Berkeley and University of Virginia.

Author information


  1. State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, College of Forestry, Northwest A & F University, Yangling, 712100, Shaanxi, China

    • Han Wang
    • , I. Colin Prentice
    •  & Changhui Peng
  2. Department of Biological Sciences, Macquarie University, North Ryde, NSW 2109, Australia

    • Han Wang
    • , I. Colin Prentice
    • , Trevor F. Keenan
    • , Ian J. Wright
    •  & Bradley J. Evans
  3. Ecosystems Services and Management Program, International Institute for Applied Systems Analysis, A-2361, Laxenburg, Austria

    • Han Wang
  4. AXA Chair of Biosphere and Climate Impacts, Department of Life Sciences, Imperial College London, Silwood Park Campus, Buckhurst Road, Ascot, SL5 7PY, UK

    • I. Colin Prentice
    •  & Tyler W. Davis
  5. Climate and Ecosystem Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA, 94720, USA

    • Trevor F. Keenan
  6. United States Department of Agriculture-Agricultural Research Service, Robert W. Holley Center for Agriculture and Health, Ithaca, NY, 14853, USA

    • Tyler W. Davis
  7. Ecology and Evolution Research Centre, School of Biological, Earth and Environmental Sciences, The University of New South Wales, Randwick, NSW 2052, Australia

    • William K. Cornwell
  8. Faculty of Agriculture and Environment, Department of Environmental Sciences, The University of Sydney, Sydney, NSW, 2006, Australia

    • Bradley J. Evans
  9. Department of Biological Sciences, Institute of Environmental Sciences, University of Quebec at Montreal, C.P. 8888, Succ. Centre-Ville, Montréal, Québec, H3C 3P8, Canada

    • Changhui Peng


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H.W. and I.C.P. derived the predictions. H.W. carried out all the analyses and constructed the Figures and Tables. I.C.P. and T.F.K. contributed to the analysis and writing. T.W.D., B.J.E. and I.C.P. developed and tested the flux partitioning method. T.W.D. developed the global flux database and all the GPP computations. I.J.W. proposed least-cost hypothesis and contributed to the analysis. W.K.C. originated and compiled the Δ13C dataset. H.W. and I.C.P. wrote the first draft, and all authors contributed to the final draft.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Han Wang or Changhui Peng.

Electronic supplementary material

  1. Supplementary Information

    Detailed description of the theoretical model.