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Optimization can provide the fundamental link between leaf photosynthesis, gas exchange and water relations


Tight coordination in the photosynthetic, gas exchange and water supply capacities of leaves is a globally conserved trend across land plants. Strong selective constraints on leaf carbon gain create the opportunity to use quantitative optimization theory to understand the connected evolution of leaf photosynthesis and water relations. We developed an analytical optimization model that maximizes the long-term rate of leaf carbon gain, given the carbon costs in building and maintaining stomata, leaf hydraulics and osmotic pressure. Our model demonstrates that selection for optimal gain should drive coordination between key photosynthetic, gas exchange and water relations traits. It also provides predictions of adaptation to drought and the relative costs of key leaf functional traits. Our results show that optimization in terms of carbon gain, given the carbon costs of physiological traits, successfully unites leaf photosynthesis and water relations and provides a quantitative framework to consider leaf functional evolution and adaptation.

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Fig. 1: Optimization scheme for predicting long-term coordination of leaf photosynthetic, gas exchange and water relations traits.
Fig. 2: Dependence of optimal leaf traits on light-saturated CO2 assimilation rate.
Fig. 3: Predicted effects of leaf-to-air water mole fraction difference and source water potential on leaf traits.
Fig. 4: Proportion of the total cost of stomata, hydraulics and osmotic pressure attributable to each trait.

Data availability

The data used are available in Supplementary Table 1. Data are available at

Code availability

Code is available at


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We thank P. Franks for discussions on the coordination of photosynthesis, stomata and leaf hydraulics; T. Buckley and R. Dewar for early discussions on optimization; and O. Binks for general discussions. This work was supported by the Australian Research Council Centre of Excellence for Translational Photosynthesis (CE1401000015). R.M.D. was supported by an ANU Gwendolyn Woodroofe PhD Scholarship.

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R.M.D., T.J.B. and G.D.F. conceived of the study. R.M.D. developed the model with input from T.J.B., F.A.B. and G.D.F. T.J.B. provided data. R.M.D. wrote the manuscript with input from T.J.B., F.A.B. and G.D.F.

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Correspondence to Graham D. Farquhar.

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Peer review information Nature Plants thanks Jaideep Joshi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Deans, R.M., Brodribb, T.J., Busch, F.A. et al. Optimization can provide the fundamental link between leaf photosynthesis, gas exchange and water relations. Nat. Plants 6, 1116–1125 (2020).

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