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Earth system models (ESMs), which integrate biogeochemical and biogeophysical land-surface processes with physical climate models, have been widely used to demonstrate the importance of land-surface processes in determining climate and to highlight the large uncertainties in quantifying land-surface processes^{4, 5, 6}. Within the biogeophysical components of land-surface processes, g_s plays a pivotal role because it is a key feedback route for carbon and water exchange between the atmosphere and terrestrial vegetation. Stomata are small pores on leaves whose aperture is actively regulated by plants in response to multiple abiotic and biotic factors, and their conductance is a major determinant of global land evapotranspiration and global water and carbon cycles. Therefore, our ability to model the global carbon and water cycles under a future changing climate depends on our ability to predict g_s globally⁷. Many ESMs at present use an empirical stomatal model to predict g_s and, in the absence of information, assume identical parameter values for all non-water-stressed C₃ and C₄ vegetation. For example, the LPJ model⁴ assumes a constant ratio of intercellular to ambient CO₂ concentration (C_i:C_a) of 0.8 for all C₃ vegetation and 0.4 for all C₄ vegetation. The CABLE model⁸ uses the empirical stomatal model of Leuning⁹ with two sets of parameter values, one for all C₃ vegetation and one for all C₄ vegetation. The CLM 4.0 model¹⁰ uses the empirical stomatal model of Ball et al.¹¹ with three sets of parameter values, one for C₄, one for needle-leaf trees, and a third for all other C₃ vegetation. Although there have been previous synthesis studies on plant stomatal conductance and related traits^{3, 7, 12, 13}, we lack a global-scale database and an associated globally applicable model of g_s that allows predictions of stomatal behaviour among PFTs and across climatic gradients.

For this study, we compiled a unique global database of field measurements of g_s and photosynthesis suitable for estimating model parameters. We employed a model of optimal stomatal conductance¹⁴ to develop hypotheses for how stomatal behaviour should vary with environmental factors and with plant traits associated with hydraulic function. The optimization premise underlying this model¹ is that stomata are regulated so as to maximize photosynthesis minus the carbon cost of transpiration, A − λE, where λ (mol CO₂ mol⁻¹ H₂O) is the carbon cost per unit water used by the plant. Intuitively, λ represents the plant’s exchange rate between carbon uptake and water use: a high value of λ indicates that transpiration is costly in carbon terms, meaning that the plant is likely to be conservative in its use of water. From this premise, the model predicts that g_s should be related to photosynthesis, vapour pressure deficit and atmospheric CO₂ concentration, with a single slope parameter, g₁, that is inversely proportional to (refs 1, 14, 15). The slope parameter g₁ is readily estimated from experimental data (Methods) and can be used as an index of λ, where small values of g₁ indicate a high λ. The model also predicts that, under constant environmental conditions, g₁ should be inversely related to plant water-use efficiency¹⁴.

We hypothesized that variation in λ, and therefore in g₁, values among climate zones and PFTs can be predicted from plant carbon–water relations. Specifically, we hypothesized that:

(1) g₁ values among PFTs should vary according to the cost of stemwood construction per unit water transport, such that C₃ herbaceous species should have the largest g₁ (that is, be least water-use efficient), followed by angiosperm trees and gymnosperm trees. We predicted that angiosperm trees would have larger g₁ than gymnosperms due to their higher sapwood permeability, which yields a lower carbon cost of construction per unit water transported. Herbaceous C₄ species form a special case. Due to the different shape of the photosynthesis—g_s response in C₄ plants, the optimal stomatal theory predicts that, for the same λ value, g₁ should be approximately one-fifth of what it would be for C₃ species (see Supplementary Note). We therefore predicted that C₄ plants would have the lowest g₁ and be the most water-use efficient PFT.

(2) For trees, λ should increase with wood density, due to the higher cost of wood construction¹⁶ per unit water transported. Therefore, within both angiosperms and gymnosperms, species with larger wood densities should lead to higher carbon cost per unit water transport (smaller values of g₁).

(3) Low soil water availability should increase λ, so plants adapted to dry environments should have larger λ and lower g₁.

(4) g₁ values should increase with growth temperature for two reasons. First, in the derivation of the optimal stomatal model¹⁴, g₁ is approximately proportional to Γ^∗ (the CO₂ compensation point in absence of photorespiration). As Γ^∗ is exponentially dependent on temperature¹⁷, g₁ should increase with temperature. Second, the viscosity of water decreases with increasing temperature, making it less costly to transport water, leading to an increased g₁ (ref. 15).

To test these hypotheses, we collated a globally distributed database of g_s and photosynthesis, including 56 field studies covering a wide range of biomes from Arctic tundra, boreal and temperate forest to tropical rainforest (Supplementary Table 2). We estimated the model coefficient, g₁, from observations of leaf-level gas exchange (g_s and rates of net photosynthesis, see Methods) and environmental drivers (vapour pressure deficit and ambient CO₂ concentration). Next, we correlated estimates of g₁ with two climatic variables: , which is the mean temperature over the period when daily mean temperatures are above 0 °C, and a moisture index (MI), which is calculated as the ratio of mean annual precipitation to the equilibrium evapotranspiration. Both and MI were derived from observed long-term meteorological data as proxies of the temperature and water availability that are relevant to plant physiological functions for each site¹⁸. Our database included a range of from 2.7 to 29.7 °C and a range of MI from 0.17 to 3.26, representing the majority of the climatic space for vegetation-covered land surfaces (Fig. 1). We then tested how g₁ varies with MI and across PFTs and biomes.

Coloured circles represent climatic space for the database, with different colours indicating different plant functional types. Grey hexagons represent global climatic space for which vegetation is present. The global climatic space data were binned by every 1 °C for temperatures above 0 °C ( ) and every 0.25 for the moisture index (MI). The grey scale bar indicates the number of 0.5 × 0.5 degree pixels for a given binned and MI combination.

Source of data.

We synthesized published and unpublished leaf-level gas exchange data for a wide range of PFTs and biomes (Supplementary Table 2). In all cases, measurements were made using leaf cuvette chambers that measure water vapour and CO₂ fluxes from leaves. We used only data sets including instantaneous measurements under ambient field conditions. We did not include any data sets from standard response curve measurements, such as CO₂ response curves or light response curves. Our database covers 314 species from 56 experimental sites around the world, with 17 sites from Australasia, 15 sites from Europe, 14 sites from North America, six sites from Asia, three sites from South America and one site from Africa. Site latitudes range from 42.9° S to 72.3° N, although the majority of the sites are within the temperate zone (n = 35; latitude range between 23.5° and 55° and between −23.5° and −55°), followed by tropical zone (n = 14; latitude range between −23.5° and 23.5°), boreal zone (n = 6; latitude range between 55° and 66.5°) and Arctic zone (n = 1; latitude range above 66.5°). The whole database is publicly available and can be downloaded from the data repository (http://figshare.com/articles/Optimal_stomatal_behaviour_around_the_world/1304289).

We derived MI and from Climate Research Unit climatology data (CRU CL1.0; ref. 26) from 1960 to 1990 with a modified version of the STASH model²⁷ at a grid resolution of 0.5°. In this derivation, was calculated as the ratio of the annual sum of linear interpolated daily temperatures above 0 °C (growing degree days) to the length of this period; MI was calculated as the ratio of mean annual precipitation to the equilibrium evapotranspiration (E_eq). We estimated E_eq from monthly mean temperature and net radiation (calculated from monthly mean percentage of cloud cover)²⁷. The Sea-WiFS fAPAR (fraction absorbed photosynthetically active radiation) product²⁸ was used to determine areas with green vegetation cover at a grid resolution of 0.5°, as shown in Fig. 1. The wood density data were obtained from the Global Wood Density Database^{2, 29}.

Data analysis.

We used leaf-level gas exchange data sets which were collected with standard portable gas exchange instruments. We used data measured at a photosynthetic photon flux density (PPFD) >0 μmol m⁻² s⁻¹, and only data collected from the top third of the canopy. In all cases, species were grown under ambient environmental conditions and were not subjected to any treatments, such as elevated CO₂, temperature, or drought treatments. We employed the optimal stomatal model¹⁴:

where D is vapour pressure deficit (kPa), A is net photosynthesis rate (μmol m⁻² s⁻¹), C_a is CO₂ concentration at the leaf surface (ppm), and g₁ is the model coefficient. We used a nonlinear mixed-effect model to estimate the model slope coefficient, g₁, for each group separately for various classification schemes, as shown in Fig. 2. In this model, individual species were assumed to be the random effect to account for the differences in the g₁ slope among species within the same group.

In the original derivation of the optimal stomatal model¹⁴, an intercept term g₀ was added to equation (1) to ensure correct behaviour of C_i as A approaches zero, following Leuning⁹. This term is often thought of as representing the minimum, or cuticular stomatal conductance. Here, we did not fit this term for several reasons. First, fitted values of g₀ and g₁ tend to be correlated, meaning that it is not possible to compare values of g₁ across data sets when g₀ has also been fitted. Second, it is not clear that adding an intercept to equation (1) is the correct way to handle a minimum stomatal conductance, because this affects all predictions of g_s, not just those where A is close to zero. It may be more appropriate to include the g₀ term as a minimum bound to equation (1).

To test how g₁ varies with climatic variables (that is, MI and ), we first estimated g₁ for each species using a nonlinear regression model (Supplementary Table 4). We then used a weighted linear mixed-effect model to test the relationship between g₁, MI and . We fitted the model as:

using the inverse of the standard error (SE) of g₁ as the weighting scale to account for the uncertainty of g₁ fitting and assuming PFTs as the random effect to account for the differences in intercept among PFTs. To evaluate the goodness of fit of the linear mixed-effect models, we calculated both the marginal R² to quantify the proportion of variance explained by the fixed factors alone and the conditional R² to quantify the proportion of variance explained by both the fixed and random factors²⁶. The relationship between g₁ and wood density was tested with a simple linear regression model. All model estimations and statistical analyses were performed with R 3.1.0 (refs 30, 31, 32).

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