Coordination of plant hydraulic and photosynthetic traits: confronting optimality theory with field measurements

Summary

• Close coupling between water loss and carbon dioxide uptake requires coordination of plant hydraulics and photosynthesis. However, there is still limited information on the quantitative relationships between hydraulic and photosynthetic traits.

• We propose a basis for these relationships based on optimality theory, and test its predictions by analysis of measurements on 107 species from 11 sites, distributed along a nearly 3000‐m elevation gradient.

• Hydraulic and leaf economic traits were less plastic, and more closely associated with phylogeny, than photosynthetic traits. The two sets of traits were linked by the sapwood to leaf area ratio (Huber value, v _H). The observed coordination between v _H and sapwood hydraulic conductivity (K _S) and photosynthetic capacity (V _cmax) conformed to the proposed quantitative theory. Substantial hydraulic diversity was related to the trade‐off between K _S and v _H. Leaf drought tolerance (inferred from turgor loss point, –Ψ_tlp) increased with wood density, but the trade‐off between hydraulic efficiency (K _S) and –Ψ_tlp was weak. Plant trait effects on v _H were dominated by variation in K _S, while effects of environment were dominated by variation in temperature.

• This research unifies hydraulics, photosynthesis and the leaf economics spectrum in a common theoretical framework, and suggests a route towards the integration of photosynthesis and hydraulics in land‐surface models.

Introduction

Water transport is essential for plant survival and growth. Hydraulic failure triggers death under severe drought (Rowland et al., ²⁰¹⁵), and differences in hydraulic traits can be used to predict drought‐induced tree mortality (Choat et al., ²⁰¹⁸). Photosynthesis is constrained by hydraulics because water transported through the xylem must replenish water lost through stomata during CO₂ uptake (Brodribb, 2009). Empirical studies (Brodribb et al., ²⁰⁰⁷; Scoffoni et al., ²⁰¹⁶; Zhu et al., ²⁰¹⁸) and optimality arguments (Deans et al., ²⁰²⁰) support a tight coordination between hydraulic and photosynthetic traits. Nonetheless, quantitative understanding of their relationships remains incomplete (Mencuccini et al., ^2019b). Embedding plant hydraulics in vegetation and land‐surface models is desirable (Christoffersen et al., ²⁰¹⁶; Mencuccini et al., ^2019a), not least because an improved understanding of drought effects on photosynthesis and transpiration could remove a leading source of uncertainty in global models (De Kauwe et al., ²⁰¹⁵). This situation provides a strong motivation for theoretical and empirical research on how whole‐plant hydraulic traits are related to (better studied) leaf photosynthetic traits.

The ratio of sapwood area to subtended leaf area (the Huber value, v _H) links whole‐plant to leaf processes (Mencuccini et al., ^2019b; Rosas et al., ²⁰¹⁹). There is a limit to the amount of leaves that a given area of sapwood can support due to its limited capacity to supply water. The plant needs to invest more carbon in sapwood to meet increasing water loss, or to shed leaves to decrease water loss. Therefore, v _H reflects not only the balance between water supply and loss, but also carbon allocation to stems versus leaves. Plants with low v _H tend to have low leaf mass per area (LMA) and low leaf stable carbon isotope ratios (δ¹³C), implying a high ratio of leaf‐internal to ambient CO₂ (χ); high maximum CO₂ assimilation rate (A _sat); high leaf water potential at the turgor loss point (Ψ_tlp, a negative quantity); and high sapwood‐specific hydraulic conductivity (K _S) (Zhu et al., ²⁰¹⁸; Mencuccini et al., ^2019b; Rosas et al., ²⁰¹⁹). High V _cmax and high LMA both require (all else equal) a high v _H, the former because high V _cmax is associated with high photosynthetic rate, stomatal conductance and transpiration, the latter because high‐LMA leaves tend to be associated with low hydraulic conductance. There is considerable independent variation in V _cmax (expressed on an area basis) and LMA that implies that these are separate dimensions influencing v _H. Previous studies have also shown that hydraulic traits are influenced by environmental variables, particularly aridity (Martinez‐Vilalta et al., ²⁰⁰⁹; Gleason et al., ²⁰¹³; Togashi et al., ²⁰¹⁵; Liu et al., ²⁰¹⁹), in a coordinated way. Drought‐adapted plants are characterised by reduced water supply through stems (low hydraulic efficiency, K _S; for example associated with narrow conduits) and/or reduced demand (high v _H), and increased leaf hydraulic safety (low Ψ_tlp). Photosynthetic and leaf economic traits are also influenced by climate. χ increases with growth temperature, and decreases with vapour pressure deficit (D) and elevation (Prentice et al., ²⁰¹⁴; Wang et al., ²⁰¹⁷). Photosynthetic capacity (maximum RuBisCo carboxylation rate, V _cmax) increases with light, and weakly with temperature and D (Smith et al., ²⁰¹⁹). LMA increases with light and aridity, and decreases with temperature (Wright et al., ²⁰⁰⁴; Poorter et al., ²⁰⁰⁹). Although these traits show strong trends with climate, phylogeny controls the variation of hydraulic traits to a large extent due to their dependence on conservative characteristics such as wood anatomy (Rosas et al., ²⁰¹⁹), while photosynthesis‐related traits regulated by biochemical processes show a high degree of plasticity (Dong et al., ²⁰²⁰).

Optimality theory allows testable predictions about trait–trait coordination and can also provide strong explanations for observed responses of traits to environment (Franklin et al., ²⁰²⁰). Among photosynthetic traits, analyses of δ¹³C data have shown quantitative agreement between observed and theoretically predicted environmental responses of χ (Prentice et al., ²⁰¹⁴; Wang et al., ²⁰¹⁷; Lavergne et al., ^2020a). Smith et al. (2019), similarly, used optimality theory to predict the observed environmental responses of V _cmax in a global data set. Sperry et al. (2017) integrated hydraulic traits with a photosynthesis model to predict stomatal conductance using optimality theory. Less attention has been paid to applying optimality theory to predict leaf economic or hydraulic traits. Here we investigated the relationships among photosynthetic, leaf economic and hydraulic traits, and between these traits and climate, using field data collected from 11 sites in the Gongga Mountain region of western China. We extend the optimality framework of Prentice et al. (2014) and Wang et al. (2017), which hypothesises that plants minimise the total cost of maintaining the capacities for photosynthesis and water transport relative to photosynthesis rate, to make explicit quantitative predictions of these relationships. K _S and V _cmax are two key traits related to water transport and photosynthesis/water demand, respectively. Based on the requirement that water transport through xylem must equal water loss via stomata, our optimality model indicates a key role for v _H in achieving this requirement (Mencuccini et al., ^2019b), and confirms a positive relationship between v _H and V _cmax but a negative one with K _S theoretically in a unified framework. Our model therefore provides a new theoretical basis to understand the variations of v _H along environmental gradients.

To test the model, we measured photosynthetic and hydraulic traits on 107 species at 11 sites located in the Gongga Mountain region of Sichuan Province, China. This region (Supporting Information Fig. S1) extends from 29°22′ to 29°55′N and 101°1′ to 102°9′E and spans an elevation range from near sea level to 8000 m, creating a long gradient in growing‐season temperature. Sites from the western side of Gongga Mountain also tend to be drier than sites at corresponding elevations on the eastern side. By sampling 11 sites over a range of nearly 3000 m in elevation, from both the western and eastern sides, we assembled a data set on woody plants encompassing a wide range of climates.

Description

Theory

The theory of v _H variation extends the least‐cost hypothesis of Prentice et al. (2014). According to Fick's law and Darcy's law respectively (Fick, 1855; Whitehead, ¹⁹⁹⁸), transpiration can be calculated from either water demand (Eqn 1) or supply (Eqn 2). The coordination of xylem water transport and stomatal water loss implies that plants should optimally allocate resources so that maximum water transport matches maximum photosynthesis, which leads to Eqn 3:

$$E=1.6g_{\mathrm{s}}D/P_{\text{atm}}$$ (Eqn 1)

$$E=K_{\mathrm{S}}\mathrm{\Delta }\mathrm{\Psi }{v}_{\mathrm{H}}/h$$ (Eqn 2)

$$1.6g_{\mathrm{s}}D/P_{\text{atm}}=K_{\mathrm{S}}\mathrm{\Delta }{\mathrm{\Psi }}_{max}{v}_{\mathrm{H}}/h$$ (Eqn 3)

where E is the transpiration rate (mol m^–2 s^–1), g _s is stomatal conductance to CO₂ (mol m^–2 s^–1), D is the vapour pressure deficit (Pa) and P _atm is the atmospheric pressure (Pa). Here h is the path length (m), roughly equivalent to plant height; K _S is the sapwood‐specific hydraulic conductivity (mol m^–1 s^–1 Pa^–1); v _H is the ratio of sapwood to leaf area (m² m^–2); ΔΨ is the difference between leaf and soil water potential and ΔΨ_max is the maximum decrease in water potential from soil to leaves (Ψ_min and Ψ_soil, Pa).

From the diffusion equation and the photosynthesis model of Farquhar, von Caemmerer and Berry (Farquhar et al., ¹⁹⁸⁰), we can calculate g _s from V _cmax, χ and m _C:

$$g_s=A/\left[\left(c_{\mathrm{a}}/P_{\text{atm}}\right)\left(1‐\chi \right)\right]$$ (Eqn 4)

$$A=m_{\mathrm{C}}{V}_{cmax}$$ (Eqn 5)

$$m_{\mathrm{C}}=(\chi c_{\mathrm{a}}‐{\mathrm{\Gamma }}^{*})/(\chi c_{\mathrm{a}}+K)$$ (Eqn 6)

where A is the assimilation (photosynthesis) rate (mol m^–2 s^–1), c _a is the ambient partial pressure of CO₂ (Pa), χ is the ratio of leaf‐internal to ambient CO₂ partial pressure (Pa Pa^–1), V _cmax is the maximum capacity of carboxylation (mol m^–2 s^–1), Γ^* is the photorespiratory compensation point (Pa), and K is the effective Michaelis–Menten coefficient of RuBisCo (Pa). The factor m _C reduces photosynthesis under natural conditions relative to V _cmax. Substituting g _s from Eqns (Eqn 4), (Eqn 5), (Eqn 6) into Eqn 3 yields Eqn 7, which represents our key optimality theory linking hydraulic and photosynthetic traits. It states that maximum rate of water transport through the xylem equals the maximum rate of water loss through the stomata:

$$\left(K_{\mathrm{S}}/h\right)v_{\mathrm{H}}\mathrm{\Delta }{\mathrm{\Psi }}_{max}=1.6\left(D/c_{\mathrm{a}}\right)m_{\mathrm{C}}{V}_{\mathrm{c}max}/\left(1‐\chi \right)$$ (Eqn 7)

As V _cmax acclimates to the environment on a weekly to monthly timescale, while K _S is determined by xylem structure and therefore less able to vary seasonally, we worked with V _cmax at the mean daily maximum temperature in July (V _cmax,jt) and K _S at the mean daily maximum temperature during the growing season (defined as the period with daytime temperatures > 0°C) (K _S,gt).

In practice, effects of K _S and h are not separable, because the tip‐to‐base widening of xylem elements implies a positive correlation between them that greatly reduces the effect of path length on whole‐stem conductance, so that the whole‐stem conductance is similar to or only slightly lower than the conductance measured near the branch tip (Christoffersen et al., ²⁰¹⁶; Mencuccini et al., ^2019b; Olson et al., ²⁰²¹). We assume ΔΨ_max to be equal to –Ψ_tlp (Ψ_soil ≈ 0 under well watered conditions) as Ψ_tlp is a proxy for Ψ_min (Hochberg et al., ²⁰¹⁸). The uncertainty of the Ψ_tlp proxy has little effect on our results as it is not a principal predictor in our model (shown in Fig. 3). Therefore, to test Eqn 7 we take –Ψ_tlp as a surrogate for ΔΨ_max (Hochberg et al., ²⁰¹⁸) and subsume the effect of height in a composite constant (C), leading to the following relationship after log_e transformation of Eqn 7:

$$\begin{array}{ll}{\text{log}}_{\mathrm{e}}(v_{\mathrm{H}})=& {\text{log}}_{\mathrm{e}}\left(D\right)+{\text{log}}_{\mathrm{e}}\left(m_{\mathrm{C}}\right)+{\text{log}}_{\mathrm{e}}\left(V_{\text{c max,jt}}\right)‐{\text{log}}_{\mathrm{e}}\left(K_{\text{S,gt}}\right)\\ & ‐{\text{log}}_{\mathrm{e}}(‐{\mathrm{\Psi }}_{\text{tlp}})‐{\text{log}}_{\mathrm{e}}\left(1‐\chi \right)‐{\text{log}}_{\mathrm{e}}\left(c_{\mathrm{a}}\right)+C\end{array}$$ (Eqn 8)

where C has a fitted value of 2.27 using all the species sampled (see Fig. S4), which suggests an average ‘effective tree height’ of 6 m.

Fig. 3.

The modelled contribution of different predictors to v _H variation at 11 sites sampled along an elevational gradient in the Gongga Mountains, China. (a) Contribution of direct predictors from Eqn 8. (b) Total contribution of environmental predictors through maximum capacity of carboxylation (V _cmax), the ratio of leaf‐internal to ambient CO₂ partial pressure (χ) and c _a, along with hydraulic traits. In each panel, the vertical black line represents the baseline log_e(v _H) across sites (on which the data were centred, such that the x‐axis represents the contribution of predictors: Δlog_e(v _H)). Transparent bars with black borders show the changes in predicted values compared with the baseline log_e(v _H). Environmental effects are shown in green; photosynthesis‐related effects in orange; hydraulic trait effects: sapwood‐specific hydraulic conductivity (K _S) and leaf water potential at turgor loss point (Ψ_tlp) are shown in blue.

Photosynthetic traits can be estimated from existing optimality models. The least‐cost hypothesis states that plants minimise the combined unit costs (that is, costs per unit of carbon assimilated) of maintaining the capacities for carbon fixation and water transport (Prentice et al., ²⁰¹⁴). The coordination hypothesis states that light‐limited and RuBisCo‐limited photosynthesis rates are approximately equal, to be able to utilise the available light while avoiding wasteful maintenance costs (Chen et al., ¹⁹⁹³). These two hypotheses have already been corroborated by many studies at regional or global scale (Smith et al., ²⁰¹⁹; Lavergne et al., ^2020b; Xu et al., ²⁰²¹). χ in Eqn 8 can be estimated as follows, based on the least‐cost hypothesis (Wang et al., ²⁰¹⁷):

$$\chi ={\mathrm{\Gamma }}^{*}/c_{\mathrm{a}}+\xi \left(1‐{\mathrm{\Gamma }}^{*}/c_{\mathrm{a}}\right)/(\xi +\surd D)$$ (Eqn 9)

where

$$\xi =\surd \left[\beta (K+{\mathrm{\Gamma }}^{*})/(1.6{\eta }^{*})\right]$$ (Eqn 10)

where β is the ratio at 25°C of the unit costs of maintaining carboxylation and transpiration capacities (146, based on a global compilation of leaf δ¹³C measurements), η* is the viscosity of water relative to its value at 25°C, and ξ (Pa^1/2) is a stomatal sensitivity parameter that increases with temperature due to the temperature dependencies of K, Γ^* (increasing) and η* (decreasing).

V _cmax,jt can also be predicted from climate, based on the coordination hypothesis (Smith et al., ²⁰¹⁹):

$$V_{\mathrm{c}max,\text{jt}}\approx {\varphi }_0{I}_{\text{abs}}\left(c_{\mathrm{i}}+K\right)/\left(c_{\mathrm{i}}+2{\mathrm{\Gamma }}^{*}\right)$$ (Eqn 11)

where ϕ ₀ is the intrinsic quantum efficiency of photosynthesis (to which we assign the value 0.085 μmol C μmol^–1 photon), I _abs is the photosynthetic photon flux density (PPFD) absorbed by leaves (mol m^–2 s^–1), and c _i is the leaf‐internal CO₂ partial pressure (c _i = χ c _a) (Pa).

Data and methods

Trait data

Trait data were measured at 11 sites in late July 2018 and August 2019, during the active growing season, in the Gongga Mountain region (29°34′16″–29°54′52″N and 101°59′08″–102°9′42″E, Fig. S1). We collected the data needed to allow the calculation of four leaf traits: leaf mass per area (LMA), leaf nitrogen per unit area (N _area), the maximum capacity of carboxylation (V _cmax), and the ratio of leaf‐internal to ambient CO₂ partial pressure (χ). Hydraulic traits, specifically the ratio of sapwood to leaf area (Huber value, v _H), sapwood‐specific hydraulic conductivity (K _S), wood density (WD) and leaf potential at turgor loss point (Ψ_tlp), were measured on all the woody broad‐leaved species. We sampled all the tree species and at least five shrub species at each site. All samples were taken from the top canopy layer receiving direct sunshine.

LMA was calculated from the measurements of leaf area and dry weight following standard protocols (Cornelissen et al., ²⁰⁰³). Multiple leaves, or leaflets for compound leaves, were randomly selected and scanned using a Canon LiDE 220 Scanner. The dry weights of these leaves were measured after oven drying at 75°C for 48 h to constant weight. We calculated LMA as the ratio of dry mass to leaf area. Leaf nitrogen content was measured using an isotope ratio mass spectrometer (Thermo Fisher Scientific Inc., Carlsbad, CA, USA). N _area was calculated from LMA and leaf nitrogen content. The LMA value for a species at a given site was the average of three separate measurements made on leaves from multiple individuals, while N _area measurements were made on pooled samples of leaves from multiple individuals.

Carbon isotopic values (δ¹³C) were measured using an isotope ratio mass spectrometer (Thermo Fisher Scientific Inc.). Values were measured on pooled samples of leaves from multiple individuals. Estimates of χ were made using the method of Cornwell et al. (2018) to calculate isotopic discrimination (Δ) from δ¹³C with a standard formula using the recommended values of a′ and b′ of 4.4‰ and 27‰, respectively (Farquhar et al., ¹⁹⁸⁹; Cernusak et al., ²⁰¹³):

$$\chi =(\mathrm{\Delta }‐a^{\prime })/\left(b^{\prime }‐a^{\prime }\right)$$ (Eqn 12)

Leaf gas‐exchange measurements were made in the field using a portable infrared gas analyser (IRGA) system (LI‐6400; Li‐Cor Inc., Lincoln, NB, USA). Sunlit branches from the outer canopy were collected and re‐cut under water immediately before measurement. In situ measurements were taken with relative humidity and chamber block temperature similar to the ambient conditions, and a constant airflow rate (500 μmol s⁻¹). V _cmax at leaf temperature (V _cmax,lt) was calculated from the light‐saturated rate of net CO₂ fixation at ambient CO₂, measured on one individual of each species, using the one‐point method (De Kauwe et al., ²⁰¹⁶) and adjusted to a standard temperature of 25°C (V _cmax25) and maximum temperature in July (V _cmax,jt) using the method of Bernacchi et al. (2001).

Branches with a diameter wider than 7 mm were sampled for hydraulic traits. We cut the branch as close to the bifurcation point as possible, to minimise any effect of the measurement location on the measured area. We measured the cross‐sectional area of the xylem at both ends of the short piece re‐cut from the bottom of the branch using digital callipers. Sapwood area was calculated as the average of these two measurements. All leaves attached to the branch were removed and dried at 70°C for 72 h before weighing. The total leaf area was obtained from dry mass and LMA. The ratio of sapwood area and leaf area was calculated as v _H. The v _H value of one species at each site was the average of three measurements made on branches from different individuals.

Five branches from at least three mature individuals of the same species at each site were collected, wrapped in moist towels and sealed in black plastic bags, and then immediately transported to the laboratory. All the samples were re‐cut under water, put into water and sealed in black plastic bags to rehydrate overnight. K _S was measured using the method described in Sperry et al. (1988). Segments (10–15 cm length) were cut from the rehydrated branches and flushed using 20 mmol l^–1 KCl solution for at least 30 min (to remove air from the vessels) until constant fluid dripped from the segment section. The segments were then placed under 0.005 MPa pressure to record the time (t) they took to transport a known water volume (W, m³). Length (L, m), sapwood areas of both ends (S ₁ and S ₂, m²) and temperature (T _m, °C) were recorded. Sapwood‐specific hydraulic conductivity at measurement temperature (K _S,m, mol m^–1 s^–1 MPa^–1) was calculated using Eqn 13. This was transformed to K _S at mean maximum temperature during the growing season (K _S,gt) and standard temperature (K _S25) following Eqns 14 and 15:

$$K_{\text{S,m}}=\left\{WL{\rho }_{\mathrm{w}}/\left[0.005t\left(S_1+S_2\right)/2\right]\right\}(1000/18)$$ (Eqn 13)

$$K_{\text{S,t}}=K_{\text{S,m}}{\eta }_{\mathrm{m}}/{\eta }_{\mathrm{t}}$$ (Eqn 14)

$$\eta ={10}^{‐3}\exp \left[A+B/\left(C+T\right)\right]$$ (Eqn 15)

where η _m and η _t (Pa s) are the water viscosity at measurement temperature and transformed temperature (i.e. mean maximum daytime temperature during the growing season and standard temperature, 25°C in this study), respectively, and ρ _w (kg m^–3) is the density of water. The parameter values adopted in Eqn 15 were A = −3.719, B = 580 and C = −138 (Vogel, 1921).

A small part of each sapwood segment was used to measure WD, the ratio of dry weight to volume of sapwood. After removal of bark and heartwood, the displacement method was used to measure the volume of sapwood and the dry weight of sapwood was obtained after drying at 70°C for 72 h to constant weight. WD was calculated as the ratio of dry weight to the volume of sapwood.

We applied the method described by Bartlett et al. (2012) for the rapid determination of Ψ_tlp. After rehydration overnight, discs were sampled from mature, healthy leaves collected on each branch, avoiding major and minor veins and using a 6‐mm‐diameter punch. Leaf discs wrapped in foil were frozen in liquid nitrogen for at least 2 min and then punctured 20 times quickly with sharp‐tipped tweezers. Five repeat experiments using leaves from multiple individuals were carried out for every species at each site. We measured osmotic potential (Ψ_osm) with a VAPRO 5600 vapour pressure osmometer (Wescor, Logan, UT, USA) and calculated Ψ_tlp (in MPa) as:

$${\mathrm{\Psi }}_{\text{tlp}}=0.832{\mathrm{\Psi }}_{\text{osm}}‐0.631$$ (Eqn 16)

Climate data

We derived climate variables at each of the 11 sampled sites using meteorological data (monthly maximum and minimum temperature, fraction of sunshine hours and water vapour pressure) from 17 weather stations in the Gongga region (http://data.cma.cn/data/cdcdetail/dataCode/SURF_CLI_CHN_MUL_MON.html) and the elevation‐sensitive ANUSPLIN interpolation scheme (Hutchinson & Xu, 2004). The meteorological data were available from January 2017 to December 2019. The monthly data were converted to daily values by linear interpolation to calculate the bioclimatic variables mean maximum temperature during the growing season (defined as the period with daytime temperature > 0°C), growing‐season mean PPFD and vapour pressure deficit under maximum daytime temperature in July, using the Simple Process‐Led Algorithms for Simulating Habitats (SPLASH) model (Davis et al., ²⁰¹⁷).

Data analysis

All statistical analyses were carried out in R v.3.1.3 (R Core Team, ²⁰¹⁵). To homogenise the variance, traits were log_e transformed and χ was logit transformed; for Ψ_tlp, the absolute value (–Ψ_tlp) was log_e transformed. Trait variance partitioning was carried out using the vegan package (Oksanen et al., ²⁰¹⁷) to quantify the amount of variation explained by different groups of factors. In this study, the groups are families (representing phylogenetic relatedness), life forms, climate and sites. Path analysis was used to characterise the trait coordination framework built on the idea that plastic traits are influenced by structural traits, using the lavaan package (Rosseel, 2012). The model was evaluated using the ratio of χ ² and degree of freedom (χ ²/df) and goodness‐of‐fit index (GFI). The χ ²/df of models using all species and only evergreen species were below 3, and the GFI values of all three models were larger than 0.9 (Fig. 2). Traits under standard conditions (V _cmax25 and K _S25) were used in variance partitioning, path analysis and bivariate regressions to eliminate the effect of temperature, while trait values under growth conditions were used for theoretical prediction.

Fig. 2.

Path analysis of hydraulic and photosynthetic traits for all species (a), separately deciduous (b) and evergreen species (c). WD is wood density, K _S25 is sapwood‐specific hydraulic conductivity at 25°C, Ψ_tlp is leaf water potential at turgor loss point, v _H is the ratio of sapwood to leaf area, LMA is leaf mass per area, χ is the ratio of leaf‐internal to ambient CO₂ partial pressure, N _area is leaf nitrogen content per area, and V _cmax25 is the maximum capacity of carboxylation at 25°C. The arrows indicate the proposed links between traits. Solid lines indicate positive relationships, dotted lines negative relationships. Standard path coefficients are shown near the line (ns, not significant). The trait coordination structure was evaluated using the ratio of χ ² and degree of freedom (χ ²/df) and goodness‐of‐fit index (GFI).

To examine the importance of each predictor in Eqn 8 for the prediction of v _H, we evaluated the contributions of each variable in four steps as follows. We analysed the contributions to variation in v _H using two sets of predictors: (1) the traits and environmental variables in Eqn 8 (D, K _S, Ψ_tlp, V _cmax, χ, c _a), with the contribution of the integrative predictor m _C included in the effects of χ and c _a; and (2) the hydraulic traits (K _S, Ψ_tlp) and environmental predictors (D, temperature, radiation, elevation) that influence v _H indirectly through their influence on photosynthesis‐related traits. First the baseline value of each predictor was defined as the median of its site mean values across the 11 sites. These baseline values were used to generate baseline, a predicted value of log_e(v _H). Second, each predictor in turn was changed to its actual values at each site, while other predictors were kept at their baseline values. We used these inputs to calculate values of log_e(v _H) representing v _H variation across sites induced by this predictor alone. Third, the contribution of each predictor at each site was calculated as the difference between simulated log_e(v _H) values from the second and first steps (indicated as Δlog_e(v _H) in Fig. 3). Last, we calculated the improvement in R ² of the relationships between predicted log_e(v _H) and contributions of each predictor across sites. R ² improvements due to each variable were averaged over orderings among predictors, yielding the relative importance of each variable. This procedure was run using the relaimpo package (Groemping, 2006). The partial residual plots from the regression model of the second set of predictors were plotted using the visreg package (Breheny & Burchett, 2017) to better understand the environmental effects on v _H variation.

To assess the predictive power of the model, we used Deming regression of site mean predicted versus observed log_e(v _H) with its corresponding standard deviation (SD). The SD of predictions came from the observed variations of sapwood‐specific hydraulic conductivity (K _S) and leaf water potential at turgor loss point (Ψ_tlp). Root mean square error (rmse) was estimated between the observed and predicted values both across sites and species. The Deming regression and rmse were calculated using the deming and xxirt packages respectively.

Results

The measured traits can be ranked by phylogenetic influence, according to the fraction of variation explained by family alone in a variation partitioning analysis (Fig. 1). The hydraulic traits WD and sapwood‐specific hydraulic conductivity at 25°C (K _S25) were most influenced by phylogeny (49–52%); LMA, leaf nitrogen per unit area (N _area) and Ψ_tlp were intermediate (28–31%); photosynthetic traits (χ and V _cmax at 25°C, V _cmax25) and v _H were least influenced by phylogeny (19–24%). These rankings are approximately mirrored by the percentages of variation explained by site factors and climate (Fig. 1).

Fig. 1.

Variance partitioning (%) for each trait. (a) K _S25 is sapwood‐specific hydraulic conductivity at 25°C, (b) WD is wood density, (c) Ψ_tlp is leaf water potential at turgor loss point, (d) v _H is the ratio of sapwood to leaf area, (e) χ is the ratio of leaf‐internal to ambient CO₂ partial pressure, (f) V _cmax25 is the maximum capacity of carboxylation at 25°C, (g) LMA is leaf mass per area, and (h) N _area is leaf nitrogen content per area.

Path analysis (Fig. 2) was used to test a framework for trait coordination, based on the hypothesis that the traits that are structurally dependent and more phylogenetically influenced impose a constraint on more plastic traits, with v _H as the key trait linking the two sets of traits. Analyses conducted separately on evergreen and deciduous woody plants revealed several general patterns. First, v _H decreased with K _S25, but increased with V _cmax25 (especially in evergreen plants) (Fig. 2). K _S25 was also lower, and v _H higher, in plants with high LMA. The leaf economics spectrum (from low to high LMA: Wright et al. (2004)) therefore also influenced v _H, both directly and indirectly through K _S25. Second, WD was negatively related to K _S25 (especially in deciduous plants), and positively related to –Ψ_tlp. Third, both LMA and –Ψ_tlp negatively influenced χ. In other words, plants with low (more negative) turgor loss point and/or high LMA tended to operate with low χ, with low χ in turn being linked to higher V _cmax and therefore higher v _H. Fourth, N _area was found to depend jointly on LMA and V _cmax25, consistent with accumulating evidence – for example Dong et al. (2017), Xu et al. (2021) – for the dependence of N _area on leaf structure (with LMA as the dominant control, here as in other analyses), and a weaker relationship to V _cmax25. Together, through direct and indirect effects, these hypothesised causal pathways accounted for all of the significant bivariate relationship among traits (Fig. S2; Table S1).

Our analyses (Figs 2, S2) indicated only a weak trade‐off between leaf drought tolerance and xylem hydraulic efficiency. K _S25 and –Ψ_tlp were negatively related for deciduous species, but this relationship was not significant for evergreen species, or across all species considered together.

The theoretical model, including just a single fitted parameter across all species (the intercept, reflecting the implicit effect of height), captured the essential trade‐off between v _H and K _S. Both quantities v _H and K _S varied greatly among species (variance of log_e‐transformed variables = 0.4 and 0.73, respectively, averaged across the deciduous and evergreen species‐sets; Table S1), allowing a wide variety of hydraulic strategies to coexist within communities. V _cmax25 also varied widely among species (0.69), and more so than either χ (0.28) or Ψ_tlp (0.03) (Table S1). The model also predicted a tendency for plants with high V _cmax to have large v _H, and/or K _S, to allow a correspondingly high rate of water loss. This prediction was consistent with the partial residual plots based on the data (Figs 2, S3). Relationships between A _sat and plant hydraulic traits found in many studies (Santiago et al., ²⁰⁰⁴; Zhu et al., ²⁰¹⁸) were consistent with this prediction. Moreover, Eqn 8 predicted environmental modulation of the relationship between v _H and other traits. Specifically, it predicted a positive impact of vapour pressure deficit (D) on v _H. As D increases, plants are therefore expected to allocate relatively less carbon to leaves, and more to stems and roots, resulting in increasing v _H. Temperature was another essential climate variable affecting v _H variation through χ and m _C with contrasting effects (positive on χ, but negative on m _C). Partial residual plots showed a net negative effect of temperature on v _H (Fig. S4a). However, elevation contributed little to v _H variation (Fig. 3b).

Predicted v _H captured 90% of the observed variation in v _H across sites (Fig. 4) and 20% across all species (Fig. S4). These predictions (see Eqn 8) were based on observed hydraulic traits and c _a, and on predicted optimal values of V _cmax, m _C and χ. Analysis of the modelled contribution of individual factors showed that K _S was the most important predictor of the variation in site mean v _H along the elevation gradient (Fig. 3). With high K _S, plants had large leaf area, leading to low v _H. In addition, χ played a crucial role in v _H variation, as well as being included in the effect of m _C. The improvement in R ² contributions for the relationships of predicted log_e(v _H) to contributions due to different predictors was 0.59 for K _S, 0.14 for D, 0.10 for χ, 0.09 for c _a, and 0.06 for V _cmax and 0.03 for Ψ_tlp (Fig. 3a); or in an alternative breakdown of controls, 0.42 for K _S, 0.21 for temperature, 0.17 for radiation, 0.10 for D, 0.06 for elevation and 0.03 for Ψ_tlp (Fig. 3b).

Fig. 4.

Comparison between site mean observed and predicted ratios of sapwood to leaf area (v _H). The gray error bar in the y‐axis direction is the standard deviation of observed log_e(v _H) at each site; that in the x‐axis direction is the standard deviation of predictions, considering observed variations of sapwood‐specific hydraulic conductivity (K _S) and leaf water potential at turgor loss point (Ψ_tlp).

Discussion

The results of path analysis (Fig. 2) and the success of the optimality model (Fig. 4) are consistent with the proposed central role of v _H in coordinating hydraulic and photosynthetic traits (Rosas et al., ²⁰¹⁹). The v _H variation mainly results from that in K _S and χ or temperature. Species deploying a larger total leaf area at a given sapwood area (lower v _H) tend to have higher K _S (Togashi et al., ²⁰¹⁵). The relatively rapid acclimation of photosynthetic traits to the local environment (Smith & Dukes, 2017) that leads to the indirect relationship between v _H and χ (Fig. S2i) has been noted before (Martinez‐Vilalta et al., ²⁰⁰⁹). However, the weak trade‐off between Ψ_tlp and K _S in deciduous species and the apparent absence of these trade‐offs in evergreen species imply that low hydraulic safety does not always accompany high K _S. Although the xylem tension at which 50% of the maximum conductivity is lost (P ₅₀) is the most commonly used index of hydraulic safety, we used Ψ_tlp for this purpose, noting that the two measures are significantly correlated (Zhu et al., ²⁰¹⁸; Joshi et al., ²⁰²⁰). Globally, a weak trade‐off between hydraulic safety and efficiency has been reported (Gleason et al., ²⁰¹⁶), and new work suggests a tight trade‐off between efficiency and safety may be a feature of climates with highly seasonal precipitation (Liu et al., ²⁰²¹). That is, plants in environments with less seasonal precipitation need not have high hydraulic efficiency, which may be accompanied by unknown costs or risks.

The key role of v _H in mediating leaf physiology and hydraulics arises because of its relative plasticity. Variance partitioning (Fig. 1) showed that WD and K _S are far more strongly linked to phylogeny than other traits. This is presumably because both are related to wood anatomy. K _S is proportional to the fourth power of mean xylem conduit diameter (according to the Hagen–Poiseuille equation; Tyree & Ewers (1991)), while WD is largely dependent on fibre wall and lumen fractions (Ziemińska et al., ²⁰¹³). Therefore, it might be expected that these traits would show a strong evolutionary convergence within lineages. By contrast, Ψ_tlp is known to change after drought through osmotic adjustment (Bartlett et al., ²⁰¹⁴), implying a higher degree of plasticity consistent with the lower influence of family, and the higher influence of environmental factors, on this trait compared with other hydraulic traits (Fig. 1). The correlation between v _H and V _cmax provides the bridge between two sets of plant traits, resulting in the observed relationship between A _sat and hydraulic traits (Zhu et al., ²⁰¹⁸; Deans et al., ²⁰²⁰). With higher V _cmax, leaves can fix more carbon, and stomata open to allow this action, entailing greater water loss. As photosynthetic traits, particularly χ and V _cmax, respond to environmental conditions on timescales of weeks to months by regulating intrinsic biochemical characteristics (Cavanagh & Kubien, 2014; Smith & Dukes, ²⁰¹⁷), plants can adjust v _H relatively quickly by shedding leaves to balance water supply and demand (Choat et al., ²⁰¹⁸), while potentially regulating K _S on a longer timescale. The acclimation timescales of different hydraulic traits lead to tight coordination with photosynthesis process. This coordination also avoids unnecessary carbon costs of hydraulic traits, and may help to ensure survival under unfavourable (drought) conditions. The prediction of v _H based on these essential trade‐offs with observed hydraulic traits proves the intrinsic adjustment of hydraulic traits, implying that there is no need to try to predict hydraulic traits individually from climate alone. The key importance of this optimality model is to successfully predict and unite the trade‐offs among traits in an optimality framework.

WD has been considered as a crucial trait in a ‘wood economics spectrum’ linking water transport, mechanical support and tree mortality (Chave et al., ²⁰⁰⁹). Dense wood, found in many species from arid habitats, is generally associated with narrow conduits (Hacke & Sperry, 2001) that restrict hydraulic conductivity (Zanne et al., ²⁰¹⁰) but also confers resistance to embolism (Anderegg et al., ²⁰¹⁶), possibly due to thicker conduit walls and smaller pores in the pit membranes (Hacke et al., ²⁰⁰¹; Pittermann et al., ²⁰¹⁰). Wood xylem is the foundation for water transport; but leaves are often a major bottleneck for water flow, contributing 30% of whole‐plant hydraulic resistance on average (Sack & Holbrook, 2006). Leaves with lower Ψ_tlp can keep their stomata open and continue photosynthesising at more negative water potentials; conversely, this strategy may incur a greater carbon cost to maintain leaf turgor (Bartlett et al., ²⁰¹²; Deans et al., ²⁰²⁰; Sapes et al., ²⁰²¹).

The tight relationships among LMA, v _H and K _S indicate biologically important interactions between carbon investment strategy and hydraulics. Leaves with low LMA tend to display a larger leaf area to fix carbon within a relatively short leaf life span. In addition, high hydraulic conductivity at both leaf and stem levels ensures that large amounts of water can be transported to leaves for transpiration, to maintain open stomata and a high rate of CO₂ uptake (Mencuccini et al., ^2019b; Joshi et al., ²⁰²⁰). This relationship between hydraulics and LMA may also be associated with physiological characteristics. Thicker leaves (high LMA) tend to have a longer diffusional pathways in the mesophyll, which increases water movement resistance outside leaf xylem and decreases hydraulic conductivity (Flexas et al., ²⁰¹³). The relationships between WD and K _S, and between LMA and K _S, for evergreen species were nonsignificant, possibly due to the relatively small sample size. Nonetheless, the fitted coefficients had the same sign and were of similar magnitude to those found for deciduous species. The reason for the weak relationship between v _H and V _cmax for deciduous species is unclear; again, the sign of the relationship was the same as that for the evergreen species.

The theory predicts direct impacts of vapour pressure deficit (D), and indirect effects of temperature, elevation and radiation, on v _H mediated by photosynthetic traits. As D increases, plants shed leaves and allocate more carbon to the root to reduce transpiration and absorb more water, leading to increasing v _H to balance water supply and demand (Trugman et al., ^2019b). High D also causes reductions in gross primary production, and tree mortality (Park Williams et al., ²⁰¹²; Yuan et al., ²⁰¹⁹). Other environmental variables, including temperature and elevation, mainly influence hydraulic traits through their coordination with photosynthetic traits, which has been less examined in the field. The theory predicts a small positive impact of elevation on v _H, consistent with the occurrence of small‐leaved species at high elevations (Wright et al., ²⁰¹⁷) and the observed negative relationship between leaf size and v _H (Mencuccini et al., ^2019b). Temperature has multiple competing effects that can be hard to disentangle, but the optimality model predicts an overall negative effect on v _H. Under future scenarios where both D and temperature are projected to increase (Grossiord et al., ²⁰²⁰), the optimality model offers a way to explore the potential v _H response as the net effect of several competing effects.

The prediction of site mean v _H using optimality theory offers a promising approach to implement hydraulics into vegetation and land‐surface models. Although hydraulic processes are incorporated into some vegetation models to constrain photosynthesis, parameterisation of hydraulic traits such as v _H is required (Christoffersen et al., ²⁰¹⁶; Eller et al., ²⁰²⁰). If the focus is on ‘typical’ vegetation in a given climate, the relationship we have predicted (and demonstrated) that applies to site mean v _H (Eqn 8), with photosynthetic traits predicted by optimality theory, could provide a straightforward way to couple photosynthetic and hydraulic traits in models. The prediction is much stronger for site means than for individual species – not surprisingly because the micro‐environmental conditions to which each species acclimates are not known, while most current model applications are concerned only with the aggregate properties of the community.

The Huber value also reflects carbon allocation to leaf and biomass, which further affects productivity. A fixed parameter is used to partition carbon into leaf and stem in many vegetation models (Trugman et al., ^2019a). With the optimality model, the fixed parameter could be replaced by acclimated variation in v _H, leading to improved realism. However, there is considerable diversity in hydraulic traits (notably K _S) that is linked to LMA, which raises two practical issues if we are concerned with functional diversity: first, how to predict environmental influences on the leaf economics spectrum; second, how to deal with the large within‐community variation in both LMA and K _S. Xu et al. (2021) have demonstrated a method to predict optimal LMA for deciduous plants, and a different approach is applicable to evergreen plants (Wang et al., ²⁰²¹). A way needs to be found to simultaneously estimate the distribution of values for highly variable, nonplastic traits. A solution to this problem would be a major step forward for modelling the terrestrial carbon, water and nitrogen cycles.

Author contributions

HX carried out the analyses and prepared the manuscript with contributions from all co‐authors. HW, SPH and ICP designed the fieldwork, collected samples and measured plant traits. ICP and IJW developed and extended the least‐cost theory. All authors contributed to the interpretation of the results.

Supporting information

Fig. S1 Locations of sampling sites and weather stations.

Fig. S2 Bivariate relationships between traits.

Fig. S3 Partial residual plots from the regression of log_e transformation of the ratio of sapwood to leaf area (v _H) against different predictors.

Fig. S4 Comparison between observed and predicted ratios of sapwood to leaf area (v _H) across species.

Table S1 Variance‐covariance matrices of traits for deciduous and evergreen species.

Table S2 The trait data used in this study.

Please note: Wiley Blackwell are not responsible for the content or functionality of any Supporting Information supplied by the authors. Any queries (other than missing material) should be directed to the New Phytologist Central Office.

Data availability

The trait data are presented in Table S2.