Leaf water content contributes to global leaf trait relationships
The theoretical modelThe model presented here builds on a recently developed metabolic theory based on biochemical kinetics. It describes a non-linear relationship between plant metabolic rate per unit of dry mass (Bs, nmol g−1 s−1), such as light-saturated photosynthetic rates and dark respiration rates, plant water content (S, g g−1), and temperature (in degrees K)19,20, i.e.$${B}_{{{{{{rm{s}}}}}}}={g}_{1}{e}^{{k}_{1}S/left({K}_{1}+Sright)}{e}^{-E/{kT}}$$
(1)
where g1 is a normalisation constant, k1 represents the maximum increase in specific metabolic rates due to changes in water content (i.e. from dehydrated to fully hydrated), K1 represents the water content when the mean reaction rate of cellular metabolism reaches one-half of its maximum, E is the activation energy, and k is Boltzmann’s constant. In this model S is defined on a dry mass basis (i.e. the ratio of plant water mass to plant dry mass) to broaden its range and better reflect the proportional changes in the amount of water in plant tissues20. Full details of the model’s assumptions can be found in the Methods and Huang et al.19,20. The model was tested and shown to hold true for a broad range of species and for whole plants and above- and belowground organs20. Here, we first applied the model to describe the quantitative effects of dry mass-based LWC (the ratio of leaf water mass to leaf dry mass) and temperature on the light-saturated leaf photosynthetic rate per unit of dry mass or leaf photosynthetic capacity (Ps, nmol CO2 g−1 s−1), which can be expressed as$${{{{{rm{ln}}}}}}left({P}_{{{mbox{s}}}}right)={{{{{rm{ln}}}}}}left(frac{{P}_{{{{{{rm{L}}}}}}}}{{M}_{{{{{{rm{L}}}}}}}}right)={{{{{rm{ln}}}}}}left({g}_{1}right)+frac{{k}_{1}cdot {{{{{rm{LWC}}}}}}}{{K}_{1}+{{{{{rm{LWC}}}}}}}-frac{E}{{kT}},$$
(2)
where PL is the light-saturated whole-leaf photosynthetic rate (nmol s−1). Equation 2 indicates that the log-transformed temperature-corrected Ps (i.e. Pscor) should increase with LWC, following Michaelis-Menten type hyperbolic response, i.e.$${{{{{rm{ln}}}}}}left({P}_{{{mbox{scor}}}}right)={{{{{rm{ln}}}}}}left({P}_{{{{{{rm{s}}}}}}}{e}^{E/{kT}}right)={{{{{rm{ln}}}}}}left({g}_{1}right)+frac{{k}_{1}cdot {{{{{rm{LWC}}}}}}}{{K}_{1}+{{{{{rm{LWC}}}}}}}.$$
(3)
Rearranging Eq. (2) shows that the temperature- and LWC-corrected whole-leaf photosynthetic rate (i.e. PLcor) should scale isometrically with ML, i.e.$${P}_{{{mbox{Lcor}}}}={P}_{{{{{{rm{L}}}}}}}{e}^{-{k}_{1}cdot {{{{{rm{LWC}}}}}}/left({K}_{1}+{{{{{rm{LWC}}}}}}right)}{e}^{E/{kT}}={g}_{1}{M}_{{{{{{rm{L}}}}}}}.$$
(4)
In this study, we refer to the temperature or water content correction as moving the temperature term ((frac{E}{{kT}})) or water content term ((frac{{k}_{1}cdot {{{{{rm{LWC}}}}}}}{{K}_{1}+{{{{{rm{LWC}}}}}}})) to the left-hand side of the model, an approach that has been commonly used in previous studies28.Following previous studies29,30,31, we assume that PL is proportional to AL, i.e. ({P}_{L}propto {A}_{L})because leaf area directly determines the light interception capacity1. Therefore, the quantitative relationship between SLA and LWC and temperature can be described as$${{{{{{mathrm{ln}}}}}}}left({{mbox{SLA}}}right)={{{{{{mathrm{ln}}}}}}}left(frac{{A}_{{{{{{rm{L}}}}}}}}{{M}_{{{{{{rm{L}}}}}}}}right)={{{{{{mathrm{ln}}}}}}}left({g}_{2}right)+frac{{k}_{1}cdot {{{{{rm{LWC}}}}}}}{{K}_{1}+{{{{{rm{LWC}}}}}}}-frac{E}{{kT}},$$
(5)
where g2 is another normalisation constant. Given that leaf area is a direct indicator of leaf photosynthetic capacity and that both traits reflect the long-term adaptation of plants to environmental change3,13, k1 in Eqs. (2) and (5) represent the maximum increase in mass-specific leaf photosynthetic capacity due to changes in water content. Since the temperature has a direct effect on the metabolic rates32 and productivity of ecosystems33, it is reasonable to assume that temperature can affect SLA globally34,35. Therefore, in this context T denotes the mean growing-season temperature (in degrees K), as SLA might be more responsive to long-term changes in temperature. Equation (5) predicts that SLA should increase with both LWC and the growing-season temperature. Rearranging Eq. (5) yields$${{{{{{mathrm{ln}}}}}}}left({{mbox{SL}}}{{{mbox{A}}}}_{{{mbox{cor}}}}right)={{{{{{mathrm{ln}}}}}}}left({{mbox{SLA}}}{e}^{E/{kT}}right)={{{{{{mathrm{ln}}}}}}}left({g}_{2}right)+frac{{k}_{1}cdot {{{{{rm{LWC}}}}}}}{{K}_{1}+{{{{{rm{LWC}}}}}}},$$
(6)
which predicts that the log-transformed temperature-corrected SLA (i.e. SLAcor) should increase with LWC following Michaelis-Menten dynamics. Likewise, by moving (frac{{k}_{1}cdot {{{{{rm{LWC}}}}}}}{{K}_{1}+{{{{{rm{LWC}}}}}}}) and (frac{E}{{kT}}) to the left-hand side and ML to the right-hand side of Eq. (5), we observe that the temperature- and LWC-corrected leaf area (i.e. ALcor) should scale isometrically with leaf mass, i.e.$${A}_{{{mbox{Lcor}}}}={A}_{{{{{{rm{L}}}}}}}{e}^{-{k}_{1}cdot {{{{{rm{LWC}}}}}}/left({K}_{1}+{{{{{rm{LWC}}}}}}right)}{e}^{E/{kT}}={g}_{2}{M}_{{{{{{rm{L}}}}}}}.$$
(7)
We note that the scaling of PLcor and ALcor with respect to ML will reveal how LWC mediates the scaling exponent of leaf trait relationships.Effects of LWC and temperature on leaf trait scalingThe numerical value of the exponent for the PL versus AL scaling relationship calculated from the empirical data was 0.99 (Supplementary Fig. 1; 95% CI = 0.95 and 1.02, r2 = 0.87), strongly supporting the model assumption that PL scales isometrically with AL. We then examined the effect of LWC on leaf trait scaling. The numerical value of the scaling exponent for the PL versus ML relationship was 0.95 (Fig. 2a; 95% CI = 0.92 and 0.99, r2 = 0.83). The non-linear relationship between Pscor and LWC described by Eq. (3) was supported by the empirical data (Fig. 2b; Supplementary Table 1). The non-linear model (Eq. 3) also had a lower Akaike’s Information Criterion score than the simple linear model between log-transformed Pscor and LWC (i.e. 793.5 versus 1988.8). After LWC and temperature were corrected (see Eq. 4), the numerical value of the scaling exponent became 0.97 (Fig. 2c; 95% CI = 0.94 and 1.01, r2 = 0.85), which was statistically indistinguishable from 1.0 (P > 0.05), as predicted by the model. Likewise, the numerical value of the exponent (i.e. α) for the AL versus ML scaling relationship was 1.02 (Fig. 2d; 95% CI = 1.02 and 1.03, r2 = 0.92). Additional analyses using the pooled dataset showed that log-transformed SLA increased with LWC following Michaelis-Menten dynamics, as predicted by Eq. (6) (Fig. 2e; Supplementary Table 1). After the effects of LWC and temperature were accounted for (using Eq. 7), the numerical value of α became 1.01 (Fig. 2f; 95% CI = 1.00 and 1.01, r2 = 0.95). Thus, both of the scaling exponents numerically converged onto 1.0 once LWC and temperature were corrected. In addition, an inspection of the locally weighted smoothing (LOWESS) curves showed that the curvature in both scaling relationships was reduced after the effects of LWC and temperature were corrected, as predicted by the model (Fig. 2).Fig. 2: The quantitative effects of dry mass-based leaf water content (LWC) on leaf photosynthesis and SLA.a Scaling of leaf photosynthetic rate (PL, nmol s−1) with leaf dry mass (ML, g). b Non-linear fit to the relationship between temperature-corrected mass-specific leaf photosynthetic rate (Pscor, nmol g−1 s−1) and LWC (g g−1) based on Eq. (3). c Scaling of temperature- and LWC-corrected leaf photosynthetic rate (PLcor, nmol s−1) with ML (g). d Scaling of leaf area (AL, cm2) with leaf dry mass (ML, g). e Non-linear fit to the relationship between temperature-corrected specific leaf area (SLAcor, cm2 g−1) and LWC based on Eq. (6). f Scaling of temperature- and LWC-corrected leaf area (ALcor, cm2) with leaf dry mass (ML, g). Data with LWC greater than 25 were not shown in panel e for a better visualisation. LOWESS curves (blue lines) and 95% confidence intervals are shown.Full size imageThe results presented here show that temperature and LWC quantitatively correlate with other leaf traits, such as Ps and SLA (or LMA), as predicted by the model. The increases in Ps and SLA attenuate with increasing LWC (Fig. 2b, e), indicating that leaf water availability sets a constraint on the maximum Ps and SLA that leaves can reach. It has long been recognised that SLA is closely correlated with leaf growth rate and metabolic activity14,36,37. Therefore, it is reasonable to also expect that SLA, as well as Ps, will be quantitatively affected by LWC, which can change as a function of developmental status (such as leaf maturation and the accumulation of lignified tissues) and transiently as a function of evapotranspiration. LWC is also a reflection of species-specific adaptation to environmental conditions in different biomes. Nevertheless, our model, as well as the empirical data used to test it, reveal a broad and statistically robust correlation between critical leaf functional traits and leaf tissue water content. However, the observed variations in Pscor (Fig. 2b) suggest that in addition to temperature and LWC, other factors (e.g. plant phylogeny and soil fertility) may also affect leaf photosynthetic capacity, which is not accounted for in our model and should be critically examined in future research.Leaf area-mass scaling among different groupsThe numerical value of α varied across different plant growth forms, ecosystems, and latitudinal zones (Fig. 3 and Supplementary Table 2). In particular, the leaf area versus mass scaling relationship showed a clear pattern along a latitudinal gradient (Fig. 3c and Supplementary Table 2). The numerical value of α decreased from 1.10 in boreal regions (95% CI = 1.08 and 1.12, r2 = 0.91) to 1.00 in temperate regions (95% CI = 0.99 and 1.01, r2 = 0.91), and to 0.94 in tropical regions (95% CI = 0.92 and 0.95, r2 = 0.91). However, after correcting for the effects of LWC and temperature, as predicted, α converged onto 1.0 across all different groupings, and the r2 values of the scaling relationships also increased (Fig. 3 and Supplementary Table 2).Fig. 3: The exponents of leaf area-mass scaling with and without temperature and LWC corrections among different groups.a Comparison of scaling exponents among plant growth forms (n = 1688, 491, 1097, and 832 for forbs, graminoids, shrubs, and trees, respectively). b Comparison of scaling exponents among ecosystem types (n = 97, 1367, 1285, 1271, and 114 for deserts, forests, grasslands, tundra, and wetlands, respectively). c Comparison of scaling exponents among different latitudinal zones (n = 1111, 2113, and 910 for tropical, temperate, and boreal zones, respectively). Error bars indicate 95% confidence intervals.Full size imageOur analyses show that LWC also affects the numerical values of the exponents of leaf trait scaling relationships, which helps to explain why different works sometimes report significant differences in the exponents governing these relationships8,10. In particular, the numerical values of the scaling exponent governing the leaf area versus mass scaling relationship differ among different plant growth forms, ecosystems, and latitudinal zones (Fig. 3 and Supplementary Table 2), indicating that no invariant “scaling exponent” (i.e. α) holds true for the leaf area-mass scaling relationship. For example, in our dataset, α is significantly smaller than 1.0 in tropical regions (i.e. in keeping with a “diminishing returns” relationship in leaf area with respect to increasing leaf mass), close to 1.0 in temperate regions (i.e. a break-even relationship), and significantly larger than 1.0 in boreal regions (i.e. an “increasing returns” relationship). This shift in α along a latitudinal gradient may be associated with the different strategies to cope with variations in water availability, e.g. the high evapotranspiration rates in tropical regions may constrain increases in leaf area with increasing leaf mass, therefore resulting in diminishing returns, whereas, in boreal regions, the reduced water stress may enable plants to maximise leaf area to achieve relatively high photosynthetic capacities. Despite the variability in the numerical values of scaling exponents across different groups, the degree of curvature in these scaling relationships is reduced, and exponents converge onto unity after the effects of LWC and temperature are accounted for (Fig. 3), as predicted by the model (Eq. 7). This finding indicates that the variations in the exponent can, at least partially, be ascribed to the effects of LWC on SLA and the relative rate of increase in leaf area versus leaf mass. It is noteworthy that the numerical value of the scaling exponent for the PL versus ML relationship is also very close to 1.0, indicating the relatively weak effects of temperature and LWC on leaf photosynthesis-mass scaling. This may be partially attributed to the relatively limited number of data with concurrent LWC measurements and the adaptation of leaf traits to long-term temperature changes (see below for detailed discussion). Nevertheless, more measurements on LWC and leaf photosynthetic rates are needed to further test how LWC mediates leaf photosynthesis-mass scaling.Given that LWC was weakly correlated with ML (Supplementary Fig. 2, log-log slope = −0.01, 95% CI = −0.02 and 0, r2 More
