Transpiration rate relates to within- and across-species variations in effective path length in a leaf water model of oxygen isotope enrichment


Correspondence: X. Song. Fax: +1 215 898 8780; e-mail:;


Stable oxygen isotope ratio of leaf water (δ18OL) yields valuable information on many aspects of plant–environment interactions. However, current understanding of the mechanistic controls on δ18OL does not provide complete characterization of effective path length (L) of the Péclet effect, – a key component of the leaf water model. In this study, we collected diurnal and seasonal series of leaf water enrichment and estimated L in six field-grown angiosperm and gymnosperm tree species. Our results suggest a pivotal role of leaf transpiration rate (E) in driving both within- and across-species variations in L. Our observation of the common presence of an inverse scaling of L with E in the different species therefore cautions against (1) the conventional treatment of L as a species-specific constant in leaf water or cellulose isotope (δ18Op) modelling; and (2) the use of δ18Op as a proxy for gs or E under low E conditions. Further, we show that incorporation of a multi-species L-E scaling into the leaf water model has the potential to both improve the prediction accuracy and simplify parameterization of the model when compared with the conventional approach. This has important implications for future modelling of oxygen isotope ratios.


The enrichment of 18O in leaf water during transpiration is the basis for a variety of isotope-based applications in a range of research fields. The oxygen isotope ratio (δ18O) of leaf water labels that of atmospheric CO2, thereby opening up the opportunity of estimating gross components of the net CO2 flux from ecosystem to global scales (Farquhar et al. 1993; Welp et al. 2011). The labelling effect of leaf water δ18O on O2 during photosynthesis allow reconstruction of global productivity over geological time scales (Bender, Sowers & Labeyrie 1994; Hoffmann et al. 2004). A more broadly utilized role of leaf water δ18O is in influencing δ18O of plant cellulose, and the latter has been widely used as an effective indicator of a suite of factors during plant growth such as stomatal conductance (Barbour et al. 2000a), humidity (Ramesh, Bhattacharya & Gopalan 1986) and leaf temperature (Helliker & Richter 2008). It is therefore essential to understand the underlying processes that govern δ18O enrichment of leaf water in order to realize the full potential of these various applications.

The mechanistic controls on isotope enrichment of leaf lamina water above plant source water (Δ18OL) can be partitioned into two components: the isotopic enrichment of 18O at the evaporative site (Δ18Oes), and the balance of evaporative site water and unenriched vein water. Δ18Oes is primarily determined by environmental factors, that is variations in the ratio of leaf and atmospheric water vapour pressures (h or ea/ei) and the isotopic composition of atmospheric water vapour (Δ18Ov) combine to determine most of the variations in Δ18Oes (Craig & Gordon 1965; Dongmann et al. 1974; Flanagan, Comstock & Ehleringer 1991b). The balance of enriched water and unenriched water, described as an advection-diffusion process, governed by a Péclet number, is largely determined by the leaf level parameters such as transpiration rate (E) and effective path length for water movement through the leaf (L). L is a product of the average length of water movement pathways inside the leaf laminar mesophyll, and a scaling factor that considers the ratio of leaf surface area (for a one-sided leaf) to total cross-sectional area perpendicular to the flows of water movement pathways (Farquhar & Lloyd 1993; Barbour & Farquhar 2004).

It is difficult if not impossible to measure L directly, which in turn makes the Péclet number a poorly constrained component in leaf water enrichment models. In practice, L is determined indirectly, as a fitted value minimizing the difference between the modelled and measured Δ18OL from controlled experiments. However, this empirical approach can be logistically challenging in field conditions, and as a result, researchers often use L-values reported in previously published studies of the same (or similar) species. Treating L in this manner implicitly invokes two assumptions: (1) there is significant variation in L among different types of species; and (2) L for a given species is constant with limited sensitivity to changes in environmental or leaf physiological conditions. Past studies have shown that L is indeed highly variable across species, ranging from several to hundreds of millimetres (Wang, Yakir & Avishai 1998; Barbour et al. 2000b; Kahmen et al. 2008), apparently justifying the validity of the first assumption and the need to treat different species with different L. In spite of this, the underlying mechanism(s) behind the across-species L variations remains poorly understood (Wang et al. 1998; Kahmen et al. 2008, 2009; but also see Ferrio et al. 2012). With regard to the validity of the second assumption, results from previous studies have been mixed. On the one hand, many previous studies have reported no or little dependence of L on various factors such as vapour pressure deficit, leaf-to-air vapour pressure difference, relative humidity, and most notably, leaf transpiration rate E (Flanagan, Bain & Ehleringer 1991a; Flanagan et al. 1994; Barbour et al. 2000b, 2004; Ripullone et al. 2008; Kahmen et al. 2009), lending support to the concept of L being constant for a particular species. On the other hand, it has been shown that changes in soil water availability, leaf hydraulic conductivity or temperature could lead L to vary by tens or even hundreds of millimetres (Ferrio et al. 2009, 2012; Zhou et al. 2011). Such within-species variation in L could lead one to conclude that some plant-based δ18O applications are compromised (Ferrio et al. 2009).

Continued research into the mechanisms behind the variation in L will enlighten us as to the patterns of water movement through leaves and will put our understanding of leaf water isotope enrichment – and the interpretation of isotopic signals in CO2, O2 and cellulose – on firmer ground. In this regard, we carried out the current study to specifically address the following questions: (1) to what extent can within-species L vary under natural conditions? (2) What are the driving factor(s) accounting for within- (if any) and across-species variations in L? (3) How will a better understanding of L inform us with respect to interpreting and modelling leaf water (or cellulose) isotope enrichment? For these purposes, we conducted two leaf water measurement campaigns that involved a total of six tree species consisting of angiosperms and gymnosperms. For each species, we collected either diurnal or seasonal series of environmental, leaf gas exchange and leaf water enrichment data to determine L at different measurement periods, and this in turn allowed us to explore the nature of L in the presence of broad environmental or leaf physiological variations. An indispensable part of the present study was to determine L using contemporary leaf water enrichment models. To do this, we adopted the models that treat the Péclet effect in one dimension, in spite of the existence of more sophisticated two-dimensional models. The two-dimensional models have been demonstrated to be useful in predicting within-leaf spatial heterogeneity of water enrichment (Farquhar & Gan 2003; Ogée et al. 2007; Shu et al. 2008). However, for describing the enrichment of bulk lamina water, several studies have shown that both one- and two-dimensional models perform equally well (Farquhar & Gan 2003; Ogée et al. 2007).

Materials and Methods

Diurnal leaf water measurement campaign

The measurements were conducted on 3- to 4-year-old saplings of five tree species consisting of both angiosperms and gymnosperms: chestnut oak (Quercus prinus), pitch pine (Pinus rigida), red maple (Acer rubrum), white cedar (Chamaecyparis thyoides) and black oak (Q. velutina). In April 2010, two outdoor experimental gardens were established on the University of Pennsylvania campus (Philadelphia, PA, USA) to grow these tree saplings. Garden 1 was used for growing chestnut oak, pitch pine, red maple and white cedar trees and garden 2 for black oak. The two gardens were c. 50 m apart and experienced similar environmental conditions, except that soil fertility in garden 2 was higher than that in garden 1 for historical reasons. All tree saplings (10–20 individuals per species) were tended using standard horticultural practices. The trees received natural precipitation as their water source, but were also watered with local tap water via a drip irrigation system, in such a way as to ensure that they had good hydraulic status throughout the growing season.

For each tree species, diurnal measurement campaigns were conducted on three selected, relatively cloud-free days in the second half of the 2010 growing season. Measurements took place on 6, 15 and 19 August for the tree species in garden 1, and on 7, 8 and 21 September for black oak in garden 2. On each measurement day, mature leaf samples were collected for isotope analysis at approximately hourly intervals starting between 1000 and 1200 h and ending between 1700 and 1800 h. At each measurement time, three plants per species were used for leaf sampling. The collected leaves were placed into and sealed in glass vials either directly (conifer leaves) or after mid-vein removal (broad leaves), and the glass vials were subsequently stored in a freezer until water was extracted. At the beginning and the end of a diurnal measurement course, we also made collections from each sampled plant of (1) additional leaves other than those collected for isotope analysis, and (2) stem water samples by cutting and transferring stem sections of 3 to 5 cm length into glass vials. Leaf area, fresh weight and dry weight were determined on these additionally collected leaves, for the purpose of calculating leaf water content (mol m−2). Stem water samples were collected for isotopic analysis of the source water. Further, water vapour was collected from the average tree canopy height three times throughout a diurnal course, by pumping air through dry ice-ethanol cold traps at a flow rate of 500 cm3 min−1 (Helliker et al. 2002).

During the measurement days, ambient air temperature and relative humidity were monitored with a HOBO data logger (H8 Pro, Onset Computer Corp., Bourne, MA, USA). Gas exchange measurements were performed hourly, concurrently with leaf sample collection. At the beginning of a diurnal course, a fully developed leaf (broad-leaved trees) or needle cluster (conifers) was selected from a tree sapling (thereafter referred to as ‘reference plant’) that was not assigned for sample collection. This same leaf/needle cluster, with its underside attached to a thermocouple to constantly monitor leaf temperature, was used for all gas exchange measurements throughout the diurnal course. At each gas exchange measurement, the selected leaf/needle cluster was inserted into a conifer leaf chamber connected to a portable gas exchange system (Licor 6400, Lincoln, NE, USA). The system was set to allow the leaf chamber to track ambient light and temperature conditions. The system was also configured in a way that transpiration rate (E), total conductance (stomatal plus boundary layer; g), stomatal conductance (gs) and water vapour concentration inside the leaf (wi) could either be monitored or calculated. Upon completion of the last set of measurements in a diurnal course, we collected the leaf/needle cluster that had been subjected to gas exchange measurement, and the projected leaf area was subsequently determined using a portable laser area meter (CI-203, CID Inc., Camas, WA, USA). For pitch pine, we used total surface leaf area, which was obtained by multiplying projected leaf area by a scaling factor of 2.36 (Gray, Lerdau & Goldstein 1997). At the end of a diurnal course, we performed measurement on plants that had undergone destructive leaf sampling, and we did not find any noticeable gs deviations of these plants from their ‘reference’ counterparts.

Midday fortnightly field measurement campaign

Long-term, midday leaf water measurements were made in Lincoln, New Zealand, on three, 8-year-old Monterey pine (P. radiata) trees over two growing seasons, between October 2004 and March 2006. The trees were approximately 7 m high in October 2004, and so 3 m of scaffolding was erected to provide access to sunlit branches in the mid-crown. The three trees were on the north-facing (sunlit) side of a group of eight trees planted in a common garden experiment and the mid-crown branches of the measured trees were fully sunlit. Every 2 weeks, needle gas exchange measurements were made between 1100 and 1300 h on three fascicles from each of the three trees using a portable gas exchange system (LiCor 6400, Lincoln, NE, USA) fitted with a transparent chamber top to provide ambient light. The CO2 concentration within the leaf chamber was controlled at 365 ppm, but the temperature and vapour pressure were allowed to track ambient conditions. Needle temperature was calculated using the leaf energy balance approach, and needle area enclosed by the chamber was expressed as total surface area. The total diameter of each fascicle used for gas exchange was measured with calipers after gas exchange measurements were complete. Measurements were recorded when the coefficient of variation for E was less than 10%, or within 5 min. Immediately after gas exchange measurements, samples were taken of needles, upper branches and water vapour for isotope analysis of water. Needles (approximately 20 fascicles) and upper lignified branches (approx. 1 cm diameter) were sampled separately from sunlit branches and immediately sealed in glass vials, then stored in a −20 °C freezer. Water vapour was trapped from air sampled at 2 m above the ground, and within the crowns of the trees, over a 15–30 min period using a cascade cold-finger trap in an ethanol-dry ice bath (Barbour et al. 2007). Half-hourly meteorological data over the entire sampling period were obtained from the Broadfields station, approximately 2 km from the trees.

Water extraction and mass spectrometry measurements

For the Philadelphia, USA samples, tissue water from needle leaves and stems was extracted by cryogenic vacuum distillation (Ehleringer, Roden & Dawson 2000). Water samples (0.5 mL) were analysed by equilibration for 48 h in 3 mL Exetainer® vials (Labco Limited, High Wycombe, UK) with a 10/90 mixture of CO2/He. Four replicates of 100 mL of the headspace gas were injected into a gas chromatography and carried in a helium air stream to a Delta Plus isotope ratio mass spectrometer (Thermo-Finnigan, Bremen, Germany). For the Lincoln, NZ samples, needle and branch water was extracted by azeotropic distillation in toluene. All liquid water samples were transferred to 500 μL sealed glass vials and sent to the stable isotope facility at The Australian National University for isotope analysis using the pyrolysis technique described by (Farquhar, Henry & Styles 1997). All molar isotope ratios were expressed in the standard ‘delta’ notation on a per mil basis by δ = [(Rsample/Rstandard) −1] * 1000‰, where R = 18O/16O and the standard was Standard Mean Ocean Water (SMOW R = 0.002005).

Leaf water models and calculation of effective path length L

Leaf laminar water isotope enrichment (Δ18OL) is conventionally modelled from the isotopic enrichment at the evaporative site (Δ18Oes) and the Péclet effect, as the following (Farquhar & Lloyd 1993):

display math(1)

Here, inline image denotes the dimensionless Péclet number, which is the ratio of advection of unenriched vein water via transpiration stream to back diffusion of the enriched water from the evaporative site, or

display math(2)

where E is leaf transpiration rate (mol m−2 s−1) and L is the scaled effective path length (m) for water transport from the veins to the site of evaporation. C is the density of water (55.56 103 mol m−3) and D is the diffusivity of H218O in water [D = 119 × 10−9 exp(−637/(136.15 + T)) m2 s−1, with T being temperature in °C] (Cuntz et al., 2007).

Here, we denote a new term f to describe the proportional difference of Δ18OL from Δ18Oes, or

display math(3)

After combining and rearranging Eqns (1) and (3), f can be rewritten as a function of the Péclet effect, as the following:

display math(4)

At isotopic steady state, Δ18Oes can be described by the Craig–Gordon model (Craig & Gordon 1965; Flanagan et al. 1991b; Farquhar & Lloyd 1993):

display math(5)

where ε+ is the temperature-dependent equilibrium fractionation factor between liquid and vapour water (Bottinga & Craig 1969), εk is the kinetic fractionation factor for water vapour diffusion from the leaf to the atmosphere (Farquhar et al. 1989; Cappa et al. 2003), Δ18Ov is the isotope ratio of atmospheric water vapour above source water and h is the ratio of ambient vapour pressure (ea) to the saturation vapour pressure at leaf temperature (ei).

At non-steady state, Δ18OL can be predicted by a model developed by Farquhar & Cernusak (2005) on the basis of Dongmann et al. (1974):

display math(6)

where α+ = 1 + ε+, αk = 1 + εk, t is time (s), W is water content of the leaf (mol m−2), g is combined conductance to water vapour of stomata (gs, mol m−2 s−1) and boundary layer (gb, mol m−2 s−1), and wi is the mole fraction of water vapour in the leaf intercellular air spaces (mol mol−1). Δ18OLs is the steady-state value of leaf water enrichment, which can be predicted by a combination of Eqns (1), (2) and (5). For our diurnally sampled species that were well watered, we observed little change in W with time (see Supporting Information Fig. S2 for details), justifying the treatment of W as being constant. In such a case, Eqn (6) is analytically solved, resulting in the following:

display math(7)

Where Δ18OL,t and Δ18OL,t − 1 refer to Δ18OL values at time t and t − 1 respectively, and Ee is defined as

display math(8)

Eqn (7) provides a way to calculate Δ18OL at time t18OL,t) after a step change in the environmental condition at time t − 1. The form of this equation is essentially the same as eqn D29 in Farquhar & Cernusak (2005) after the Péclet effect is accounted for.

For each species in the diurnal campaign, we used Eqn (7) to calculate L at each sampling time point during a given diurnal course. In the calculation, L at a certain time step t was iteratively solved using Microsoft Excel Solver to set the difference between measured (left side of Eqn (7)) and modelled Δ18OL,t (right side of Eqn (7)) to zero. It should be pointed out that this non steady-state approach to calculating L (i.e. at time t) requires two measured Δ18OL values – Δ18OL at both the current (Δ18OL,t) and previous (Δ18OL,t-1) time step, and therefore that it is not possible to determine L at the first sampling time point of any diurnal course.

For the Monterey pine samples collected in the long-term midday campaign, steady state was assumed such that L was determined by fitting Eqn (1) (through Eqns (2) and (5)) to the measured Δ18OL, and Eqns (2) and (5) parameterized using half-hourly average meteorological data and gas exchange data.

Model parameterization

The equilibrium fractionation factor ε+ was determined following Bottinga & Craig (1969):

display math(9)

Kinetic fractionation factor εk was calculated as (Farquhar et al. 1989; Cappa et al. 2003):

display math(10)

gb values are needed for parameterizing both εk and g in the models. We estimated gb for each of the three broad-leaved species used in the present study, by measuring the rate of evaporative water loss from water-saturated filter papers that simulated the leaf shape and size typical of each of the species (Licor 6400 manual). The values of gb obtained for black oak, chestnut oak and red maple were 1.7, 2 and 1.6 mol m−2 s−1, respectively. We did not apply the paper replica method to the coniferous species, and we assigned a realistic gb of 2.5 mol m−2 s−1 to each of them.

During leaf water sample collection, we were unable to remove mid-veins from the sampled needles of the coniferous species. As a result, mean needle lamina water of the conifers was calculated by assuming that bulk needle water contains 5% unenriched mid-vein water, similar to Barnard et al. (2007).


Figures 1 and 2 show Δ18O of the measured leaf water and of the predicted evaporative site water at each sampling time for each species over the sampling campaigns. For any of the sampled species, Δ18Oes was consistently higher than the measured Δ18OL throughout the sampling periods. Regardless of this general pattern, the offset between Δ18Oes and Δ18OL averaged 5.5‰ ± 0.2 (SE) for the diurnally sampled species, but 7.6‰ ± 0.4 (SE) for Monterey pine in the long-term sampling campaign. Environmental fluctuations throughout the diurnal sampling periods were lower than those through the long term, seasonal sampling periods (Supporting Information Fig. S1), and this led to less overall Δ18OL variation in the species of the diurnal study (13.4‰) than with Monterey pine (18.3‰).

Figure 1.

Values for the measured Δ18OL (denoted by circles), the predicted Δ18Oes (denoted by triangles) and calculated effective path length (L, denoted by vertical bars) for each of the five tree species in the diurnal measurement campaign. Δ18Oes was predicted by Eqn (5) and L was calculated by Eqn (7). Data for the measured Δ18OL represent the means of three replicates. Horizontal lines represent species-mean values of L.

Figure 2.

Values for the measured Δ18OL (denoted by circles), the predicted Δ18Oes (denoted by triangles) and calculated effective path length (L, denoted by vertical bars) for Monterey pine in the midday fortnightly measurement campaign. Δ18Oes was predicted by Eqn (5) and L was calculated by Eqn (1) assuming steady state. Data for the measured Δ18OL represent the means of three replicates. Horizontal lines represent species-mean values of L.

Figures 1 and 2 also present the calculated L-values of each species at each measurement time. Among all species, Monterey pine displayed the largest within-species variation, ranging from 63 to 2505 mm. While the maximum value of 2505 mm was more than a meter greater than the next smallest estimate of L (1443 mm), large L estimates in Monterey pine were not anomalous, that is, of the 36 sampling periods, 23 had a L estimate exceeding 220 mm – the upper range of the literature reported L-values for field-grown tree species (Kahmen et al. 2008). For the diurnally sampled species, within-species L variations were much smaller in amplitude compared to Monterey pine. Nevertheless, they still spanned considerable ranges in values (with black oak being the only exception). For these species, the ranking of the amplitudes of L variations from high to low is as follows: pitch pine (24 to 402 mm), red maple (28 to 126 mm), chestnut oak from (13 to 89 mm), white cedar (12 to 62 mm) and black oak (15 to 26 mm). The grey, horizontal lines in Figs 1 and 2 represent species mean values of L averaged across all sampling points. Comparing all species in this study, we found that the species with the largest variation in L also had the highest species mean value of L (403 mm in Monterey pine), and the smallest mean value of L mean was seen in the species with the least L variation (20 mm in Black oak; Figs 1 & 2).

There was a significant inverse (negative power) relationship between L and leaf transpiration rate E in all species except black oak (Fig. 3). Among the inverse relationships obtained, the highest and lowest R2 values were found for red maple (R2 = 0.713) and white cedar (R2 = 0.370), respectively. Black oak was the only species that showed no correlation between L and E (Fig. 3e). One reason for the lack of L-E correlation in black oak could be that E was relatively high in this species (i.e. all E-values were greater than 3 mmol m−2 s−1). The inverse L-E trend was detected in the other species assessed when much lower values of E were observed (taking white cedar for an example, the inverse trend cannot be detected until E decreases to a range of values less than 2 mmol m−2 s−1; Fig. 3d). When data from all six tree species were combined, a single power function (L = 2.36 × 10−5 E−1.20, P < 0.0001; Fig. 4) fitted the dataset well, with E explaining more of the variation (81.3%) in L than it did in any of the individual species. In the combined dataset, L tended to remain within a narrow range of small values when E was in the high range (i.e. E > 1 to 2 mmol m−2 s−1, while once E reached the low range of values (i.e. E < 1 to 2 mmol m−2 s−1), L increased sharply with the decrease in E towards zero.

Figure 3.

The relationship between effective path length (L) and leaf transpiration rate (E) for each of the six studied species, across all sampling periods. Note that the regression functions are expressed in Système International units (L in m and E in mol m−2 s−1).

Figure 4.

The relationship between effective path length (L) and leaf transpiration rate (E) across all species/sampling periods. The inset is an expansion of the bottom portion of the main graph. Note that the regression function is expressed in Système International units (L in m and E in mol m−2 s−1).

With the calculated L-values, we were then able to use Eqn (4) to determine f, a term that describes the proportional difference of Δ18OL from Δ18Oes. When the calculated f was plotted against E across all species/sampling periods, we found a negative relationship between f and E (P < 0.0001, data not shown). Close examination of this relationship revealed a potential breakpoint around which there would be two different relationships between f and E (Fig. 5). A segmented linear regression analysis of the data identified a cut-off E-value of 1.50 mmol m−2 s−1 as the breakpoint. As is shown by Fig. 5, for the data points with E > 1.50 mmol m−2 s−1, f was significantly positively related to E (f = 23E + 0.14; P < 0.001, R2 = 0.23), while for the data points in the low E range (or E < 1.50 mmol m−2 s−1), f had a significant negative relationship with E (f = −223E + 0.511; P < 0.001, R2 = 0.19).

Figure 5.

The relationship between proportional difference of Δ18OL from Δ18Oes (f) and leaf transpiration rate (E) across all species/sampling periods. F-values were calculated using Eqn (4) for all species. Vertical line represents E = 1.50 mmol m−2 s−1, the cut-off value separating low and high E regions. Note that the regression functions are expressed with E in mol m−2 s−1. As an example, the predicted relationship at the species mean L (L = 19.7 mm) for black oak was plotted as the dotted line. The figure legend is the same as in Fig. 4.

The observed L-E dynamics allowed us to evaluate/compare the performance of different approaches to parameterizing L in modelling leaf water enrichment. In the first approach, we treated L as a species-specific constant by using species-mean values of L in Δ18OL modelling. Across all species/sampling periods, the measured Δ18OL was correlated with the modelled Δ18OL with a correlation coefficient of 0.815. The measured:modelled relationship (y = 0.85x + 3.82) deviated from the 1:1 relationship (differences in slope and intercept were statistically significant, P < 0.05; Fig. 6a). In the second approach of modelling, we used the best fit L-E power functions of each individual species (the non-significant regression line as shown in Fig. 3e was used for black oak) to parameterize L; this approach led to a tight agreement between the measured and modelled data (R2 = 0.939), and moreover, the measured:modelled relationship (y = 0.99x + 0.06) was not significantly different from the 1:1 line (P = 0.91 and 0.83 for the comparisons in slope and intercept, respectively; Fig. 6b). Lastly, we modelled Δ18OL by parameterizing L with the single, across-species scaling of L with E (as shown in Fig. 4) applied to all species. The correlation coefficient of the measured:modelled regression line was 0.879, which is higher than that of the first approach but lower than that of the second approach. The regression line (y = 1.09x – 1.89) significantly deviated from the 1:1 line in both slope and intercept (P < 0.05); nevertheless, the degree of this deviation was small, especially when compared with that in the first approach.

Figure 6.

The measured Δ18OL plotted against the modelled Δ18OL across all species/sampling periods. Δ18OL was modelled by (a) the species-specific L approach where L was treated as species-specific constant using species mean values; (b) the species-specific L-E approach where L was parameterized by the L-E relationships fit to each individual species as shown in Fig. 3; (c) the multi-species L-E approach where the across-species L-E relationship as shown in Fig. 4 was applied to all species. Δ18OL values for species in the diurnal and long-term midday campaigns were predicted by the NSS and SS leaf water models, respectively. The dashed lines represent a 1:1 agreement between the modelled and measured Δ18OL. The figure legend is the same as in Fig. 4.


The relationship between L and E

Our results place E in a central position to explain variations in L, at both within- and across-species levels. Of the six tree species examined in this study, five exhibited both considerably large variations in L, and significantly inverse relationships of L with E. Black oak was the only species that displayed no covariance between L and E; nevertheless, the fact that the consistently low L-values were observed across a range of high E-values (i.e. >3 mmol m−2 s−1) does not preclude the possibility that L would increase to large values if E decreases to lower range of values. When data from all six species were combined, we show that all data points fell along a single inverse trend, in which L has a high correlation with 1/E. The strong across-species L versus E relationship is remarkable because (1) it highlights the role of leaf physiology (e.g. E) in driving L variations at the across-species level (at least among tree species as phylogenetically different as angiosperms and gymnosperms); and (2) it alternatively implies that species-specific factors such as leaf anatomical or morphological traits are of little importance in determining L. It is for this latter reason, presumably, that previous attempts to search for a linkage between L and any leaf anatomical/morphological traits have largely failed (Wang et al. 1998; Kahmen et al. 2008, 2009).

Inverse L-E patterns similar to what we show here can also be inferred from data reported by some previous studies. For example, in a recent study performed by Ferrio et al. (2012) to look at the relationship between L and leaf hydraulic conductivity, a within-species (grapevine) inverse scaling of L with E was clearly evident when the data from the entire range of E variation were analysed. In another study, Kahmen et al. (2008) investigated leaf water enrichment in 17 field-grown Eucalyptus species, across which L was found to be positively related to 1/E, suggesting that the inverse L-E scaling operates at the across-species level. Similar across-species L-E scaling was also revealed by re-analysis of data presented in the study of Zhou et al. (2011), where L and E were shown to respond to growth temperature in opposite directions in a number of C3 and C4 grasses (see Supporting Information Fig. S3 for details). In potential contrast, several past studies performed on crop species have shown relatively constant (and small) L-values in spite of variations in E (or vapor pressure deficit; Flanagan et al. 1991b; Barbour et al. 2000b; Ripullone et al. 2008). These results, however, were obtained under high E conditions (i.e. E-values greater than c. 2 mmol m−2 s−1), and therefore actually fit within our observed L-E covariance pattern, where L clearly shows the tendency of remaining within a narrow range of relatively low values when E is in the range of high values (i.e. when E > 1 to 2 mmol m−2 s−1).

There is some concern that the observed L-E covariance patterns may be artefacts resulting from potential underestimation of the size of the unenriched water pool in the leaf. We addressed this concern through a simulation study that is detailed in Supporting Information Note S1. As shown by Supporting Information Note S1, the L-E negative patterns largely hold, even if we arbitrarily set the portions of the unenriched water pool at unrealistic, maximal possible values during L calculation. Another concern regarding the calculations of L lies in our simplistic assumption that no isotope enrichment would occur in leaf vein xylem water. As discussed by Ferrio et al. (2009), if evaporative enrichment of leaf vein water were accounted for in the calculation, one would expect a further increase in the calculated L-values, with the magnitude of L increase being more pronounced under low E than under high E. This indicates that correcting for leaf vein water enrichment would actually serve to strengthen (instead of ‘dampen’) the original L-E inverse pattern.

The possible mechanisms behind the L-E dynamics

The mechanism behind the observed L-E dynamics must explain the overall inverse relationship between L and E and must be intrinsically related to the pathways of water movement through a leaf. The observed inverse correlation between L and E is likely to be a result of the interaction between water movement pathways within a leaf and the environmental/physiological factor(s) that induced variation in E. For example, in the studies of Zhou et al. (2011) and Ferrio et al. (2009, 2012) where variations in E were primarily caused by experimental treatments imposed to alter plant growth temperature or water status, the observed significant increase in L under low E had been ascribed to the influence of changes in temperature or water stress on aquaporin activity. However, in the present study – in the five diurnally sampled tree species – plant water status or growth temperature were unlikely significant driving factors for E variation because (1) all plants were well watered to avoid water stress from occurring during the sampling periods, and (2) no significant positive correlation was observed between variation in leaf temperature and variation in E in any of the species (data not shown).

The transpiration stream moving through a leaf can follow an apoplastic (cell walls) path, or a cell-to-cell (symplastic via plasmodesmata or aquaporin-mediated transcellular) path. According to Barbour & Farquhar (2004), different water movement pathways are associated with different effective path lengths; hence, it is the relative contribution of these pathways to the overall water flow that determines the overall effective path length, L. The inverse L-E relationship may be a result of water movement following a predominately small L pathway when E is high (i.e. E > 1 to 2 mmol m−2 s−1), and when is E is low (i.e. E < 1 to 2 mmol m−2 s−1), there is a proportionally greater flux through a large L pathway. The exact nature of which pathway or combination of pathways controls this relationship is relatively unknown.

Using leaf anatomical data and a number of assumptions regarding cross-sectional area for water flow, Barbour & Farquhar (2004) estimated that the symplastic (plasmodesmatal) pathway should have a larger L than the apoplastic pathway and that aquaporin-mediated transcellular movement represents the smallest L. Zhou et al. (2011) and Ferrio et al. (2009, 2012) concluded that the apoplastic pathway had the larger L than cell-to-cell flow path and possibly confounded symplastic and transcellular flow paths. In contrast, in an experimental study that involves direct L comparisons between wild type, aquaporin overexpressor and aquaporin antisense (or reduced expression) lines of tobaccos plants, L was found to be highest in the overexpressing line and lowest in the antisense line, suggesting that the aquaporin-gated transcellular pathway actually has a longer L than the apoplastic pathway (Kodama et al. unpublished data, cited in Flexas et al. 2012). Moreover, Morillon & Chrispeels (2001) showed that when E decreased to low levels, the activity of water channel proteins (aquaporins) became up-regulated, resulting in an increase in water permeability of the cell membranes. They argued that when the rate of water flow is high, leaf water moves along the apoplastic pathway, which has low hydraulic resistance; conversely, when the rate of water flow is low, water movement would follow a pathway of high hydraulic resistance, such as the cell-to-cell pathway. Considering the significant role aquaporins play in transcellular water movement (Maurel et al. 2008), such a result is support for the idea that low transpirational flux – and large L – is associated with the cell-to-cell pathway (either symplastic or transcellular flow). Therefore, we hypothesize that the L-E inverse pattern may be the result of proportionally more water moving through the apoplastic pathway (characterized by small L) under high E but through the transcellular and/or symplastic pathway (characterized by large L) under low E.

Further, it should be mentioned that although our proposed pathway shift concept is compatible with the general bimodality of ‘low L, high E’ versus ‘high L, low E’, it may still not be sufficient to explain the full range of L variations seen under low E. Rather, to account for the orders of magnitude change in L in these conditions, there may also be a need to consider potential changes that could occur in the scaling factor (denoted as ‘k’ in the literature). For example, in the case of low E and therefore limited water flow, the attenuation of the leaf transpiration stream would likely render the stream to be either ‘thinner’ or restricted to fewer channels (either through aquaporins or plasmodesmata, even without requiring further pathway shift); either way a reduction in the total cross-sectional area perpendicular to the flow of water could ensue, leading to an increase in k and consequently L. It is possible that the extent of this kind of k-driven change in L can reach several orders of magnitudes, covering the full range of L variations observed in the current study, if the transpiration stream would be so attenuated as to be restricted to only very few narrow channels.

The E-dependent bimodality in the relationship between f and E

Variation in Δ18O of plant dry matter (Δ18Op) has been used as a proxy for changes in gs or E in studies where plants experience similar source water and ambient air conditions (Barbour et al. 2000a; Scheidegger et al. 2000; Brooks & Coulombe 2009; Ramirez, Querejeta & Bellot 2009; Cabrera-Bosquet et al. 2011; Moreno-Gutierrez et al. 2011). Given the current experimental evidence suggesting that Δ18O of leaf photosynthetic products such as sucrose is a reflection of that of average lamina leaf water (Barbour et al. 2000b; Cernusak, Wong & Farquhar 2003; Gessler et al. 2007; but see Roden, Lin & Ehleringer 2000), a key mechanistic basis underlying the application of Δ18Op to indicate changes in gs or E is that a positive relationship should be present between f and E (Barbour et al. 2000a; Barbour 2007; Farquhar, Cernusak & Barnes 2007). However, our data indicate that the f-E relationship is actually bimodal depending on E (Fig. 5). The theoretical expectation that f would increase with an increase in E was found to be valid only under high E conditions, whereas in the low E range (i.e. E < 1.50 mmol m−2 s−1) where large variation in L is the norm, we found that f was negatively related to E.

It can be seen from Fig. 5 that the negative f-E relationship under low E was largely driven by one single species (Monterey pine); nevertheless, such a result provides a cautionary note regarding using Δ18Op as a proxy for gs or E. Specifically, it suggests that the Δ18Op-based application may be problematic if it involves low transpirational conditions, which most likely occur in plants with inherently low E, or when environmental stress (drought, cold temperatures, low light levels, etc.) has constrained plants to grow with limited stomatal opening. Regardless, it is rather reassuring that the observed f-E bimodality should not compromise the emerging application of Δ18Op in agriculture to select for crop cultivars of higher yield potential (a gas exchange correlated trait), simply because the high E nature of the crop species dictates that their transpiration rates during active growth would seldom fall into what we categorize as low E conditions (i.e. <1.5 mmol m−2 s−1) here, even under water stress (Cabrera-Bosquet et al. 2011).

Implications of the L-E dynamics for Δ18OL modelling

The observation of within-species variations in L indicates that the conventional treatment of L as species-specific constant could lead to considerable error when leaf water models are used in predicting Δ18OL (or consequently Δ18O of plant cellulose). This point was illustrated by our modelling exercise that showed a large deviation of the measured:modelled Δ18OL relationship from the 1:1 line when L was parameterized using species-specific mean values (Fig. 6a). In contrast, incorporating the characterized L-E covariance patterns into the model led to much improvement in the model performance (Fig. 6b,c). The fact that the multi-species L-E approach performed reasonably well in predicting Δ18OL indicates that this approach may be used in future modelling of Δ18OL in tree species as phylogenetically diverse as angiosperms and gymnosperms. Such an approach apparently represents a simplification compared to the alternative approaches that would otherwise require a priori knowledge of species-specific L or L-E relationships. Nevertheless, we should be careful to emphasize that it remains uncertain (and to be further tested) whether the L-E scaling relationship can be directly applied to other non-woody plant groups. It is likely that the exact L-E scaling patterns may differ among widely different groups of plants. In this regard, future investigations should experimentally derive/test the L-E scalings for more plant types. Such efforts will have important implications for large-scale modelling of Δ18OL (e.g. isoscape modelling), where a variety of species/vegetation types is usually involved.


We would like to thank Erin Wiley, Tracy Byford, Tom McNichols, Vanessa Jerolmack, Brenda Casper and Dustin Bronson for their help in establishing and maintaining the experimental gardens, and Juan Xiong for her assistance with the sample collection. We thank Ansgar Kahmen and two anonymous reviewers for their comments on early versions of the manuscript. MMB thanks Dr. David Whitehead and Mr. Graeme Rogers for assistance with measurements and sample collection in New Zealand. This work was supported in part by the National Science Foundation under award numbers IOB-0615501 (to BRH) and IOS-0950998 (to BRH and XS), the Marsden Fund of the Royal Society of New Zealand (contract LCR201 to MMB and GDF), Foundation for Research, Science and Technology, New Zealand (contract C09X0701; MMB) and the Australian Research Council (FT0992063 to MMB; and DP1097276 to GDF).