## Introduction

The Earth’s vegetation is an integral part of both the global hydrological cycle and the global carbon cycle, annually transpiring more than twice the amount of water vapour in the atmosphere1, and processing ca. 120 Gt carbon through photosynthesis2, 3. Changes in the functioning of Earth’s vegetation therefore affect these cycles and future climate change4, and are also a concern on their own. There is thus great interest in understanding plant responses to recent human-induced changes in physical conditions at the Earth’s surface. Recent increases in atmospheric CO2 concentrations, nitrogen deposition and rising temperatures all potentially affect plant growth. The increase of atmospheric CO2 in particular is expected to benefit growth, as it facilitates the uptake of carbon, and potentially leads to an increase in plant water use efficiency. Water use efficiency is defined as the amount of carbon gained by plants per unit water lost5. Such responses have indeed been observed in CO2 enrichment experiments in greenhouses and under natural conditions6, in ecosystem flux studies7 and in tree ring and foliar carbon isotopes studies8,9,10,11,12. However, the magnitude of measured responses varies between methods, and thus large uncertainty remains with regard to the magnitude of water use efficiency changes over time.

A popular method of studying plant water use efficiency is to use the carbon isotope composition of tree rings (δ13Cplant, see Methods section). It is attractive because it provides long-term annual records. From tree ring δ13C and historical records of atmospheric δ13C, plant isotope discrimination (Δ13Cplant) can be calculated (see Methods section), which provides an estimate of changes in the ratio between assimilation and stomatal conductance for water vapour (A/g w ). This ratio is called intrinsic plant water use efficiency (W i ). Most studies which perform trend analysis of past change in W i use tree cores from large trees, which inherently include all developmental effects within individual trees. Typically, these studies find increases in trees’ intrinsic water-use efficiency in all biomes in the order of 10–30% over the past 150 years5, 8, 9, 13,14,15,16,17,18,19,20,21,22.

As already mentioned, common to most of these studies is the implicit assumption that developmental and stand level environmental effects on W i over a trees’ lifespan are negligible. However, various existing studies cast doubt on this assumption. These studies show that plant isotope discrimination (and thus W i ) changes strongly as trees grow in height (McDowell et al.23 and refs therein), giving rise to an age effect24 that may confound the interpretation of W i in terms of climate or CO2. This phenomenon is also called the ‘juvenile effect’25 or ‘canopy effect’26, and will be further referred to as ‘developmental effects’.

That there are developmental effects is not very surprising. First, as trees grow older they increase in height, which imposes gravitational constraints on water transport to leaves in the upper canopy, affecting potentially stomatal conductance27,28,29. In addition, trees in closed-canopy forests experience strong increases in irradiance from the understory to the canopy, which affect rates of photosynthesis30. These changes in stomatal conductance and photosynthesis as trees grow both affect plant isotope discrimination23, 31. Associated developmental changes in tree morphology and physiology may further affect isotope discrimination28, 32,33,34,35. Yet another factor that influences tree δ13C, and thus estimation of W i based on isotopes, is the uptake of soil-respired CO2 by trees growing close to the forest floor26, 36. As respired soil carbon is dead organic plant material, it increases the CO2 concentration in air above the forest floor and lowers δ13Cair of CO2 in the air37, potentially affecting the isotope signal for small trees.

Despite the results of these studies, with obvious implications for the interpretation of tree ring-derived time trends in W i , not many studies have explicitly assessed the magnitude of these effects (but see Marshall and Monserud38). A possible method to study developmental effects is the use of old fossil trees that grew their entire life under more or less constant CO2 and climate39. Unfortunately such ancient trees are rare. An alternative method is to sample trees across all size classes at the same CO2 level at a single site (i.e., size-stratified sampling), which in addition allows to disentangle the specific causes behind developmental changes in W i . The few studies that followed this approach show that tree ring-derived W i increases may be strongly overestimated when neglecting age effects38, 40. However, only a few single species have been studied, and it is still quite unclear to what degree developmental trends affect W i in the majority of the species used in isotope dendrochronology studies. It also remains unclear to what extent these developmental effects are indeed just simply related to tree age, or rather caused by a change in tree height, a changing light environment of trees, or uptake of soil-respired CO2 when growing under the canopy. We also do not know whether developmental effects halt at a mature tree stage, an assumption made by several studies attempting to reconstruct historical water use efficiency41,42,43. Therefore, here we collect new data using a systematic size-stratified approach that controls for CO2 to quantify, and unravel developmental effects on W i in three species commonly used in temperate zone isotope studies (Pinus sylvestris, Quercus robur and Fagus sylvatica) and one representative of tropical species (Cedrela odorata). For Pinus, we furthermore study the change of W i over the lifetime of individual trees from sub-fossil trunks from Finland. These have been recovered from lakes and grew their entire life under more or less constant pre-industrial CO2 levels39. Altogether, our data set encompasses a variety of ecosystems (arctic, temperate and tropical forests), time-scales (recent to sub-fossil, Holocene material) and species.

The specific aims of this paper are to assess the magnitude of changes in W i across different life stages of trees, to identify the drivers behind changes in W i over a trees’ life cycle, including tree height, light, age and soil respiration effects, and to discuss the implications of these developmental changes in W i on estimates of responses to atmospheric CO2. The basic method we use to evaluate the effect of tree developmental changes on W i is to compare W i of the last five rings formed under nearly the same atmospheric CO2 conditions from a range of trees varying in age, size and light availability. While this approach does not fully control for each of these co-varying factors, the relatively large sample size does allow for separation of the various effects on W i . To assess to what degree observed trends in W i may be affected by trees’ ontogeny, we juxtapose the developmental changes in W i with observed time trends. We further use the isotope data to discuss lifetime changes in the context of proposed strategies for gas-exchange regulation11, 12, 17.

We find that developmental trends in W i are very strong in the three broadleaf species, doubling or tripling over a trees’ lifetime. These trends are primarily caused by increases in tree height and changes in light environment. Trends are of comparable magnitude to observed time trends in literature questioning the interpretation of these records as W i responses to climate and CO2.

## Results

### Age and time trends in W i

The three broadleaf species, Quercus, Fagus and Cedrela, exhibit strong increases in W i , doubling or even tripling from the youngest to the oldest trees, corresponding to increases in the order of 35–70 ppm over 100 years (Fig. 1a, c, e, g). In contrast, the only coniferous species included in this study, Pinus, showed only a very weak trend in W i of just 4 ppm over 100 years. In all four species the trends in W i persisted over the full extent of the studied age range, and remained strong after an age of 50 years (Table 1). The only species for which we could test the persistence of trends in W i for trees older than 100 years was for Pinus using sub-fossil data from Helama et al.39, revealing that even in trees older than 100 years, W i continued to increase with age (Table 1; Supplementary Fig. 1).

We next compared the observed developmental trends in W i with time trends in W i estimated based on traditional tree ring approaches (Fig. 1b, d, f, h). As mentioned these approaches reconstruct historical changes in W i by looking backwards in time using individual tree ring series of big trees. Thus they implicitly include the full developmental trajectory for each tree growing from seedling into a large adult tree. Time trends in W i were collected from the literature (coloured lines, see Supplementary Table 1 for details) and from dominant trees from the same sites as the age trends in Fig. 1a, c, e, g (grey lines). The comparison reveals that for the three broadleaf species, time trends in W i derived from dominant trees obtained from literature (coloured lines, Fig. 1, see Supplementary Table 1 for details) and complemented with new data collected from the four sites in this study (grey lines, Fig. 1) are of a similar or lesser magnitude than the observed change in W i with tree age. Only for Pinus we observe a much stronger increase in W i over time (i.e., with calendar year) than the increase with biological age (26 vs. 4 ppm (100 yr)−1).

### Causes of developmental trends in W i

To obtain insight into the ultimate causes of the developmental change in W i , we analysed the relationship between the average W i of tree rings from the last 5 years of growth with age, diameter, height and crown illumination. While these factors are intrinsically linked, the comparison (Fig. 2; Table 2) does indicate that ageing per se is not the main cause. For Pinus, Quercus and Fagus, age explains less variation (lower R-squared) compared to a trees’ size (diameter, height) or crown illumination, and in none of the four species is age included in the most parsimonious regression models (Table 2). Variation in W i is most strongly related to trees’ size and crown illumination, which together explain between 56 and 78% of the variation in W i for the three broadleaf species (Table 2). Similarly, the linear mixed-effects model, including data from all four species, indicates that crown illumination and tree height, and not age, explain the largest proportion of variation in W i (Table 2). In Pinus only a small portion of the total variation in W i (18%) is explained by any of the measured developmental variables. Finally a comparison of trends in δ13C with age and height shows that height trends in the three broadleaf species converge nearly to the same magnitude of change in isotope ratios with height (i.e., 1.58–1.77‰ (10 m)−1), while age trends vary more between species (Supplementary Fig. 2).

To assess the contribution of CO2 from soil respiration to the observed developmental effects, we compiled δ13Cair and CO2 data for temperate and tropical forests (Supplementary Fig. 3). The data reveal that during daytime, soil respiration affects δ13Cair and CO2 in the first few metre(s) above the ground with slightly larger effects for tropical forests compared to temperate forests37, 44. We estimated the contribution of this effect on observed trends in W i by taking into account estimated values of δ13Cair and [CO2] at crown height for each tree (see Methods section and Supplementary Fig. 3). We find that inferred increases in W i with tree age for Fagus, Quercus and Cedrela are rsp. 11, 14 and 20% lower when using below-canopy values of CO2 and δ13Cair (Supplementary Fig. 4). However, an alternative analysis in which we excluded data from small trees (e.g., lower than 1, 2, 5 or 10 m in total tree height) demonstrates that W i trends with tree height remain strong, even for trees bigger than 5 or 10 m in height (Table 1). Together these results suggest that below-canopy variation in source CO2 explains only a very small portion of variation in W i .

## Discussion

We show here that W i increases strongly with tree age in the three broadleaf species Quercus, Fagus and Cedrela and weakly in Pinus. This is an important finding as it invalidates the assumption of most tree ring isotope studies aiming at reconstruction of tree water use efficiency over time that developmental trends are negligible. Using a simple, size-stratified sampling approach we demonstrate that developmental increases in W i in individual tree ring series are strong for three out of four species, and thus will be wrongly interpreted as responses of trees to global change unless the records are corrected for these effects (Fig. 1). For example, comparison of the increases in W i with age for Cedrela from our study with results from Nock et al.16 and Hietz et al.45 shows that observed increases in their tropical tree species (including Cedrela) are of the same order of magnitude as the developmental effects for Cedrela. The lack of size-stratified sampling in these studies makes it hard to unambiguously isolate the CO2 effects. Our findings similarly question to what degree reported increases in W i in European Quercus and Fagus 10, 11, 41, 46 are indeed due to CO2, or rather primarily the result of developmental effects. We find that P. sylvestris is much less affected by tree development, consistent with other indications for this species42, 43. Reported estimates of W i increases for this species in, for example, the European tree ring isotope networks11, 41 are thus more likely to be correctly attributed to external changes like, e.g., rising CO2 although still with a caveat since the strength of developmental effects may vary between sites and with local climate.

A second important finding of our study is that developmental trends are not limited to the earliest phases of a trees’ life, but within the maximum age limits of our sample seem to last over the entire lifetime of trees. In P. sylvestris, W i increases with age even for trees older than 100 years (Supplementary Fig. 1), reflecting earlier observations by Helama et al.39 using δ13C. For the three broadleaf species W i also continues with age, even after trees have reached an age of 50 years (Table 1). The age of 50 years is a commonly suggested cut-off to remove developmental effects (in this connection usually dubbed ‘juvenile effect’)24, 43, 46, 47. Our results indicate this is not a valid approach as W i continues to increase even in old trees.

Analysis of the relationship of W i with various tree developmental characteristics (Fig. 2; Table 2) shows that the observed trends are not driven by age per se. Instead increases in tree height and changing crown illumination over a trees’ life are the principal drivers. In our analysis these two variables, tree height and crown illumination, explain over 60% of the variation in W i in the broadleaf species. As tree height and crown illumination increase simultaneously in trees over the course of their life, it is however impossible to fully separate the effect of the two variables with our methods. Nevertheless, for Fagus and Quercus, we collected and analysed samples from trees that were of similar size (all small saplings), but which differed strongly in their light environment. W i ‘s differed markedly revealing light exposure as an important driver of variation in W i , irrespective of the trees’ size. For Cedrela tree height plays a more important role compared to crown illumination, likely via hydraulic limitation, while the combined results for all four species suggest that variation in W i is driven by these two variables approximately equally.

The effect of tree height on leaf isotope discrimination is well-known and attributed to increasing constraints on water transport to the canopy with increasing tree height23. Irradiance has an additive effect on the height–discrimination relationship by increasing assimilation more than stomatal conductance for sunlit leaves resulting in lower partial pressure of CO2 inside the leaf, at any given height23, 48. While these two factors seem to be the main controls of change in isotope discrimination with tree height, various related plant physiological changes may play a role as well. For example, change in rooting depth and water uptake49, leaf morphology and physiology28, 32, 33, 50, leaf nitrogen through its effect on photosynthetic capacity51, changing leaf area to sapwood area ratios34, 35 and increases in average branch length52 as trees grow bigger are all known to affect isotope discrimination. In addition, decreases in relative humidity from lower to upper canopy may also affect isotope discrimination when trees grow higher53. The contribution of soil-respired carbon to the tree height-δ13C relationship, which has been the focus of several of the earlier isotope studies26, 36, seems to be comparably small. In the case of Cedrela growing in dense tropical rainforests, where these soil contributions were found to be highest37, 44, we estimated that no more than 20% of the trend in W i can be explained by soil respiration, with soil respiration contributions to W i trends in the two temperate broadleaf species being even lower (11 and 14%, Supplementary Fig. 4). We further find that for all four species, W i continues to increase with tree height beyond the first few metres (Table 1). Thus, changes in W i with tree height observed in this study are mainly related to plant physiological and environmental changes, such as tree hydraulics and crown illumination.

Our analysis includes only four species, and thus caution is needed with generalisation to other species and biomes. Nonetheless while the type of tree ring studies that we performed here are scarce, various studies have analysed variation in leaf isotope discrimination with tree height. This raises the question whether variation in isotope discrimination with leaf height in the canopy can be used as an indicator for trends in wood δ13C (i.e., for the change in tree ring δ13C with total height of the tree at the time of ring formation). The answer is not so clear because wood δ13C integrates the isotope signal from the entire canopy, mixing carbohydrates produced by leaves at different height54. For trees with deep crowns and heavy self-shading one would therefore expect trends in wood δ13C with tree height to be weaker than the trends of leaves with height23, 55. On the other hand, sunlit leaves at the top of the canopy are expected to assimilate comparably more carbon and contribute disproportionally to the average isotope signal found in the main trunk54. A review of published isotope data by McDowell et al.23 shows indeed weaker trends with tree height for wood compared to leaves. Notwithstanding these results, we observe that the average change in carbon isotope discrimination in leaves with tree height (1.9 ‰ (10 m)−1) from the analysis of McDowell et al.23 is quite similar to the trends in carbon isotope discrimination in wood for the three broadleaf species in our study, which vary between 1.6 and 1.8 ‰ (10 m)−1 (Supplementary Fig. 3). Furthermore, a comparison of height trends in tree ring δ13C in our study with leaf δ13C collected at different heights in a single Fagus tree by Schleser56 shows that trends in wood δ13C are only slightly weaker compared to foliar δ13C trends (Fig. 3). This suggests that leaf δ13C may indeed be used as an indicator for the existence of trends in wood δ13C, although not necessarily for the absolute magnitude of the trends. According to the meta-analysis by McDowell et al.23 height trends in leaf isotope discrimination are common across a wide range of habitats and species (37 of the 38 different species showed a decrease in leaf discrimination with tree height, or an increase in W i ). While more investigation into wood and leaf δ13C trends with height for a large range of species is needed, this is a strong indication that height trends in tree ring δ13C are probably very common and may be the rule rather than the exception.

Surprisingly, for both Fagus and Quercus, we find that time trends in W i for the dominant trees (by looking backwards in time using individual tree ring series of big trees, Fig. 1b, d, f, h) are much weaker than the increase in W i with tree age for the same species from the same sites (Fig. 1a, c, e, g). We attribute this to distinctly different growing conditions for these dominant trees when they were small, compared to current small trees from our sample. The dominant Fagus and Quercus trees from Bishop Wood, UK, were indeed planted and probably grew up in quite open conditions with high light availability and low humidity. This is in agreement with our results about the overwhelming influence of historical growing conditions on trees’ variation in W i . It also calls for more investigation into the influence of historical stand development, specifically the role of competition, light availability and height gains on W i trends.

Overall, our results reveal a clear need to account for developmental effects in tree ring δ13C if the aim is to extract long-term trends in W i due to, for example, CO2 or climate. This recommendation has been made in previous studies25, 40, 42, but has rarely been followed. Recent tree ring isotope studies from the European isotope networks do not account for developmental effects, and rings of different ages for the same calendar year are even commonly pooled prior to δ13C analysis11, 41. Such approaches will inevitably obscure developmental trends, and make it virtually impossible to separate such trends from real changes in W i . Developmental effects in tree ring data are commonly removed using Regional Curve Standardisation57,58,59 applied to age. Our results argue instead for an approach that removes the effect of tree size (similar as in van der Sleen et al.8), as this is the parameter most strongly related to W i . It should be noted however that all of these approaches are prone to additional biases60, 61. These biases arise because of differences in survival changes for fast- and slow-growing trees (which may have different W i ), and/or due to specific stand history development. Bias correction as described in Brienen et al.60 is needed when these approaches are used to estimate long-term W i changes in response to CO2 and climate. The importance of knowing specific stand history of the sampled trees is nicely illustrated in the comparison of developmental and time trends for Quercus and Fagus (Fig. 1); using the age-W i curve in these two species to detrend the historical time series of W i in current dominant trees would have resulted in negative trends in W i over time. The very site-specific nature of these effects means that it may be very difficult or perhaps impossible to remove these effects from many previously published records, but it is recommended that future studies collect and evaluate stand history data.

It is well-known that rising CO2 affects stomatal regulation of leaf gas exchange5. As a general framework to evaluate trees’ responses to increases in CO2, researchers have proposed three strategies for homoeostatic gas-exchange regulation11, 12, 17, 25, which are maintaining a constant leaf internal CO2, c i , a constant air-to-leaf CO2 difference, c a c i , or equivalently W i (≡ (c a c i )/1.6 ≡ A/g w ) or a constant ratio of leaf-to-air CO2, c i /c a . These strategies have guided the interpretation of tree ring and isotope-derived changes in leaf gas exchange to increasing CO2. However it is largely unknown to what extent trees follow just one of these specific gas-exchange strategies over their lifetime, if any at all, and how they vary between species. This question is relevant for the interpretation of long-term responses to CO2, and is also interesting by itself. In Fig. 4, we show age trends in c a −c i , c i and c i /c a . for Fagus and Pinus, as derived from the developmental trends in carbon isotope discrimination (see Methods section). Trees clearly do not adhere to a single gas regulation strategy over their life. For example, in Fagus observed increases in c a −c i correspond to strong decreases in c i and decreases in c i /c a . with tree age. Thus, young Fagus trees have significantly higher leaf internal CO2 concentrations, c i , compared to older, and thus larger, trees, presumably due to increased stomatal limitations on assimilation as trees grow taller. There are also strong differences between species, as Pinus shows much weaker change in c i and c i /c a with age. These differences may be related to taxonomy (conifers vs. broadleaf species), difference in shade tolerance between species or growing conditions (open sites vs. forests). These results illustrate that trees do not adhere to a single gas regulation strategy over their lifetime, but that strategies vary between different developmental stages and species, reminiscent of observations of gas-exchange responses to CO2 12.

Finally, we would like to emphasise that, while our results cast doubt on interpretations of tree rings isotope trends of W i in the context of long-term responses to CO2, the purpose of this paper is not to dispute the existence of beneficial CO2 effects on plant growth. As already mentioned, various studies that do control for developmental effects in tree ring data report relatively large increases in W i 8, 40, 62 (but see Marshall and Monserud38), consistent with ecosystem flux measurements7, and with δ13C observations in paleo records and CO2 enrichment studies12. However, tree ring δ13C can only be used for improving our understanding of CO2 effects on W i if developmental effects are taken fully into consideration. We also would like to point out that the identified developmental effects have similar implications for the use of tree ring δ13C to study tree responses to, e.g., nitrogen deposition14, air pollution63 and climate11, as well as, for any palaeo-climate reconstructions24, 64.

In summary, we here report that some species show very strong developmental changes in isotope discrimination with a doubling or even tripling of W i over a trees’ lifetime without any change in atmospheric CO2. These effects are highly species-specific and predominantly related to increases in tree height and accompanying increases in light availability. In three of the four species the effects of developmental change in W i were of similar magnitude as estimated time trends of W i from tree ring δ13C series of big trees, suggesting that these may very well just be artefacts. We also observed that the developmental trends are not limited to the earliest life phases, but continue all the way through to old age. These results provide a stark warning against ignoring developmental trends and show that existing reports on increases in W i need to be interpreted very cautiously, and effectively require re-evaluation.

## Methods

### Isotope analysis

We isolated and analysed bulk samples containing the last five rings for Fagus, Quercus and Pinus. For Cedrela, we analysed the isotope ratio for each ring over the last 5 years, and then took the average of those years. For Cedrela the sampling date differed by 9 years between the two sites that were used, but this did not affect the results, as we find no difference in W i between these periods (data not shown). Long isotopes series from large, dominant trees were reconstructed either by measuring δ13C for each individual ring (Cedrela), or by measuring δ13C in ring sections of 10 years (Fagus, Quercus and Pinus). Rings or ring sections were cut up using a scalpel, and cellulose was extracted following the batch method of Wieloch et al.68. Cellulose was homogenised using a mixer mill (Resch MM301) and then freeze-dried. Samples were then weighed into tin capsules for isotope analysis. The isotope analysis was done at four different labs: the British Geological Survey’s Stable isotope Facility (Part of NERC Isotope Geosciences Facilities) (NIGF, Keyworth, Nottingham, UK), the School of Earth and Environment (SEE) at the University of Leeds, the German Research Centre for Geosciences (GFZ, Postdam and Julich, Germany) and the Laboratory of Chronology at the University of Helsinki (Finland). Analysis of the Cedrela samples from Selva Negra were performed at British Geological Survey utilising a Costech Elemental Analyser (EA) online to a VG TripleTrap and Optima dual-inlet isotope mass spectrometer (IRMS). Cedrela cellulose samples from Purissima at GFZ were converted to CO2 in an excess of oxygen using an elemental analyser (Carlo Erba NA 1500) coupled to an OPTIMA (Micromass Ltd, UK) IRMS. The remaining samples for Fagus, Quercus and Pinus (Scotland) were analysed at University of Leeds using an Elementar Vario Pyrocube coupled to a GV Isoprime mass spectrometer. Analysis of the sub-fossil samples from Finland was analysed in duplicate on a DELTA Advantage isotope ratio spectrometer coupled to a CN2500 elemental analyser at the Laboratory of Chronology at the University of Helsinki (Finland). All laboratories used standards that included IAEA-CH7 and/or IAEA-CH3, or in-house standards calibrated against at least one of these IAEA international standards.

### Data analysis

Carbon isotope ratios (δ13C) were calculated as

$${{\rm{\delta }}^{{\rm{13}}}}{{\rm{C}}_{{\rm{plant}}}}\left[ {\textperthousand\, {\rm{vs}}{\rm{.}}\,{\rm V}-{\rm{PDB}}} \right]{\rm{ = }}\left( {{R_{{\rm{sample}}}}/{R_{{\rm{standard}}}}-1} \right) \times 1000$$
(1)

with R representing the abundance ratios, 13C/12C, of the sample and the standard (Vienna Pee Dee Belemnite (V-PDB)). The unit permille plant carbon isotope ratios were converted to plant to air isotope discrimination (Δ, Farquhar and Richards69),

$${{\rm{\Delta}}^{{\rm{13}}}}{{\rm{C}}_{{\rm{plant}}}}{\rm{ = }}\left( {{{\rm{\delta }}^{{\rm{13}}}}{{\rm{C}}_{\rm{a}}} - {{\rm{\delta }}^{13}}{{\rm{C}}_{{\rm{plant}}}}} \right)/\left( {1 + {{\rm{\delta }}^{13}}{{\rm{C}}_{{\rm{plant}}}}/1000} \right)$$
(2)

with δ13Ca representing the isotopic composition of atmospheric CO2, which is becoming depleted in heavier 13CO2 over the last two centuries due to combustion of isotopically light fossil fuels. We used records of δ13Ca obtained from Antarctic ice cores70, complemented with recent data from Mauna Loa from http://www.esrl.noaa.gov/gmd/ccgg/trends/full.html. Following Farquhar et al.71, plant discrimination is assumed to be related to the ratio of intercellular to atmospheric [CO2] (c i /c a ) by the following equation:

$${{\rm{\Delta}}^{{\rm{13}}}}{{\rm{C}}_{{\rm{plant}}}}=a \times \left( \frac{c_a -c_i}{c_a}\right) + b \times \left({\frac{{c_i}}{c_a}},\right)$$
(3)

where a (=4.4‰) results from the slower diffusion of 13CO2 relative to 12CO2 through the stomata and b (=27‰) is the fractionation by Rubisco against 13CO2 inside the leaf. C i can be calculated directly for each ring, or ring section using c a , atmospheric CO2 data from http://www.esrl.noaa.gov/gmd/ccgg/trends/full.html. This equation ignores mesophyll conductance72 and assumes that post-photosynthetic factors beyond the formation of primary leaf sugars73, do not change discrimination. It is well-known that this assumption is not correct, as various environmental and physiological processes (including temperature and tree- or leaf age) affect mesophyll conductance and post-photosynthetic discrimination72, 74. However, considering current lack of knowledge on these processes73, and specifically how they vary between species and environmental conditions, we choose not to correct for the mesophyll conductance term or leaf-to-wood offsets. Many studies on water use efficiency similarly ignore these effects, or apply a fixed term to account for post-photosynthetic processes11, which does not change the trend analysis which is the focus of our analysis.

Intrinsic water-use efficiency (W i ) is defined as the ratio of assimilation rate (A) to stomatal conductance for water vapour (g w ), and can be calculated if c i and c a are known using Fick’s Law,

$$A = {g_c} \times \left( {{c_a}-{c_i}} \right)$$
(4)

Stomatal conductance for water (g w ) is 1.6 × g c (stomatal conductance for CO2), where 1.6 is the ratio of molecular diffusivity of water vapour and CO2 in air.

Combining Eqs. [2], [3] and [4], we calculate W i as follows,

$${W_i} \equiv A/{g_w}=A/\left( {1.6 \,\times \,{g_c}} \right) = \left( {{c_a} - {c_i}} \right)/1.6 = {c_a}\left( {b - {\Delta ^{{\rm{13}}}}{{\rm{C}}_{{\rm{plant}}}}} \right)/1.6\left( {b{\rm{ - }}a} \right)$$
(5)

Note that we use the shorter parts per million (ppm) notation as units for W i , which is the equivalent of the mole fraction (µmol mol−1). The sub-fossil δ13C data from Pinus from Helama et al.39 originated between 5630 BC and 1930 AD, and to calculate W i for these trees we assumed a constant, pre-industrial atmospheric CO2 level of 280 ppm and δ13Cair of −6.4‰ based on Francey et al.70. Slight temporal variations in CO2 and δ13Cair during this period will not cause any systematic bias in the calculation of development trends in W i as the trees represent an average from very different time periods (Helama et al.39).

To study the effect of tree age, diameter, height and light availability on carbon isotope discrimination, we plotted W i against each of these variable for rings that were formed in the same calendar years thus controlling for the effect of CO2 on W i . We estimated developmental trends and time trends in W i using general additive mixed models from the gamm4 R package75. To estimate long-term linear W i trends we used linear mixed-effects models from lme4 R package76. In the comparison of developmental trends with time trend in tree rings, we excluded trees lower than 1 m in height from the developmental trend analysis (Fig. 1a, c, e, g) to avoid influence of soil-respired carbon, and because tree ring analysis usually does not sample trees at height lower than 1.30 m. Our estimates of time trends in W i included time trends from trees collected in this study complemented with literature data. To account for differences in sampling intensity between studies, we used weighting in the calculations of the time trends according to the number of study sites for each W i trend. See Supplementary Table 1 for a list of sourced literature data and the number of sites that were included. For display purposes (Fig. 1) we smoothed the annual Cedrela W i series for each tree using a cubic smoothing spline function.

### Soil respiration

To estimate the contribution of soil respiration to age and height trends in tree ring-derived estimates of W i , we compiled literature data on differences in CO2 concentrations and δ13C in CO213Cair) under the forest canopy compared to values above the canopy. We approximated the change in CO2 and δ13Cair with height above the forest floor by a negative exponential function for temperate and tropical forests (Supplementary Fig. 4). Using total tree height data for individual trees collected in our study, we then estimated the available CO2 concentration and δ13Cair for each tree. As total tree height is probably not the best measure of a trees’ actual uptake of CO2, we assumed that average CO2 uptake by the trees’ canopy occurred slightly below the top of the trees, at 0.9 × total tree height. We then re-calculated W i for each tree corrected for below-canopy effects, and re-estimated W i trends with age and height. This analysis was done only for the three broadleaf trees, and not for Pinus as this species grew mostly in open areas.

### Data availability

All the data used in this publication are available from the authors upon request.