Previous work suggests that the relationship between the carbon isotope composition of air (δ13Ca) and plant leaf tissue (δ13Cp) can be used to track changes in the carbon isotope composition of paleo-atmospheric CO2. Here we test this assertion in a series of experiments using the model plant Arabidopsis thaliana grown under a range of atmospheric CO2 concentrations relevant to geologic time (380, 760, 1000, 1500, 2000 and 3000 ppm). Nested within these CO2 experiments water availability was controlled (giving two sets of experimental plants; low and high water treatment at each CO2 concentration) to manipulate stomatal opening, a key process governing carbon fixation and isotope discrimination. Results show a highly significant relationship between δ13Ca and δ13Cp under both experimental water treatments. To test the utility of δ13Cp to predict δ13Ca we compare calculated δ13Ca to measured values of δ13Ca. These data show that although there is a significant relationship between calculated and measured δ13Ca, there is disparity between the two values of δ13Ca and a large difference between calculated values under different water treatments even when grown in a common CO2 concentration. These results demonstrate that environmental factors that alter stomatal opening can severely impact on the use and reliability of δ13Cp to predict δ13Ca and as such, results should be interpreted with caution.
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 The fourth International Panel on Climate Change (IPCC) assessment states that evidence for global warming is unequivocal and that this warming is very likely to have been caused by human activity via the combustion of fossil fuels accelerating the release of stored (fossil) carbon into the atmosphere [Intergovernmental Panel on Climate Change, 2007]. However, climate change and the associated perturbations of the carbon cycle are not solely an anthropogenic phenomenon. Throughout the majority of the Phanerozoic the Earth's climate state has been that of a greenhouse world, with equitable temperatures, a low tropic to pole heat gradient and little polar ice [Frakes et al., 1992]. The unlocking of this record will enhance our understanding of and capacity to predict future climate change scenarios and importantly help to reduce uncertainty around these predictions. To achieve this it is necessary to develop well constrained and robustly tested paleo-proxies.
 Plants as sessile organisms must adapt to meet environmental challenges and several extant plants can be considered “living fossils” which make them ideal foundations for the development of quantitative paleo-proxies. Studies of plant adaptation to changes in atmospheric CO2 have shown that as CO2 has increased plants have responded by decreasing the number of stomata (stomatal density and index, SD and SI respectively) on the leaf surface [Woodward, 1987]. This finding has subsequently been used to produce estimates of paleo-CO2 concentrations either on a semiquantitative or quantitative basis. Semiquantitative reconstructions are achieved by comparing the stomatal numbers of extant plants with the stomatal numbers of their nearest living relative (NLR) or their nearest living ecological equivalent (NLE) [McElwain and Chaloner, 1995; Chaloner and McElwain, 1997; McElwain et al., 1999]. Quantitative use of SD and SI to estimate palaeo-CO2 is based on the development of species specific training sets that characterize the stomatal response to known historical changes in atmospheric CO2 through the analysis of specimens stored in herbaria. These herbaria studies are often supplemented by experiments on closely related species for example Ginkgo biloba [Royer et al., 2001] and Stenochlaena palustris [Beerling et al., 2002] grown in controlled environments with atmospheric CO2 held at a specific, geologically relevant concentrations.
 A further mechanism for investigating changes to the long-term carbon cycle is the carbon isotope analysis of terrestrial organic matter (TOM). TOM has been used to examine the carbon cycle over times of rapid change; for example over the Cretaceous/Tertiary boundary mass extinction event [Schimmelmann and Deniro, 1984; Beerling et al., 2001] and over the longer term for example, providing evidence of an increase in carbon burial in the Late Palaeozoic [Peters-Kottig et al., 2006]. The major constituent of TOM is higher plant tissue and the carbon isotope composition of TOM (the ratio of 12C to 13C relative to the Peedee belemnite standard (VPDB, on a per mil basis, δ13C)) is primarily a reflection of the environment experienced by this vegetation during growth.
 Terrestrial plant δ13C is chiefly controlled by photosynthetic pathway; C3 plants have an isotopic signature of between −23 to −30‰; C4 plants −10 to −18‰ and CAM plants a value between −12 and −30‰ [Park and Epstein, 1960; Bender, 1971; Smith and Epstein, 1971; Tieszen, 1991; Vogel, 1993] (reviewed in Gröcke ). Imposed on this, different plant tissue types can have a significantly different isotopic value based on fractionation processes associated with the carbon compounds involved in their construction, for example plant lipids and lignin are typically depleted in 13C when compared to bulk plant tissue [e.g., Loader et al., 2003] (reviewed in Gröcke ).
 Impinging on these processes within C3 plants is an environmental signal which is controlled by the stomatal pore complex. During photosynthesis there is open exchange of gases between the leaf and the atmosphere such that the internal CO2 concentration (Ci) in the sub-stomatal cavity approaches that of the atmosphere (Ca). This leads to the preferential fixation of 12C (fractionation) by the primary C-fixing enzyme RuBisCO (Ribulose-1, 5-Bisphosphate Carboxylase Oxygenase) as a carbon source to derive carbohydrate (Figure 1a). Conversely closure of the stomatal pore complex (Figure 1b) leads to the isolation of the sub-stomatal cavity, limiting diffusion resulting in a decrease in the loss of 13C from the sub-stomatal cavity. This when combined with the re-fixation of respired CO2 leads to depleted carbon resulting in the plant tissue isotopic ratio becoming less negative [Farquhar et al., 1989].
 The exhaustive meta-analysis on natural and experimental plant material undertaken by Arens et al.  revealed a liner correlation between plant δ13C (δ13Cp) and δ13C composition of air (δ13Ca) leading to the suggestion that the isotopic value of fossil C3 plants could be used as a quantitative paleoproxy to determine paleoatmospheric δ13Ca [Arens et al., 2000]. This interpretation was subsequently criticized: (1) on the grounds of the potential for a nonlinear fractionation of CO2 at geologically elevated atmospheric CO2 concentrations [Gröcke, 2002]; (2) from an ecophysiological perspective [Beerling and Royer, 2002] due to the importance of environmental conditions that control fractionation [Farquhar et al., 1989]. A further criticism raised here is that the original regression was performed on a multi species database, whereby regressions that are preformed across different species have an inherent problem in that some species are more closely related than others. This condition violates the fundamental assumption of regression analysis that all data points are independent. There are methods to account for the relatedness of species in multi species regressions and failure to do so could introduce confounding factors into the analysis. This possibility remains unexplored for these data.
Jahren et al.  set out to address some criticisms identified (nonlinear fractionation of CO2 at geologically elevated atmospheric CO2 concentrations) via a series of experiments in which replicates of Raphanus sativus were grown in low light analogous to very deep shade, at extremely low relative humidity (RH) of ∼20%, (compared for example to an RH of 40% in the stable upland zone of Antarctic dry valleys [Marchant and Head, 2007]), with little water. These environmental manipulations should lead to closure of the stomatal pore, isolation of the sub-stomatal cavity and a reduction in Ci/Ca, effectively minimizing the environmental signature recorded within δ13Cp. The authors report their experimental plants as grown “free from environmental stress” [Jahren et al., 2008] However, the growing conditions as reported by [Jahren et al., 2008] would place a serious physiological stress in terms of water shortage. The data showed evidence for a consistent correlation between δ13Ca and δ13Cp and these results led Jahren et al.  to conclude that in the absence of environmental stress δ13Cp could be used in a mechanistic way to provide quantitative estimates of paleo δ13Ca.
 The authors further concluded that their study raises the possibility of combining stomatal and isotopic analysis of fossil plant material to develop quantitative measurements of the long-term carbon cycle by tracking changes in both the concentration and isotopic composition of paleo-CO2. However, what is required is an experimental study to determine whether C3δ13Cp can be used as a proxy to predict δ13Ca over varying environmental conditions which manipulate Ci/Ca, over a broad range of atmospheric CO2 concentrations.
 We set out to provide such experimental data to fully test the hypothesis [Arens et al., 2000; Jahren et al., 2008; Jahren and Arens, 2009] that δ13Cp can be used to predict δ13Ca. We also fully test the original regression using independent contrasts analysis to robustly incorporate and test for potential phylogeny effects within the original meta-analysis.
2. Materials and Methods
2.1. Statistical Analysis of Phylogeny
 To test for a phylogenetic signal in the regression of Arens et al.  we applied independent contrasts analysis [Felsenstein, 1985]. A consensus ‘megatree’ phylogeny with the most current molecular diversification times [Wikström et al., 2001] of the species in the data set was constructed, resulting in 142 unique taxa (Figure 2). We then used the analysis of traits (AOT) module (developed by Ackerly et al. ) of Phylocom [Webb et al., 2008] to perform independent contrasts on our ‘megatree’ phylogeny. The AOT algorithm calculates standardized divergences of extant species and estimates internal node averages and divergences incorporating branch lengths [Ackerly et al., 2006]. A unique feature of AOT is that it can handle polytomies (regions of the phylogeny that cannot be fully resolved either thorough a lack of phylogenetic data or due to one species giving rise to more than one direct descendant species). Our ‘mega-tree’ phylogeny contained seven polytomies, including a large one in the Asterales and Fabales (Figure 2). AOT uses the method developed by Pagel  to calculate independent contrasts with phylogenies that contain polytomies. AOT takes a particular polytomy and ranks species based on the value of the independent variable, where the median value is then used to create two groups. Mean values are calculated for each trait between the two groups and the difference between these means is treated as a single independent contrast. These independent contrasts are then used in a model II regression (calculated using the “lmodle2” regression package in R) to calculate the correlation through the origin (PicR) through the contrast values. Using a model II regression allows each variable to vary independently and in turn allows variations in trends between individual groups and the data set as a whole to be analyzed. The output of an independent contrast analysis is a correlation through the origin (PicR) from the contrast values. We used a model II regression to calculate our PicR. Therefore, our PicR test does allow for each variable to vary independently (a type II test).
2.2. Experimental Setup
 Seeds of Arabidopsis thaliana (ecotype Col-0) were sown onto multipurpose compost (Arthur Bowyers, UK) covered with plastic film and stratified for 3 days at 4°C. They were transferred into controlled environment growth cabinets (Sanyo-Fitotron Model: SGC097.PPX.F, UK) and grown under a day/night regime of 8/16 h at 25/21°C and 55% RH. Six separate CO2 experiments were conducted, with CO2 held at geologically relevant [Berner, 2006] concentrations of 380, 760, 1000, 1500, 2000 and 3000 ppm (parts per million). CO2 was constantly monitored via an integrated cabinet infrared gas analyzer (IRGA – ADC Bioscientific Ltd, Hoddesdon, UK) with automatic injection of CO2 to maintain the set point. Nested within each CO2 treatment, plants after four weeks growth were subjected to one of two watering regimes, low water treatment (LWT 10 ml day−1) or high water treatment (HWT constantly moist compost). Following the imposition of water treatment plants were left to develop for a further 2 weeks and leaves that had developed under each treatment where subsequently harvested. Despite its poor fossil record and relatively recent geological/evolutionary history; (stem group age of ∼92 million years before present [Magallón and Castillo, 2009] and a crown group age of ∼13 million years before present [Beilstein et al., 2010]) Arabidopsis thaliana was chosen as an experimental study organism because its stomatal response to a doubling of atmospheric CO2 is representative of the responses seen in 110 species and is therefore viewed as an acceptable model plant with which to investigate the environmental controls of stomatal development and numbers [Woodward et al., 2002], which may in turn influence δ13Cp [Sekiya and Yano, 2008]. Furthermore growth from seed to maturity can occur within ∼5–6 weeks allowing for rapid throughput of a large series of experiments to fully characterize the relationship between δ13Ca and δ13Cp over a wide variety of atmospheric CO2 concentrations.
 Five plants of each treatment were analyzed; plant material was collected and dried for one week at 70°C and then ground with a pestle and mortar. 0.1 mg of leaf material per plant was used for carbon isotope analysis. Measurements were made using an ANCA GSL preparation module, coupled to a 20–20 stable isotope analyzer at the University of Sheffield (PDZ Europa, Cheshire, U.K.). Air samples were collected from growth cabinets by extraction pump into 10 ml evacuated gas tight vials (Labco Exetainer Vials, Labco Ltd, UK) previously flushed with nitrogen gas (BOC, UK) and analyzed on the same analyzer. All results are reported in the delta notation relative to the VPDB standard in parts per mil.
3. Results and Discussion
 Analysis of the δ13Cp reveals that there is a significant relationship between δ13Cp and CO2 and between δ13Cp and water treatment; there is also a significant interaction between CO2 and water (Table 1). Pairwise multiple comparison (Holm-Sidak method) shows a significant difference between all CO2 treatments (overall significance P = 0.05) and a difference between HWT and LWT (P = < 0.001). Comparison of water availability (HWT and LWT) within CO2 treatments reveals a statistically significant difference (P = < 0.05) between HWT and LWT plants at 760, 1500 and 3000 ppm (Table 2).
Table 1. Two Way ANOVA of the Effects of CO2 and Water Treatment (High Water Treatment (HWT) Constantly Moist Compost Plants, Low Water Treatment (LWT) 10 ml day−1) and Interaction Between CO2 and Water Treatment on δ13Cp
CO2 x water
Table 2. Pairwise Multiple Comparison (Holm-Sidak Method) of the Difference in Means Between Water Availability Treatment (High Water Treatment (HWT) Constantly Moist Compost Plants, Low Water Treatment (LWT) 10 ml day−1) Within CO2 Treatments
 Re-running the original analysis of Arens et al.  using Ordinary Least Squares regression shows that the statistical power of the regression is greatly reduced when we compare our results to those of Arens et al.  (Figure 3a). Although the regression is still highly significant (P = < 0.001) the r2 is very low (0.12) which compares to an r2 = 0.34 in the original analysis of Arens et al. ; the R value in our reanalysis is however 0.34. Using independent contrasts analysis to test for the effects of phylogeny within the data set shows that there is a significant phylogenetic signal in the data set of Arens et al.  (Figure 3b).
 The PicR value for the analysis was 0.502, P = <0.001 with an r2 = 0.25. After incorporating potential effects of phylogeny, the r2 value increased from 0.12 to 0.25. Independent contrasts analysis also allows for paired (i.e., within species) versus unpaired analyses to be differentiated, although no differences between paired versus unpaired were noted in our analyses. These data indicate that the amount of variance explained by phylogeny within the relationship between δ13Cp and δ13Ca was relatively low, but does increase the amount of variance explained by approximately 10% (r2 0.12 to 0.25). These highly significant regression and independent contrast analyses with weak r2 values suggest that other unidentified factor(s) may significantly impact on the utility of fossil δ13Cp to predict paleo-δ13Ca. As the r2 increases when accounting for phylogeny suggests an evolutionary signal within the data set may explain some of the missing variance in the original analysis of Arens et al. .
 Analysis of the relationship between δ13Cp and growth CO2 concentration reveals a very strong (r2 > 0.85) highly significant (P < 0.001) relationship for both HWT and LWT plants. Our experimental data show that the δ13C composition of both air and plant tissue become more negative as the atmospheric CO2 increases from 380 ppm to 3000 ppm (Figure 4a), in line with previous experimental findings [e.g., Fletcher et al., 2005] reflecting the fossil fuel derived nature of the CO2 (13C depleted) used in the experimental setup. As expected there is a very strong (r2 0.80) highly significant (P < 0.005) relationship between δ13Ca and CO2 concentration. This in turn translates into a highly significant relationship between δ13Ca and δ13Cp for both HWT (r2 = 0.99, P < 0.001) and LWT (r2 = 94, P < 0.001) plants (Figures 4b and 4c). These data suggest a high degree of auto correlation driven by δ13Ca becoming more negative as atmospheric CO2 is increased within the experimental setup. To test for differences between the regressions, the slope and standard error of the slope where compared, (HWT slope 1.312, standard error of the slope 0.057; LWT slope, 1.263 standard error of the slope 0.149). The overlap between slope and standard error for the different treatments shows that the regressions are not significantly different from each other.
 To explore the relationship between water availability and pCO2 on δ13Cp we calculate Ci/Ca using:
 Where a = discrimination limited by diffusion (4‰) and b = discrimination limited by RuBisCO (27–30‰); in our calculations b = 27 [Farquhar et al., 1989]. The data shows (Figure 5) a steady increase in Ci/Ca with both water treatments as CO2 increases. This manifests as a highly significant positive linear relationship between Ci/Ca and CO2 in HWT plants (r2 = 0.94, P = < 0.001). In LWT plants the relationship is of marginal significance (LWT r2 = 0.51 P = 0.067).
 To test the original hypothesis of Arens et al.  we use their original equation (2) to derive estimates of δ13Ca based on our δ13Cp values for both HWT and LWT plants.
 Although there is a very strong (r2 > 0.95) highly significant (P < 0.001) relationship between the predicted and measured δ13Ca using both LWT and HWT δ13Cp values, the predicted δ13Ca fall well below the one to one fit line (Figures 6a and 6b) indicating that the model predicts a less negative δ13Ca than measured result. Using our experimental LWT δ13Cp values to calculate δ13Ca results in a mean difference (prediction – measured) of −4.69‰, a maximum of −7.90‰ and a minimum of −2.33‰. Using HWT δ13Cp values to derive estimates of δ13Ca results in a mean difference of −6.32‰, a maximum of −9.37‰ and a minimum of −3.16‰. The difference between the predicted and measured δ13Ca becomes more pronounced as atmospheric CO2 increases (Figure 6c) suggesting that the relationship between fractionation (discrimination) and CO2 may vary and is potentially nonlinear.
 Using equation (2) we also predict δ13Ca from the δ13Cp of Jahren et al.  (estimated from Jahren et al. [2008, Figure 7]) and compare the predicted δ13Ca to the measured δ13Ca (again estimated from Jahren et al. [2008, Figure 7]). This analysis (Figure 6d) also shows a large disagreement between predicted and measured δ13Ca across different CO2 treatments and between plants grown at different temperatures. However, there is no systematic change in fractionation as atmospheric CO2 increases. These discrepancies could either be due to different species, growth environment or a combination of both.
 The fossil record acts as a strong filter leading to the deposition of mixed assemblages representing different environments resulting in the smoothing of environmental signatures retained in the δ13C of terrestrial organic carbon. This has led to the suggestion [Jahren and Arens, 2009] that the δ13C signature of dispersed TOM or a mixture of fossil material could be used as to track changes in δ13Ca. To test this assertion the experimental data sets (HWT and LWT) were combined (Figure 7a) to produce an analogue of an allochthonous time averaged deposit which would have experience different local environmental conditions (in this case water availability) but grown under a common atmospheric condition. This combined data set was used to derive our own equation (3) to predict δ13Ca from δ13Cp
 Using equation (3)δ13Ca was calculated from our experimental plant material and the plant material in the original meta analysis of Arens et al. . In both cases the calculated δ13Ca is compared to the measured values (Figures 7b and 7c) to determine the utility of δ13Cp from mixed environments to predict δ13Ca. These data again clearly show a disagreement between calculated and measured δ13Ca values. Furthermore the time averaging/mixing that occurs leading up to fossilization and the deposition of TOM may also lead to the mixing of tissue type with different isotopic signatures [Gröcke, 2002; Jahren, 2004]. This could result in large oscillations in the δ13C signature of TOM driven by diagenetic or taphonomic factors unrelated to changes δ13Ca.
 Experimental data (HWT and LWT) demonstrates that environmental factors that alter Ci/Ca can severely impact on the utility of δ13Cp to predict δ13Ca. As even a small manipulation of Ci/Ca via changing water availability can result in large changes to δ13Cp which are not related to δ13Ca. These results indicate that environmental factors play a more important role in determining the isotopic composition of plant material than the isotopic value of the CO2 atmospheric substrate alone. The breakdown of the prediction at extreme δ13Ca values and the lack of convergence between calculations made on HWT and LWT plants support the original criticism of Gröcke  and those of Beerling and Royer  suggesting that the use of fossil δ13Cp to accurately predict the isotopic composition of paleo-CO2 is invalid. Furthermore, as the combined experimental data set, analogous to an allochthonous fossil assemblage fails to adequately predict δ13Ca from δ13Cp and given the problems with mixing as a result of changes in tissue type; the use of δ13C from either TOM and/or mixed fossil leaves as a substrate to predict δ13Ca is invalid.
 The question remains as to whether our experimental data which indicate large changes in fractionation with elevated CO2 are truly representative of the real world. Our elevated CO2 concentrations also lead to depletion in 13C, for example at 3000 ppm δ13Ca = −30.25‰ (Figure 4a) and δ13Cp = −56.59 for HWT plants. Such extreme isotope depletion is unlikely to have occurred over geological time. As δ13Ca and CO2 co-vary in the experimental set-up (Figure 4), in order to fully explore discrimination at elevated CO2 concentrations, experiments where the δ13Ca ratio is held constant as pCO2 increases could be performed –either through controlling the source though the provision of CO2 with a known δ13Ca or via CO2 scrubbing and subsequent re-injection of CO2. This would elucidate if elevated levels of pCO2 that are relevant over evolutionary/geological time scales alter photosynthetic discrimination and fully test the significance of δ13Ca in determining δ13Cp. This experimental procedure would also identity the potential for the refixation of respiratory CO2 within plant tissue. However, data presented in this paper clearly indicates that changes in Ci/Ca alter δ13Cp which in turn reduces the capacity of δ13Cp to predict δ13Ca. Consequently we suggest that experiment in elevated CO2 that controlled for δ13Ca would not alter the fundamental conclusions of this study - that the use of δ13Cp as a substrate to predict δ13Ca is invalid.
 BHL was funded through a Leverhulme Trust Early Career Fellowship (ECF/2006/0492); JAL through a Royal Society Dorothy Hodgkin Fellowship. This study was supported by a University of Sheffield Biology Division Small Grant to BHL and JAL. BHL thanks Steve Pinfold for advice on optical character recognition software, we also thank Isabel Montanez and an anonymous reviewer for their constructive reviews of an earlier version of this paper and the reviewers and editors of G3 for their constructive comments.