• stomatal conductance;
  • elevated [CO2];
  • meta-analysis;
  • model parameters;
  • forests;
  • acclimation


  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. The Jarvis (1976) model: Environmental effects on stomatal conductance
  7. The model: relationship between stomatal conductance and assimilation
  8. Discussion
  9. Acknowledgements
  10. References
  • • 
    Data from 13 long-term (> 1 yr), field-based studies of the effects of elevated CO2 concentration ([CO2]) on European forest tree species were analysed using meta-analysis and modelling. Meta-analysis was used to determine mean responses across the data sets, and data were fitted to two commonly used models of stomatal conductance in order to explore response to environmental conditions and the relationship with assimilation.
  • • 
    Meta-analysis indicated a significant decrease (21%) in stomatal conductance in response to growth in elevated [CO2] across all studies. The response to [CO2] was significantly stronger in young trees than old trees, in deciduous compared to coniferous trees, and in water stressed compared to nutrient stressed trees. No evidence of acclimation of stomatal conductance to elevated [CO2] was found.
  • • 
    Fits of data to the first model showed that growth in elevated [CO2] did not alter the response of stomatal conductance to vapour pressure deficit, soil water content or atmospheric [CO2]. Fits of data to the second model indicated that conductance and assimilation responded in parallel to elevated [CO2] except when water was limiting.
  • • 
    Data were compared to a previous meta-analysis and it was found that the response of gs to elevated [CO2] was much more consistent in long-term (> 1 yr) studies, emphasising the need for long-term elevated [CO2] studies. By interpreting data in terms of models, the synthesis will aid future modelling studies of responses of forest trees to elevated [CO2].


  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. The Jarvis (1976) model: Environmental effects on stomatal conductance
  7. The model: relationship between stomatal conductance and assimilation
  8. Discussion
  9. Acknowledgements
  10. References

It is well documented that stomatal conductance (gs) declines when exposed to a transient increase in atmospheric CO2 concentration; a doubling of [CO2] from the present ambient concentration generally results in a reduction in gs of the order of 40% (Morison, 1987). If this reduction in gs should also occur in response to the current gradual increase in atmospheric [CO2], there could be important implications for forest carbon and water balance (Field et al., 1995). Using models based on the transient response of gs to increasing [CO2], it is generally predicted that forest canopy evapotranspiration is likely to be reduced, with a resulting increase in soil moisture, and possible consequences for a wide range of ecological processes including run-off, production, soil mineralization, and regional climate change (Field et al., 1995, Sellers et al., 1996, Thornley & Cannell, 1996, Kellomäki & Vaisanen, 1997).

However, recent results have called into question whether longer-term exposure to elevated [CO2] results in a similar reduction in stomatal conductance, particularly in woody species (Saxe et al., 1998, Mooney et al., 1999). For example, in a meta-analysis of 48 studies with woody plants, Curtis and Wang (1998) report a modest and nonsignificant reduction of just 11% in response to growth in elevated [CO2]. Many of the studies incorporated in Curtis and Wang’s review were, however, relatively short-term (< 1 yr), pot-based studies. Mature, field-grown trees are subject to extremely different environmental conditions and constraints, and therefore may not respond in the same way as pot-grown seedlings (Norby et al., 1999). Thus, the first aim of this paper is to apply the meta-analysis approach of Curtis & Wang (1998) to examine how stomatal conductance changes in field-grown trees after several years’ exposure to elevated [CO2].

The second aim is to interpret the stomatal conductance data in terms of the models commonly used to extrapolate from leaf gs responses to stand scale. To predict effects of elevated [CO2] on stand carbon and water balance it is not enough to know the average effect of elevated [CO2] on stomatal conductance; we also need to know how to incorporate that effect in models. Currently, there are two main models used to describe stomatal conductance. The first, proposed by Jarvis (1976), is based on empirical stomatal responses to environmental conditions including incident radiation, vapour pressure deficit (VPD), temperature, soil water potential, and atmospheric [CO2]. These empirical responses may be altered in plants grown in elevated [CO2]. For example, growth in elevated [CO2] has been observed to cause reduced sensitivity of gs to VPD (Heath, 1998), reduced sensitivity to drought (Heath & Kerstiens, 1997), and reduced sensitivity to atmospheric [CO2] (Santrucek & Sage, 1996). Here, we investigate how the sensitivity of gs to environmental conditions changed under elevated [CO2] by fitting the Jarvis (1976) model to a range of data sets.

The second commonly used model of stomatal conductance (Ball et al., 1987) is based on the observed correlation between stomatal conductance and assimilation (Wong et al., 1978). Assimilation rates are often observed to acclimate to growth in high [CO2] (Medlyn et al., 1999) and many models assume implicitly that stomatal conductance acclimates in parallel, based on the Ball et al. (1987) function (Sellers et al., 1996). The question of whether assimilation and gs acclimate to elevated [CO2] in parallel or independently is only just beginning to be tackled (Morison, 1998). In order to address this question, Drake et al. (1997) examined the Ci : Ca ratio (intercellular : atmospheric [CO2]) and reported that there was no change in this ratio overall, suggesting that gs and assimilation do acclimate in tandem. However, as noted by Santrucek & Sage (1996), this ratio is not a very sensitive indicator. In this paper, we address this problem by fitting the Ball et al. (1987) model to a range of experimental data sets, and observing whether the parameters of this model change in response to elevated [CO2].

Materials and Methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. The Jarvis (1976) model: Environmental effects on stomatal conductance
  7. The model: relationship between stomatal conductance and assimilation
  8. Discussion
  9. Acknowledgements
  10. References


The experimental data were obtained from experiments carried out under the auspices of two major European collaborative programmes: ECOCRAFT (Jarvis, 1998) and the Nordic Research Project ‘The Likely Impact of Rising CO2 and Temperature on Nordic Forests at Limiting and Optimal Nutrient Supply’ (Roberntz et al., Sigurdsson et al., unpublished). Brief details of the experiments involved are given in Table 1. More information on the design of each experiment may be found in Pontailler et al. (1998) or in the individual references given in Table 2. The experiments differed in a number of ways. They used 15 different European forest tree species, including the most important commercial forestry species. Four main types of CO2 exposure facilities were employed: branch bags (BB), open-top chambers (OTC), whole-tree chambers (WTC) and mini-ecosystems (ME). Some experiments also included nutrient, drought, temperature, or ozone factorial treatments. However, there were two factors common to all experiments: they were all done on freely rooted plants, and all continued for at least two growing seasons. In what follows, individual experiments will be referred to by the experiment names given in Table 1.

Table 1.  Details of experiments from which stomatal conductance data were obtained
Experiment NameSite Name, Institution1Lat.Long.SpeciesStressAdditional factorsInitial age (yr)Length of exposure2 (yr)Stocking3No. of Replicates
  1. Notes: (1) Institution Codes: ARI, Icelandic Agricultural Research Institute; FC, U.K. Forestry Commission Research Agency; FUSAG, Faculté Universitaire des Sciences Agronomiques de Gembloux; JOY, University of Joensuu; RVAU, Royal Veterinary and Agricultural University; SLU, Swedish University of Agricultural Sciences; TUB, Technical University of Berlin; UE, University of Edinburgh; UIA, Universitaire Instelling Antwerpen; UPS, Universite de Paris-Sud; UVT, University of Viterbo. (2) Length of exposure in growing seasons. (3) Stocking is in stems ha−1 for branch bag experiments, otherwise in plants per chamber. (4) Values from plants exposed to elevated ozone were omitted from this review.

Branch bags
Denmark Fagus BBGrib Skov, RVAU55°59′N12°16′EFagus sylvaticaNone 36 2 800 8
Scotland Picea BBGlencorse, UE55°31′N 3°12′WPicea sitchensisNutrient 16 41600 6
Sweden Picea BBFlakaliden, SLU64°07′N19°27′EPicea abiesNutrient, NoneNutrition29 3.52400 6
Open-top chambers
Belgium Picea OTCVielsalm, FUSAG50°17′N 5°55′EPicea abiesNutrient, NoneNutrition11 9  14 2
Belgium Populus OTCUIA Campus, UIA51°10′N 4°24′EPopulus cv. Robusta, Populus cv. BeaupreNone  0 3  15 2
England Mixed OTCHeadley, FC52°08′N00°50′WQuercus petraea,Fraxinus excelsiorWater, NoneWater, Ozone4 2 3  16 2
England Quercus OTCHeadley, FC52°08′N00°50′WQuercus petraea, Quercus robur Quercus rubraNoneOzone4 1 2  36 4
Finland Pinus OTCMekrijärvi, JOY62°41′N30°57′EPinus sylvestrisNutrientTemperature20 4   1 4
Italy Macchia OTCMontalto di Castro, UVT42°22′N11°32′EQuercus ilex, Pistacia lentiscus, Phillyrea angustifoliaWater 30 6  13 3
Scotland Betula OTCGlencorse, UE55°31′N 3°12′WBetula pendulaNutrient  0 4   1 6
Germany Fagus METUB Campus, TUB52°28′N13°18′EFagus sylvaticaNone  1 4  25 1
Germany Quercus METUB Campus , TUB52°28′N13°18′EQuercus roburNone  1 3  16 1
Whole-tree chambers
Iceland Populus WTCGunnarsholt, ARI63°51′N20°13′WPopulus trichocarpaNutrient, NoneNutrition 4 3   1 4
Table 2.  Details of stomatal conductance measurements from which data were obtained
Experiment NameEquipmentField/LabClimatic ConditionsSamplingReferences
  1. VPD, Vapour pressure deficit; T, temperature.

Branch bags     
Denmark Fagus BBCiras-1 (PP Systems)FieldLight saturation. ambient T (23–30°C). Ambient VPD (1.7–3.2 kPa). Growth [CO2]Three leaves from each branch. (Branches in mid-canopy)Freeman (1998)
Scotland Picea BBADC LCA3 + light sourceFieldLight saturation. Ambient T (18–35°C). Ambient VPD (0.7–3.1 kPa). Growth [CO2]One shoot of each age class. (Branches of 3rd whorl)Barton & Jarvis (1999)
Sweden Picea BBLi-Cor 6200FieldLight saturation. Ambient T (5–24°C). Ambient VPD (0–1.1 kPa). Growth [CO2]Current shoots. (Branches in mid-canopy)Roberntz & Stockfors (1998)
Open-top chambers
Belgium Picea OTCBinos 100 IRGAFieldLight saturation (> 800 mol m−2 s−1). T (15–20°C). VPD: < 1.0 kPa. Growth [CO2].Randomly sampled.Laitat et al. (2000)
Belgium Populus OTCADC-LCA3FieldLight saturation. T: 25–30°C. rh: 30–50%. Growth and reciprocal [CO2].2 or 3 ramets per clone.Will & Ceulemans (1997)
England Mixed OTCDelta-T AP4 porometerFieldAmbient PAR (25–1100 µmol m−2 s−1). Ambient T (20–35°C). Ambient VPD (0–4 kPa). Growth [CO2]Youngest fully expanded mature leaves sampled from top of canopy growing in full sun.Broadmeadow & Jackson (2000)
England Quercus OTCADC-LCA3FieldAmbient PAR (25–1200 µmol m−2 s−1). Ambient T (10–34°C). Ambient VPD (0–4 kPa). Growth [CO2]Youngest fully expanded mature leaves sampled from top of canopy growing in full sun.unpublished
Finland Pinus OTCADC-LCA4LabT: 7.0–33.0°C. PAR: 50–1400 µmol m−2 s−1[CO2]: 20–1400 µmol mol−1. VPD: 0.3–2.0 kPa.Current shoot from second whorl.Kellomäki & Wang (1996)
Italy Macchia OTCADC-LCA4FieldAmbient PAR. Ambient T (25–38°C). Ambient VPD (0–6 kPa). Growth [CO2].Five to 10 sun leaves for each species.Scarascia-Mugnozza et al. (1996)
Scotland Betula OTCLi-Cor 6200 + home-made light sourceFieldLight saturation. Ambient T (20–30°C). Ambient VPD (0.8–3.0 kPa). Growth [CO2]Three leaves per tree from the middle-bottom crown.Rey & Jarvis (1998)
Germany Fagus MEWalz CMS-400FieldLight saturation. T (25°C). VPD (1.3 kPa). Eight [CO2].Range of canopy depths.Strassemeyer & Forstreuter (1998)
Germany Quercus MEWalz CMS-400FieldLight saturation. T (25°C). VPD (1.3 kPa). Eight [CO2].Range of canopy depths.unpublished
Whole-tree chambers
Iceland Populus WTCLi-Cor 6200 + QB6200 light sourceFieldLight saturation. Ambient T (2–20°C). Ambient VPD (0.1–0.9 kPa). Growth and reciprocal [CO2]Youngest fully expanded sun leaves.Sigurdsson et al. (2001)

Brief details of the measurements of stomatal conductance are given in Table 2. Most measurements were made using gas exchange equipment, although porometers were also used in the English Mixed OTC experiment. Only data where stomata were given enough time to equilibrate with measurement conditions were included. Data from high-ozone treatments were also excluded from the analysis.

Statistical analysis

Meta-analysis was used to estimate the mean ratio of stomatal conductance of plants grown in elevated (700 µmol mol−1) to that of plants grown in ambient (350 µmol mol−1) [CO2] (the E/A ratio). The meta-analysis techniques used are those described by Curtis & Wang (1998) and implemented in the statistical software MetaWin (Rosenberg et al., 1997). The mean, standard deviation, and number of observations for each parameter value were required. The standard deviation was taken to be the between-chamber standard deviation, and the number of observations was taken as the number of chamber replicates. The standard deviation is used in the meta-analysis to weight each observation. Some observations in the dataset had no corresponding standard deviation because there was only one chamber replicate. These observations were included conservatively, by assigning to them the smallest of the weights of the other experiments. In order to satisfy the requirement that observations be independent, the observation made in mid-growing season in the final year of the experiment was used if more than one observation was available (Table 3). The meta-analysis was done on the natural logarithm of the response ratios, as described by Hedges et al. (1999). A mixed-model analysis was assumed (Gurevitch & Hedges, 1993). Further details of the meta-analysis procedure are given by Medlyn et al. (1999).

Table 3.  Mean values of stomatal conductance to water vapour at ambient and elevated [CO2] taken from experiments listed in Table 1
SpeciesDateTreatmentTreatmentAmbient SDnMeanElevated SDnE : A
  1. Values are given in mmol m−2 s−1. For conifers, values are expressed on a projected leaf area basis. Values indicated with* were included in the meta-analysis. SD, standard deviation of replicates; n, number of replicate chambers in which gs was measured; E : A, ratio of mean value at elevated [CO2] to that at ambient [CO2]. Note: (1) C, current-year needles.

Sweden Picea BB
Picea abies1994Unfert.10720.15 91 29.850.85
Picea abies1994Fert.103 8.64107 38.941.04
Picea abies*1995Unfert.13422.66126 24.460.94
Picea abies*1995Fert.15720.96149 45.160.95
Belgium Picea OTC
Picea abiesJul 96Fert. 47 1 48 11.01
Picea abiesJul 96Unfert. 75 1 53 10.70
Picea abies*Aug 97Fert.101 1104 11.03
Picea abies*Aug 97Unfert.126 1 82 10.66
Scotland Picea BBNeedle age1
Picea sitchensis13/7/93C + 1 7528.16 30  3.430.40
Picea sitchensis22/7/93C + 1 7752.14 74 57.140.96
Picea sitchensis10/8/93C + 1 8956.35 56 28.750.64
Picea sitchensis24/8/93C + 1 7934.66 56 35.760.71
Picea sitchensis28/9/93C + 1 9338.86 47 25.560.50
Picea sitchensis12/7/93C14340.46108 42.360.76
Picea sitchensis22/7/93C11751.84124 35.531.05
Picea sitchensis10/8/93C11232.85120 74.151.07
Picea sitchensis*24/8/93C 9830.96 94 39.660.96
Picea sitchensis28/9/93C 6726.26 73 45.661.10
Finland Pinus OTC
Pinus sylvestris*1994Amb. T14510.64121 10.440.84
Pinus sylvestris*1994Elev. T152 8.74142  9.340.94
Italy Macchia OTC
Measurements at low VPD (1 kPa)
Quercus ilex*Jun 94 15353.02135  0.020.89
Pistacia lentiscus*Jun 94 30514.12183102.520.60
Phillyrea angustifolia*Jun 94 234 1.82188 10.80
Measurements at normal VPD (2–4 kPa)
Quercus ilexJun 94  47 3.83 44  7.130.93
Pistacia lentiscusJun 94 10528.53 59  5.030.56
Phillyrea angustifoliaJun 94 10310.33 88 34.930.85
England Mixed OTC
Quercus petraea*Jun 96+H2O21347.52156 37.520.73
Quercus petraea*Jun 96−H2O15219.62 99 23.720.65
Fraxinus excelsior*Jun 96+H2O18559.42 99 11.320.54
Fraxinus excelsior*Jun 96−H2O 68 4.92 44  6.320.65
England Quercus OTC
Quercus petraea*Aug 98 175 4.64122 27.040.70
Quercus robur*Aug 98 18049.34 99 17.940.55
Quercus rubra*Aug 98 108 1.84 67 15.640.62
Germany Quercus ME
Quercus roburAug 96 131 1 96 10.73
Quercus roburAug 97 116 1102 10.87
Quercus robur*Aug 98  80 1 51 10.63
Scotland Betula OTC
Betula pendulaJun 94 289202.65193155.650.67
Betula pendulaJul 94 279102.46235136.050.84
Betula pendula*Aug 94 220 65.96167 78.960.76
Betula pendulaSept 94 177 39.36103 24.360.58
Belgium Populus OTC
Populus cv. BeaupréMay 95 214 18.42200  2.320.94
Populus cv. Beaupré*Aug 95 244 10.02222 24.920.91
Populus cv. RobustaMay 95 231  3.32203  7.920.88
Populus cv. Robusta*Aug 95 243  9.02217 41.520.89
Iceland Populus WTC
Populus trichocarpa15/6/96Unfert.143 43.24153  9.641.07
Populus trichocarpa15/7/96Unfert.239 89.04260 21.641.09
Populus trichocarpa*30/7/96Unfert.352 80.13400114.041.14
Populus trichocarpa15/8/96Unfert.344 76.34448109.041.30
Populus trichocarpa11/9/96Unfert.346 62.64400263.441.16
Populus trichocarpa15/6/96Fert.239105.94150 48.540.63
Populus trichocarpa15/7/96Fert.377 33.84375 53.841.00
Populus trichocarpa*30/7/96Fert.555145.44493106.140.89
Populus trichocarpa15/8/96Fert.507 76.74437 71.140.86
Populus trichocarpa11/9/96Fert.589 77.04512116.340.87
Germany Fagus ME
Fagus sylvatica1994  88 1 67 10.76
Fagus sylvatica1995  74 1 42 10.57
Fagus sylvatica1996  91 1 78 10.86
Fagus sylvatica*1997  74 1 62 10.85
Denmark Fagus BB
Fagus sylvatica*Jul 96 179 72.18171 61.680.96

Meta-analysis was first used to compare the results from the data set compiled here with that compiled by Curtis & Wang (1998), by combining the two data sets. We then performed a meta-analysis of long-term, field-based studies only; four of the studies considered by Curtis & Wang (1998) fitted these criteria and hence were retained in the data set for this meta-analysis. These four studies were on Liriodendron tulipifera and Quercus alba (Gunderson et al., 1993), Maranthes corymbosa (Eamus et al. 1995) and Pinus taeda (Liu & Teskey, 1995).

In addition to the statistical meta-analysis, data were fitted where possible to one or both stomatal conductance models (Jarvis, 1976, Ball et al., 1987). The Jarvis (1976) model expresses stomatal conductance as a multiplicative combination of responses to several environmental factors, for example:

  • image(Eqn 1)

(gsmax, the maximum value of stomatal conductance under optimal environmental conditions; f1… f5, functions ranging from 0 to 1; Ca, atmospheric [CO2] (µmol mol−1); D, leaf to air vapour pressure deficit (kPa); T, leaf temperature (°C); I, incident PAR (µmol m−2 s−1); ψ, soil water potential (MPa).) The derivation of all parameters of this model requires measurements of gs under varying conditions of all variables, and the variables should not be correlated (Jarvis, 1976). Such datasets are difficult to obtain in practice; in most cases the datasets we had available included responses to only one or two of these variables. Thus, in place of the full model, we individually fitted as many of the functions f1… f5 as possible to each dataset.

We also fitted the Ball et al. (1987) model, which relates stomatal conductance to assimilation as follows:

  • image(Eqn 2)

(An, the net assimilation rate (µmol m−2 s−1); hs, the relative humidity at the leaf surface; g0 and g1, the parameters to be fitted.) All model fits were performed using SigmaPlot for Windows Version 5.0 (SPSS Inc.). Stomatal conductance parameters obtained were stored for future reference in the ECOCRAFT parameter database (Medlyn & Jarvis, 1999).


  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. The Jarvis (1976) model: Environmental effects on stomatal conductance
  7. The model: relationship between stomatal conductance and assimilation
  8. Discussion
  9. Acknowledgements
  10. References


Response of stomatal conductance to growth in elevated [CO2]

The mean values of stomatal conductance under ambient and elevated [CO2] from each experiment in the Ecocraft/Nordic data set are given in Table 3. Meta-analysis was used to calculate the mean effect of [CO2] on stomatal conductance from these values (Table 4). A significant reduction in gs of 21% was found. By contrast, in the dataset compiled by Curtis & Wang (1998), there was a nonsignificant reduction in stomatal conductance of 10% in elevated [CO2]. However, the probability that the mean responses in the two data setswere different was not significant (P = 0.245). To examine further the differences between the two datasets, we combined them and then tested for differences between pot-grown and freely rooted plants, and between short-term (< 1 yr) and long-term (> 1 yr) studies. As shown in Table 4, there was no significant difference in the [CO2] effect on stomatal conductance between pot-grown and freely rooted plants. However, there was a difference between short-term and long-term studies. In studies of < 1 yr, there was no significant effect of [CO2] on stomatal conductance, while in longer studies, there was a significant reduction of 23%.

Table 4.  Output from the meta-analysis of the effect of growth in elevated [CO2] on mean stomatal conductance, measured at the growth [CO2] concentration. For each category, the estimate of the mean E : A ratio (value in elevated [CO2] : value in ambient [CO2]) and the 95% confidence interval on this ratio is given. n, number of observations in each category, and P, probability that response was different among the categories. * indicates probability significant at the 5% level.
 Mean Response95% CInP
All experiments0.860.78–0.9674 
Comparison withCurtis & Wang (1998)    
ECOCRAFT/Nordic experiments0.790.67–0.9525 
Curtis & Wang (1998)0.900.79–1.03490.24
Pot vs field based    
Freely rooted0.890.75–1.04340.63
Length of experiment    
< 1 yr0.950.83–1.0942 
> 1 yr0.770.66–0.90320.05*
Long-term, field-based experiments only    
Tree age    
Mature (> 10 yr)0.910.82–1.0210 
Young (< 10 yr)0.750.69–0.82190.01*
Functional group    
Coniferous0.920.81–1.03 8 
Broadleaf evergreen0.790.55–1.14 3 
Broadleaf deciduous0.760.69–0.83180.04*
Exposure facility    
Open-top chamber0.760.69–0.8320 
Branch bag0.960.80–1.14 5 
Mini-ecosystem0.760.56–1.04 2 
Whole-tree chamber0.990.73–1.36 20.07
Nutrient stress0.900.79–1.03 7 
Water stress0.690.56–0.86 5 

Meta-analysis was also used to test for differences in stomatal response within the set of long-term, field-based experiments. There was a difference in response between functional groups of tree species, with the reduction in gs being less for conifers than for deciduous species (Table 4). Responses were also found to differ between mature (> 10-yr-old) and young trees, with older trees showing a smaller response. However, there was a confounding effect with functional group, as most of the experiments with older plants were carried out on conifers. The test for differences in response between different types of exposure facility was not powerful because the majority of observations came from open-top chamber studies. There did appear to be a small difference between open-top chamber and branch-bag studies, with branch-bag studies showing a smaller reduction in gs. This result is also confounded with other factors, however, since all the branch-bag studies were performed on mature trees. Finally, plants were also categorised according to stress level. Although the differences were not significant, there was a clear trend for the reduction in stomatal conductance in elevated [CO2] to be greater when plants were water stressed, and less when plants were nutrient stressed.

Acclimation of stomatal conductance to growth in elevated [CO2]

Acclimation of photosynthesis to growth in elevated [CO2] is commonly tested for by measuring photosynthesis of ambient- and elevated-[CO2] grown plants at the same [CO2] (e.g. Drake et al., 1997, Curtis & Wang, 1998). However, a similar test for acclimation of stomatal conductance to growth in elevated [CO2] is rarely performed. Here, we tested for acclimation by using meta-analysis to test whether stomatal conductance measured at 700 µmol mol-1[CO2] differed between treatments. Across the dataset compiled here, no significant effect of elevated [CO2] on gs at 700 µmol mol−1[CO2] was found (Table 5). This conclusion was unchanged when the database was expanded by including the data compiled by Curtis & Wang (1998). This result suggests that there was no acclimation of stomatal conductance to elevated [CO2].

Table 5.  Meta-analysis of the effect of growth in elevated [CO2] on mean stomatal conductance, measured at a constant [CO2] concentration (700 µmol mol−1).
 Mean Response95% CInP
All experiments0.940.84–1.0521 
Comparison withCurtis & Wang (1998) ECOCRAFT/Nordic experiments1.020.85–1.23 9 
Curtis & Wang, 19980.890.77–1.03120.25

The Jarvis (1976) model: Environmental effects on stomatal conductance

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. The Jarvis (1976) model: Environmental effects on stomatal conductance
  7. The model: relationship between stomatal conductance and assimilation
  8. Discussion
  9. Acknowledgements
  10. References

Response to vapour pressure deficit (VPD)

For several of the datasets, the only independent variable to which stomatal conductance could be related was VPD. Light levels varied but did not appear to affect stomatal conductance, and temperature was highly correlated with VPD. The Finland Pinus OTC dataset, by contrast, included response curves of stomatal conductance to VPD with all other variables held constant. We chose to fit a simple linear response to VPD to ensure that the same model could be fitted to all data sets. The equation fitted (cf. eqn 1) was:

  • image( Eqn 3)

(D0, the value of VPD at which stomatal conductance becomes zero.)

We tested whether the response of gs to VPD is affected by growth in elevated [CO2], examining whether the parameter D0 was altered between treatments. As a note of clarification: we chose to test for changes in D0 rather than changes in the slope of the gs-VPD response because it is well known that the slope is highly correlated with the magnitude of gs at low VPD (e.g. Oren et al., 1999), which is often reduced by growth in elevated [CO2].

The values of D0 found for each experiment are shown in Table 6, and the responses of gs to VPD are illustrated in Fig. 1. The experiments included studies on mature conifers, mature beech, oak saplings, and water-stressed macchia species. In none of these experiments did the value of D0 change significantly, indicating that the response of gs to VPD is unaffected by growth in elevated [CO2] for a wide range of environmental conditions and species.

Table 6.  Values of D0 (kPa), the Jarvis model parameter describing the response to VPD (eqn 5). The standard error is given in parentheses. 1Needles from previous year.
ExperimentSpecies/TreatmentAmbient [CO2]Elevated [CO2]
Denmark Fagus BB 3.42 (0.60)3.62 (0.34)
England Mixed OTCWatered (Q. robur)6.66 (0.99)4.43 (0.41)
England Mixed OTCDroughted (Q. robur)5.75 (1.00)5.95 (1.38)
Finland Pinus OTCAmbient temperature4.72 (0.38)3.85 (0.26)
Finland Pinus OTCElevated temperature7.30 (0.79)6.29 (0.56)
Italy Macchia OTCQ. ilex8.56 (1.26)7.92 (1.06)
Italy Macchia OTCP. angustifolia9.71 (5.61)14.4 (5.34)
Scotland Picea BBC + 1 needles14.00 (0.90)3.64 (0.76)

Figure 1. Response of stomatal conductance to vapour pressure deficit (VPD). Closed squares, ambient [CO2]; open squares, elevated [CO2]. Solid and dotted lines show regressions fitted to ambient and elevated [CO2] treatments, respectively. (a) Scotland Picea BB, C + 1 needles. (b) Finland Pinus OTC, ambient temperature treatment. (c) Finland Pinus OTC, elevated temperature treatment. (d) England Mixed OTC, Quercus robur, watered treatment. (e) England Mixed OTC, Quercusrobur, droughted treatment. (f) Denmark Fagus BB. (g) Italy Macchia OTC, Quercus ilex. (h) Italy Macchia OTC, Phillyrea angustifolia.

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Response to soil water content

The response to soil water content was examined by comparing the watered and droughted low-ozone treatments in the England Mixed OTC experiment. A set of data with VPD < 1.0 kPa was used. Values from both irrigation treatments were combined to obtain a response of stomatal conductance to soil water content, shown in Fig. 2. To these responses the following simple model was fitted (cf. eqn 1):


Figure 2. Response of stomatal conductance to soil water potential. Closed squares: ambient [CO2]; open squares: elevated [CO2]. Solid and dotted lines show regressions fitted to ambient and elevated [CO2] treatments, respectively. (a) England Mixed OTC, Quercus robur. (b) England Mixed OTC, Fraxinus excelsior.

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  • image( Eqn 4)

0, the value of soil water potential (MPa) at which stomatal conductance becomes zero.) The parameter ψ0 was examined to test whether sensitivity to soil water content changed in elevated [CO2]. The values of this parameter are given in Table 7 and illustrate that, while sensitivity of gs to soil water potential was much higher in F. excelsior than in Q. robur, there was no effect of growth [CO2] on this sensitivity for either species.

Table 7.  Values of ψ0 (MPa), the Jarvis model parameter describing response to soil water potential (eqn 6). The standard error is given in parentheses
ExperimentSpeciesAmbient [CO2] (MPa)Elevated [CO2] (MPa)
England Mixed OTCQ. robur0.45 (0.23)0.36 (0.14)
England Mixed OTCF. excelsior0.18 (0.02)−0.20 (0.02)

Sensitivity to atmospheric [CO2]

The effect of long-term growth in elevated [CO2] on stomatal conductance is indicated by the results of the meta-analysis (Table 4). However, one can also ask whether the sensitivity of stomata to transient changes in [CO2] is affected by growth at elevated [CO2]. To investigate this possibility, we utilised measurements of gs made at ambient and doubled [CO2] in both ambient and elevated [CO2] treatments. To these data we fitted the linear model:

  • image( Eqn 5)

(the parameter a, the fractional response in gs to a doubling in [CO2] from 350 to 700 µmol mol−1, and is comparable to the E : A ratio obtained in the meta-analysis.) Values of this parameter are shown in Table 8. The sensitivity to [CO2] over the range 350–700 µmol mol−1 in ambient conditions varied considerably between experiments. In the two conifer experiments, stomatal conductance showed a relatively small sensitivity to [CO2] (a approx. 0.8–1.0), and this sensitivity was unchanged by growth in elevated [CO2]. A similar pattern was seen for the two poplar cultivars in the Belgium Populus OTC experiment. By contrast, for the other broad-leaf species, the sensitivity of gs to [CO2] was strong in the ambient [CO2] treatments (a approx. 0.6) but tended to be reduced slightly by growth in elevated [CO2].

Table 8.  Values of a, the Jarvis model parameter describing the short-term response to atmospheric [CO2] (eqn 7). The standard error is given in parentheses
ExperimentSpecies/TreatmentAmbient [CO2]Elevated [CO2]
Belgium Populus OTCPopulus cv. Beaupré1.02 (0.04)0.94 (0.02)
Belgium Populus OTCPopulus cv. Robusta0.93 (0.04)0.91 (0.03)
Finland Pinus OTCAmbient temperature1.07 (0.06)1.03 (0.07)
Finland Pinus OTCElevated temperature1.04 (0.04)1.00 (0.04)
Germany Fagus ME 0.61 (0.03)0.76 (0.03)
Germany Quercus ME 0.60 (0.12)0.67 (0.05)
Italy Macchia OTCQ. ilex0.60 (0.04)0.71 (0.04)
Italy Macchia OTCP. lentiscus0.65 (0.04)0.80 (0.09)
Scotland Picea BBC needles0.79 (0.02)0.83 (0.02)

The Ball et al. (1987) model: relationship between stomatal conductance and assimilation

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. The Jarvis (1976) model: Environmental effects on stomatal conductance
  7. The model: relationship between stomatal conductance and assimilation
  8. Discussion
  9. Acknowledgements
  10. References

The meta-analysis of stomatal conductance measured at 700 µmol mol−1[CO2] indicated that there was no acclimation of stomatal conductance to elevated [CO2] (Table 5). By contrast, a similar meta-analysis of photosynthesis data from the same experiments indicated that photosynthetic rates measured at 700 µmol mol−1[CO2] were significantly reduced by 9% in elevated [CO2] (Medlyn et al., 1999). Thus, a preliminary conclusion might be that stomatal conductance and photosynthesis do not respond to long-term growth in elevated [CO2] in the same way. This question was investigated in more detail using the Ball et al. (1987) model (eqn 2), which is based on the relationship between photosynthesis and stomatal conductance. If photosynthesis and stomatal conductance acclimate to long-term growth in elevated [CO2] in parallel, then the parameters of the model should not change. Applying the model at ambient and elevated [CO2] concentration, we have

  • image(Eqn 6)


  • image( Eqn 7)

Dividing eqn 7 by eqn 6, and assuming the parameter g0 to be negligible, if the parameter g1 is unchanged between ambient and elevated [CO2] then the E/A ratio of photosynthesis (An(Ca=700)/An(Ca=350)) should be approximately twice the E/A ratio of stomatal conductance (gs(Ca=700)/gs(Ca=350)), whether or not acclimation has occurred. Thus, as a first test of whether stomatal conductance and assimilation acclimate (or do not acclimate) in parallel to growth in elevated [CO2], we plotted the E/A ratio of gs against the E/A ratio of An and compared the plot to the 1 : 2 line (Fig. 3). Some scatter is to be expected, since gs and An were not always measured under the same conditions. However, the plot appears to follow the 1 : 2 line, suggesting that the linkage between stomatal conductance and assimilation is unchanged by growth in elevated [CO2].


Figure 3. Effect of elevated [CO2] on stomatal conductance, expressed as a ratio of the elevated [CO2] value to the ambient [CO2] value, versus the effect on assimilation. Closed symbols, conifers; open symbols, broadleaved species. The dashed line indicates the 1:2 line.

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A better test of this conclusion was made by fitting the Ball et al. (1987) model to a series of data sets to test how the relationship changed between ambient and elevated [CO2] grown plants. Parameters from the model fits are given in Table 9, and the data are illustrated in Fig. 4. In the nonwater-stressed experiments (Sweden, Denmark, Scotland) the slope of the relationship tended to increase slightly but this shift was not significant. In the water-stressed Italian experiment, different species responded in strikingly different ways. For one shrub, Phillyrea angustifolia, there was a small increase in the slope of the relationship, as for the nonwater-stressed experiments, whereas for a different shrub, Pistacia lentiscus, there was a highly significant reduction in the slope of the relationship. These species clearly have different strategies to cope with water limitation (Scarascia-Mugnozza et al., 1996). In summary, it seems fair to conclude that, in general, the slope of the Ball et al. (1987) relationship is unlikely to be changed significantly by growth in elevated [CO2], indicating that stomata and photosynthesis do respond in parallel. However, the divergent results obtained in the Italian Macchia OTC experiment suggest that this conclusion should be further tested under water-stressed conditions.

Table 9.  Parameters of the Ball et al. (1987) model (eqn 2). P, probability that fitted lines for ambient and elevated [CO2] treatments are coincident
 Ambient equationr2nElevated equationr2nCombined equationr2nPCO2 effect on slope
Denmark Fagus BBy = −0.02 + 12.7x0.95 8y = −0.003 + 12.1x0.91 8y = −0.008 + 12.3x0.93 16  0.260.95
Italy Macchia OTC           
Phillyrea angustifoliay = 0.033 + 10.09x0.6624y = 0.048 + 1.85x0.2223y = 0.039 + 6.47x0.36 47< 0.0010.18
Pistacia lentiscusy = 0.042 + 8.16x0.7323y = 0.028 + 13.41x0.5020y = 0.042 + 8.62x0.63 43  0.181.64
Quercus ilexy = 0.024 + 6.23x0.5225y = 0.029 + 3.28x0.3523y = 0.030 + 3.68x0.37 46  0.150.53
Scotland Betula OTCy = 0.084 + 9.37x0.1569y = −0.018 + 18.62x0.4266y = 0.043 + 12.1x0.30135  0.061.99
Scotland Picea BB (C needles)y = 0.043 + 6.44x0.2029y = 0.023 + 7.62x0.7427y = 0.031 + 7.29x0.73 56  0.541.18
Scotland Picea BB (C + 1 needles)y = 0.027 + 5.19x0.7129y = 0.009 + 7.05x0.8328y = 0.018 + 5.88x0.88 57  0.151.36
Sweden Picea BBy = 0.054 + 2.93x0.6721y = 0.032 + 4.56x0.5321y = 0.052+ 3.21x0.59 42  0.071.56

Figure 4. Fits of the Ball et al. (1987) stomatal conductance model (eqn 2). Closed squares, ambient [CO2]; open squares, elevated [CO2]. Solid and dotted lines show regressions fitted to ambient and elevated [CO2] treatments, respectively. (a) Denmark Fagus BB. (b) Italy Macchia OTC, Phillyrea angustifolia. (c) Italy Macchia OTC, Pistacia lentiscus. (d) Italy Macchia OTC, Quercusilex. (e) Scotland Betula OTC. (f) Scotland Picea BB, C needles. (g) Scotland Picea BB, C + 1 needles. (h) Sweden Picea BB.

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  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. The Jarvis (1976) model: Environmental effects on stomatal conductance
  7. The model: relationship between stomatal conductance and assimilation
  8. Discussion
  9. Acknowledgements
  10. References

Effect of elevated [CO2] on mean stomatal conductance

The meta-analysis of stomatal conductance values (Table 4) indicates that there was a significant 21% decrease of stomatal conductance in response to growth in elevated [CO2] across this set of 13 long-term studies with woody species. This result contrasts with the study by Curtis & Wang (1998) who performed a similar meta-analysis on stomatal conductance in 48 studies with woody plants and found a modest and nonsignificant reduction of 11% in response to elevated [CO2]. An analysis of our database combined with that of Curtis & Wang (1998) indicated that the chief difference between the two databases was the length of the studies included. Experiments of less than 1 year showed no reduction in gs in elevated [CO2], while experiments of > 1 yr showed a significant reduction in gs of 23%. This result appears to run counter to the idea recently put forward that the transient reduction in gs in response to elevated [CO2] will be attenuated by long-term growth in elevated [CO2] (Saxe et al., 1998, Mooney et al., 1999, Norby et al., 1999). However, a plot of the response of gs to elevated [CO2] versus length of exposure (Fig. 5) illustrates that the key difference between ‘short-term’ (< 1 yr) and longer-term experiments is variability. Reported responses of gs in short-term experiments are highly variable, whereas the responses in long-term experiments are much more consistent. The reason for the high variability in short-term experiments is not immediately evident. There is no similar distinction between pot-grown and freely rooted plants, thus ruling out any artefact related to restricted root volume, such as that proposed by Saxe et al. (1998). However, one conclusion that may be drawn from Fig. 5 is that long-term experiments are essential in studies of elevated [CO2] effects on stomatal conductance.


Figure 5. Effect of elevated [CO2] on stomatal conductance, expressed as a ratio of the elevated [CO2] value to the ambient [CO2] value, as a function of length of exposure to elevated [CO2]. Filled symbols, data from Curtis & Wang (1998); open symbols, data from the current set of experiments. The dashed line indicates a ratio of 1.

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The meta-analysis (Table 4) indicated a significant effect of functional type on the response of stomata to [CO2], with conifers responding less strongly to elevated [CO2] than deciduous and evergreen broadleaf species. Saxe et al. (1998) also reported a similar difference between functional groups. However, the meta-analysis also showed a significant effect of tree age on stomatal response. The two factors were confounded, with most experiments on older trees (> 10 yr) being on conifers, and most experiments on saplings being with deciduous species. Hence, from the meta-analysis, it was not possible to determine which was the principal cause of the difference between categories. Examination of nonconfounded cases tends to suggest that the difference may lie in tree age rather than functional type. In a branch bag study on mature beech there was no reduction in stomatal conductance or transpiration in elevated [CO2] (Dufrêne et al., 1993, Pontailler et al., 1994). In a second study on mature beech, the [CO2] effect on stomatal conductance varied through the season, with decreases in June and September but no effect in July and an increase in August (Freeman, 1998). On the other hand, literature reports from long-term field-based experiments with young conifers tend to show a strong reduction in gs (−17% in Pinus ponderosa, Surano et al., 1986, −38% in P. taeda, Fetcher et al., 1988, up to −40% in P. taeda, Tissue et al., 1997, −35% in current needles of P. sitchensis, C. Barton, unpublished). Differences in the stomatal response related to age or to functional type both appear plausible. The observation that stomata of conifers are generally unresponsive to Ca has been invoked to explain the difference in response of gs to elevated [CO2] between conifers and broadleaf species (Saxe et al., 1998), while many studies have shown a reduction in stomatal conductance with increasing tree age (Kolb et al., 1997). New FACE (free-air CO2 enrichment) studies on mature trees may shed some light on this question (e.g. Ellsworth, 2000).

Effect of elevated [CO2] on responses of gS to environmental factors

Curtis (1996) found that the response of gs to elevated [CO2] was strongest in unstressed plants, and noted that this appeared to conflict with the observation by Sage (1994) that environmental stress accentuates the effect of elevated [CO2] on gs. Meta-analysis of our data suggests that this conflict may be resolved by observing that different kinds of stress affect the response of gs to elevated [CO2] in different ways. Nutrient stress (the most common type of stress in the dataset of Curtis (1996)) appeared to reduce the response of gs to elevated [CO2], whereas water stress increased the response, as noted by Sage (1994).

The response of gs to elevated [CO2] under water stress is of particular interest, since the higher temperatures predicted to follow increases in atmospheric [CO2] are likely to increase potential evapotranspiration and thus the frequency of drought stress. The enhanced water-use efficiency almost universally observed under elevated [CO2] seems to offer the potential for protection from this stress. For this reason we examined the effect of elevated [CO2] on responses of stomatal conductance to two important factors influencing plant water relations, leaf to air vapour pressure deficit and soil water potential.

We found that stomatal sensitivity to VPD was unchanged by growth in elevated [CO2] in any of the experiments (Fig. 1), in that the value of VPD at which stomatal conductance became zero (D0) was unchanged. A number of studies have found similar results. Will & Teskey (1997) reported no change in VPD sensitivity in three species (Quercus rubra, Populus deltoides×nigra, Pinus sylvestris) with a small increase in sensitivity in a fourth species (Cercis canadensis). Goodfellow et al. (1997) and Tognetti et al. (1998) present data showing that D0 is unchanged by growth in elevated [CO2] in Mangifera indica and Quercus ilex, respectively. Morison & Gifford (1983) also noted that the most common pattern was for stomatal responses to humidity to remain unchanged by growth in elevated [CO2]. However, there are exceptions to this pattern, such as the study by Heath (1998), where strongly decreased stomatal sensitivity to VPD was found in seedlings of F.sylvatica, Castanea sativa and Q. robur. Hollinger (1987) also reported reduced sensitivity to VPD in two young conifers. These two studies were, however, carried out on pot-grown seedlings exposed to elevated [CO2] for less than 1 year and hence may be less likely to reflect responses of field-grown trees than the experiments considered here.

With regard to soil water potential, we present data indicating that stomatal sensitivity to soil water potential was unchanged by growth in elevated [CO2] for young saplings of oak and ash (Fig. 2). Similar results have been demonstrated by Morison & Gifford (1984) and Centritto et al. (1999) for wheat and potted cherry (Prunus avium) seedlings, respectively. However, a convincing counter-example to this pattern was presented by Heath & Kerstiens (1997), who show a much-reduced response of stomatal conductance to soil water content in potted beech seedlings exposed to elevated [CO2] for two growing seasons.

In summary, therefore, we found that mean stomatal conductance tended to be reduced strongly by growth in elevated [CO2] when plants were water-stressed, but that the sensitivity of stomatal conductance to VPD and soil water potential was unchanged. Other literature studies are generally in agreement with these observations, except for those presented by Heath & Kerstiens (1997) and Heath (1998), in which stomatal conductance was found to be less sensitive to VPD and soil water content when grown in elevated [CO2]. We do not currently have a framework that would allow us to interpret these results. Optimality arguments, for example, would suggest that stomata should be more sensitive to soil water content at elevated [CO2], since under elevated [CO2] water availability is relatively more limiting to growth. The behaviour observed by Heath and Kerstiens (1997) would, as they note, lead to increased risk of drought damage.

Acclimation of stomatal conductance and relationship with assimilation

Although the acclimation of photosynthesis to elevated [CO2] has been much studied (Gunderson & Wullschleger, 1994, Sage, 1994, Besford et al., 1998, Medlyn et al., 1999), less attention has been paid to the acclimation of stomatal conductance. A particularly important question, highlighted by Morison (1998), is whether stomata acclimate in parallel to photosynthesis, maintaining the tight linkage between the two processes observed at ambient [CO2] (Wong et al., 1978), or whether they can acclimate independently.

We examined whether stomatal conductance acclimated to growth in elevated [CO2] by performing a meta-analysis of gs data measured at a constant [CO2] (700 µmol mol−1) (Table 5). This analysis indicated that, overall, there was no acclimation of gs to elevated [CO2]. Pursuing this further, we also examined the sensitivity of stomata to [CO2] under ambient and elevated [CO2] growth conditions (Table 8). In ambient conditions, stomatal sensitivity to [CO2] differed greatly between species, with responses ranging from zero to a 40% decrease in stomatal conductance in response to a doubling of [CO2] from 350 to 700 µmol mol−1. Growth in elevated [CO2] appeared to slightly attenuate [CO2] sensitivity in those species that were [CO2] sensitive, but not to affect the species that were not. Other studies generally show no change in [CO2] sensitivity of gs (Radoglou et al., 1992, Johnsen, 1993, Berryman et al., 1994, Tuba et al., 1994), although one study reports a greatly reduced sensitivity to [CO2] (Santrucek & Sage, 1996).

While this analysis indicates little or no acclimation of stomatal conductance to elevated [CO2], a similar meta-analysis of photosynthesis data from the same set of experiments suggested that photosynthesis did acclimate (Medlyn et al., 1999). Hence, we examined whether the relationship between stomatal conductance and photosynthesis was changed under elevated [CO2]. First, we compared the effect of elevated [CO2] on stomatal conductance with the effect on photosynthesis (Fig. 3) and found a close coupling between the two processes, suggesting that they do acclimate in parallel. Taking this further, we applied a model of stomatal conductance that is based on the relationship with assimilation (Ball et al., 1987) to eight separate datasets. We found that the model parameters did not change after growth in elevated [CO2], except under conditions of water stress (Table 9).

Other studies using the Ball et al. (1987) model have generally also found no change in model parameters between ambient and elevated [CO2] treatments (Kellomäki & Wang, 1997, Strassemeyer & Forstreuter, 1997; Liozon et al., 2000). Other authors have examined the linkage between assimilation and stomatal conductance by examining the ratio of intercellular to atmospheric [CO2] (Ci : Ca ratio) and have generally observed no effect of elevated [CO2] on this ratio (Sage, 1994, Drake et al., 1997). The exceptions noted by Sage (1994) were under conditions of water stress. Hence, we conclude that the relationship between assimilation and stomatal conductance is generally unchanged by growth under elevated [CO2], but may change under conditions of water stress.

This conclusion appears difficult to reconcile with the observation that stomatal conductance does not acclimate to elevated [CO2], while photosynthesis does. One problem is that stomata respond much more slowly to changes in environmental conditions (scale of hours) than does photosynthesis (scale of minutes). Although we attempted to exclude data where stomata would not have had time to respond fully to imposed measurement conditions, it is possible that stomata had not reached equilibrium conditions in some of the measurements, which would affect the observed relationship between gs and assimilation. However, the more likely reason for the apparent contradiction is that significantly fewer datasets were available to assess the acclimation of stomatal conductance (9, Table 5) than acclimation of photosynthesis (17, Medlyn et al., 1999). This limited number of data sets may not have been sufficient to detect a small acclimation in stomatal conductance.

Implications for modelling

To assess the implications of changes in stomatal conductance in elevated [CO2] on future forest stand growth and water use, it is important to be able to predict stomatal conductance (Morison, 1998). Hence, in this paper, we have focused, not merely on the absolute size of the response of gs to [CO2], but also on how to model gs under elevated [CO2].

There are drawbacks to the way that the models were fitted. The meta-analysis was performed on mid-season values, omitting values from early and late-season, which could cause problems when scaling up to a whole year. However, there does not appear to be a strong seasonality in the response of gs to elevated [CO2] (Table 3), so this omission may not be grave. The parameterisation of the model of Jarvis (1976) requires an extensive dataset including measurements of gs under varying conditions of all variables, and the variables should not be correlated. In the absence of such comprehensive data sets, we could only fit individual response curves (equations 3–5). Furthermore, we chose to use simple linear response curves, instead of the nonlinear functions commonly used (Jarvis, 1976). This choice was made to minimise the number of parameters fitted and enhance comparability of parameters between datasets. For the second model, we chose to use the form presented by Ball et al. (1987) rather than the alternative formulation suggested by Leuning (1995) that is currently gaining ground amongst modellers (Van Wijk et al., 2000). The Ball et al. (1987) form is easier to fit and more readily compared across experiments because it has fewer parameters and is linear.

Despite these drawbacks to the way the models were fitted, this study has enabled some general conclusions about modelling of stomatal conductance in elevated [CO2] conditions – and highlighted several areas in which more data are required before we can have confidence in modelling.

To reflect the reduction in gs indicated by the meta-analysis (Table 4), the maximum stomatal conductance (gsmax) in the Jarvis (1976) model (eqn 1) could be reduced by 21%. However, the meta-analysis indicated that either different functional groups, or different ages of trees, respond differently to elevated [CO2]. This issue must be resolved before we can confidently model the response of gsmax to elevated [CO2]. Also in the Jarvis (1976) model, our review has shown that the functions relating stomatal conductance to VPD (f(D0)), soil water potential (f0)) and atmospheric [CO2] (f(Ca)) were generally unchanged in elevated [CO2] and hence do not need to be modified. However, these functions have been shown to be altered in some studies: in particular, Heath & Kerstiens (1997) and Heath (1998) found reduced sensitivity to VPD and soil water potential in young deciduous trees. More careful, quantitative studies of the interactive effects of VPD, water stress and elevated [CO2] on stomatal conductance in freely rooted plants are required to clarify whether, and how, the functions f(D0) and f0) are altered by growth in elevated [CO2].

For the Ball et al. (1987) model it appears that parameters are unchanged under elevated [CO2] and hence the model may be applied unmodified in most circumstances. However, the model may need to be modified for plants growing in water-limited environments, as suggested by the strongly significant shift in the relationship observed for the macchia shrub species Phillyrea angustifolia. Further work needs to be undertaken to investigate how this relationship is be affected by water stress and its interaction with [CO2].

After many years of research, we thus now have a consistent body of data on which to base models of stomatal conductance under elevated [CO2]. We note in conclusion, however, that the models of stomatal conductance used in this paper are entirely empirical, and our description of stomatal responses to elevated [CO2] is essentially phenomenological. A major challenge that remains is to develop mechanistic models of stomatal conductance that will allow us to explain, rather than to merely describe, the response of stomatal conductance to elevated [CO2] (e.g. Assmann, 1999).


  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. The Jarvis (1976) model: Environmental effects on stomatal conductance
  7. The model: relationship between stomatal conductance and assimilation
  8. Discussion
  9. Acknowledgements
  10. References

This work was supported by the EC Environment and Climate Research Programme, Climate and Natural Hazards subprogramme (contract ENV4-CT95-0077). This work contributes to the Global Change and Terrestrial Ecosystems (GCTE) core project of the International Geosphere-Biosphere Programme (IGBP).


  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. The Jarvis (1976) model: Environmental effects on stomatal conductance
  7. The model: relationship between stomatal conductance and assimilation
  8. Discussion
  9. Acknowledgements
  10. References
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  • Ball JT, Woodrow IE & Berry JA. 1987. A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions. In: BigginsJ, ed. Progress in photosynthesis research. Dordrecht, The Netherlands: Martinus-Nijhoff Publishers, 221224.
  • Barton CVM & Jarvis PG. 1999. Growth response of branches of Picea sitchensis to four years exposure to elevated atmospheric carbon dioxide concentration. New Phytologist 144: 233243.
  • Berryman CA, Eamus D & Duff GA. 1994. Stomatal responses to a range of variables in two tropical tree species grown with CO2 enrichment. Journal of Experimental Botany 45: 539546.
  • Besford R, Mousseau M & Matteucci G. 1998. Biochemistry, physiology and biophysics of photosynthesis. In: JarvisPG, ed. European forests and global change: the likely impacts of rising CO2 and temperature. Cambridge, UK: Cambridge University Press, 2978.
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  • Centritto M, Magnani F, Lee HSJ & Jarvis PG. 1999. Interactive effects of elevated [CO2] and drought on cherry (Prunus avium) seedlings. II. Photosynthetic capacity and water relations. New Phytologist 141: 141153.
  • Curtis PS. 1996. A meta-analysis of leaf gas exchange and nitrogen in trees grown under elevated carbon dioxide. Plant, Cell & Environment 19: 127137.
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