Desert dogma revisited: coupling of stomatal conductance and photosynthesis in the desert shrub, Larrea tridentata


Kiona Ogle. E-mail:


The success of the desert shrub Larrea tridentata (creosotebush) has been largely attributed to temperature acclimation and stomatal control of photosynthesis (A) under drought stress. However, there is a paucity of field data on these relationships. To address this void, we conducted a joint field and modelling study that encompassed a diverse set of environmental conditions. At a Larrea-dominated site in southern New Mexico we manipulated soil moisture during the growing season over a 2-year period and measured plant pre-dawn water potential (Ψpd), stomatal conductance (g) and A of individual shrubs. We used these data to develop a semi-mechanistic photosynthesis model (A–Season) that explicitly couples internal CO2 (Ci) and g. Vapour pressure deficit (VPD) and Ψpd affect instantaneous g in a manner that is consistent with a biophysical model of stomatal regulation of leaf water potential. Ci is modelled as a function of g, derived from a simplification of a typical ACi curve. After incorporating the effects of growing temperature on stomatal behaviour, the model was able to capture the large diurnal fluctuations in A, g and Ci and the observed hysteresis in g versus Ci dynamics. Our field data and application of the A–Season model suggest that dogma attributed to Larrea's success is supported with regard to stomatal responses to VPD and Ψpd, but not for mechanisms of temperature acclimation and CO2 demand.


The evergreen shrub, Larrea tridentata (creosotebush), is a major dominant in the warm deserts of North America (Barbour et al. 1977; Solbrig 1977). Larrea's success has been largely attributed to its ability to remain metabolically active year-round (Oechel, Strain & Odening 1972; Reynolds 1986), with a unique capacity to tolerate large fluctuations in temperature (T), vapour pressure deficit (VPD) and soil moisture. For example, Larrea is able to adjust its photosynthetic machinery in response to prevailing growth temperature (Strain & Chase 1966), where growth at low temperatures results in increased capacity to fix CO2 during cool periods and growth at high temperatures results in heightened stability of photosynthesis during heat stress (e.g. T > 45 °C) (Mooney, Björkman & Collatz 1978). Larrea can also endure extreme atmospheric and soil water deficits (Oechel et al. 1972; Odening, Strain & Oechel 1974; Reynolds et al. 1999; Hamerlynck, McAuliffe & Smith 2000b). In the Chihuahuan Desert, Cunningham & Burk (1973) reported pre-dawn water potentials (Ψpd) surpassing −10 MPa. Under these conditions, most plants show signs of desiccation, but Larrea can sustain positive, albeit low, net photosynthesis (A) (Odening et al. 1974).

In contrast, little is known about Larrea and other desert plants regarding seasonal and diurnal fluctuations in demand for CO2, as indicated by internal CO2 (Ci). Wong, Cowan & Farquhar (1979) suggest that plants generally maintain Ci roughly constant for fixed VPD, atmospheric CO2 (Ca) and near-optimal T (see also Yoshie 1986). However, Mielke et al. (2000) found that mean daily Ci/Ca in a semi-arid Eucalyptus spp. varied by a factor of two during a year. In situ studies on diurnal variability of Ci of desert plants are infrequent and it is likely that instantaneous Ci exhibits even greater variability, especially in desert species where A is often constrained by CO2 supply (Dunn 1975).

Surprisingly, there is a paucity of field data for evaluating the dogma attributed to Larrea's ecological success with regard to stomatal control of photosynthesis under variable T, VPD and soil water. To address this void, we conducted a joint field and modelling study designed to encompass a diverse set of environmental conditions. At a Larrea-dominated site in southern New Mexico, we manipulated soil moisture during the growing season over a 2 year period and measured Ψpd and diurnal A, g and Ci of individual shrubs. We used these data to develop A–Season, a semi-mechanistic photosynthesis model that explicitly couples Ci and g. We employ the Hybrid model (Katul, Ellsworth & Lai 2000) to describe Ci as a function of g and model g as a function of VPD, Ψpd and average growing temperature. The g-submodel is consistent with a hydraulic model describing stomatal regulation of leaf water potential and the growing temperature function enables us to capture seasonality in stomatal behaviour and carbon gain. We parameterized A–Season with data collected in 1998 and to independently evaluate its robustness, we tested it with data collected in 1999.

Application of the A–Season model is crucial to our study as it enables us to tease-apart complicated plant–environment interactions. We apply our field data and the A–Season model to explore Larrea's photosynthetic behaviour over a broad set of abiotic conditions to re-evaluate three main tenets regarding this species success in arid systems: (1) photosynthetic temperature acclimation and the role of biochemistry versus stomatal behaviour; (2) stomatal control of photosynthesis under atmospheric and soil water stress; and (3) diurnal and seasonal dynamics of internal CO2.

A–season model description

A–Season is a semi-mechanistic model of photosynthesis that explicitly couples CO2 assimilation, stomatal conductance and leaf internal CO2. A list of its variables and parameters is provided in Table 1. Net photosynthesis (A, µmol CO2 m−2 s−1) is described as:

Table 1.  Description of model dependent, auxiliary and driving variables and parameters
Dependent variables
ANet photosynthesisµmol m–2 s−1
CiLeaf internal CO2p.p.m.
gStomatal conductance to H2O vapourmol m–2 s−1
Auxiliary variables
ΓCO2 compensation pointp.p.m.
Γ*CO2 compensation point in the absence of Rdp.p.m.
aCarboxylation efficiencyµmol m−2 s−1 p.p.m.−1
bValue of A when Ci = 0, from ACi curveµmol m−2 s−1
gmaxMaximum conductance to H2O vapourmol m−2 s−1
R25Value of Rd at 25 °Cµmol m−2 s−1
RdDay respirationµmol m−2 s−1
Driving variables
ΨpdPre-dawn plant water potentialMPa
CaAtmospheric CO2p.p.m.
PFDPhoton flux densityµmol m−2 s−1
TgroMean 24 h, 7 d temperature°C
VPDVapour pressure deficitkPa
Γ25Value of Γ* at 25 °Cp.p.m.
ρRelated to the sensitivity of gmax to Ψpd/Tgro°C MPa−1
τMaximum value of gmaxmol m−2 s−1
a1Related to the dependence of a on PFDp.p.m.−1
b0Related to the dependence of g on VPDmol m−2 s−1
gcritValue of g where Ci in constant for larger gmol m−2 s−1
mRelated to the sensitivity of g versus loge(VPD)mol m−2 s−1(loge(kPa))−1
r1Related to the dependence of R25 on Ψpdµmol m−2 s−1
r2Related to the dependence of R25 on Ψpdµmol m−2 s−1 MPa−1
TmaxMaximum value of Tgro that stomata operate°C
TminMinimum value of Tgro that stomata operate°C

where g is stomatal conductance to water vapour (mol H2O m−2 s−1), Ca is ambient CO2 (p.p.m), Ci is leaf internal CO2 (p.p.m) and 0·625 is the ratio of the diffusivity of H2O vapour to CO2 in air. A–Season is composed of submodels for Ci and g.

Ci submodel

We employ the basic structure of the Hybrid model proposed by Katul et al. (2000) to model Ci as a function of g. This model is based on a linearization of the ACi curve and assumes that field plants typically operate in the CO2-limited (or RuBP-saturated) part of the curve where A @ a · Ci − b; a is carboxylation efficiency and b=, where Γ is the CO2 compensation point (Farquhar & Sharkey 1982; Lambers, Chapin & Pons 1998; Katul et al. 2000). Setting A = 0·625 · g · (Ca − Ci) @ a · Ci − b, simple algebraic manipulation results in a solution for Ci. The Hybrid model also assumes that for large values of g (g ≥ gcrit), Ci is nearly constant; Ci is given by:


To fully describe Ci, we need expressions for Γ, b, a, Rd and Γ*; Rd is day respiration (CO2 evolution in the light independent of photorespiration) and Γ* is the value of Ci when carboxylation and photorespiration balance each other (Brooks & Farquhar 1985). Because A versus Ci is approximately linear for Ci between Γ* and Γ, Γ = Γ* + Rd/a and b = a · Γ* + Rd. We use the temperature response functions of Bernacchi et al. (2001) for Rd and Γ*:


where T is (leaf) temperature (°C). Experimental evidence suggests that leaf-level respiration varies with leaf water potential (e.g. Kellomäki & Wang 1996; Haupt-Herting, Klug & Fock 2001); in an exploratory analysis where we looked for a linear effect of pre-dawn plant water potential (Ψpd, MPa) on the ‘biochemical’ parameters, we found that R25 (the value of Rd at 25 °C) was the only one that varied significantly with Ψpd such that:


Similarly, Γ25 is the value of Γ* at 25 °C (e.g. Bernacchi et al. (2001) found that R25 varied between plants and that Γ25 was approximately constant at 42·75 p.p.m). Additionally, we assume that carboxylation efficiency (a) varies with photon flux density (PFD, µmol m−2 s−1) (e.g. see Brooks & Farquhar 1985), such that:


where a1 is a fitted parameter.

g submodel

Yan et al. (2000) reported that mid-morning g in Larrea growing in Texas decreased with increasing water stress. Hence, we assume that there is a maximum g (gmax, mol H2O m−2 s−1) that stomata can potentially achieve and that if Ψpd is low, reflecting high water stress, then gmax is reduced; conversely, if Ψpd is high, reflecting low water stress, then gmax should be relatively high. However, Meinzer et al. (1988) suggest that Ψpd cannot solely explain seasonal variation in gmax of Larrea. Thus, we assume that the prevailing growth temperature alters the response of gmax to Ψpd, i.e.


where Tgro is a running 7 d mean 24 h temperature and Tmax and Tmin are parameters that describe the maximum and minimum Tgro at which stomata operate (i.e. gmax = 0 if Tgro > Tmax or Tgro < Tmin). Additionally, gmax is highest (i.e. gmaxτ) when Tgro = (Tmax + Tmin)/2 and Ψpd@ 0. Parameter ρ is related to the sensitivity of gmax to changes in Ψpd/Tgro (i.e. temperature-corrected Ψpd).

Following de Soyza et al. (1996), Prior, Eamus & Duff (1997) and Bond & Kavanagh (1999), we assume that instantaneous g cannot exceed gmax and that diurnal fluctuations in g are stimulated by interactive effects of vapour pressure deficit (VPD, kPa) and Ψpd. We formulate this using a multiplicative constraint model (Jarvis 1976):


This threshold function (e.g. see Fig. 4) is consistent with a biophysical model that assumes stomata regulate evaporation rate to maintain constant leaf water potential (Oren et al. 1999). The parameters b0, m and τ determine the value of VPD at which this threshold occurs. Similar to Oren et al. (1999), the m parameter is related to the sensitivity of g to changes in loge(VPD) in the region where g varies with VPD (i.e. ∂g/∂loge(VPD) = gmax · m/τ).

Figure 4.

Plots of observed versus predicted photosynthesis (A) for different assumptions regarding the effect of Tgro. (a) A, g and Ci are independent of Tgro, modified Eqn 7: gmax = τ · eρΨpd; (b) Ci depends on Tgro and gmax is independent of Tgro, modified Eqn 7: gmax = τ · eρΨpd and Eqn 6: a = a2 · Tgro · PFD; (c) gmax depends on Tgro and Ci is independent of Tgro, kept original Eqns 6 and 7; and (d) gmax and Ci depend on Tgro, kept original Eqn 7 and modified Eqn 6: a = a2 · Tgro · PFD. Spring 1999 data are shown by ▵ and summer 1999 data are d. The thick diagonal line is the 1 : 1 line.

Alternative g models

Because of the crucial nature of stomatal response, we replaced the g module in A–Season, while retaining the same Ci module, with several commonly employed models that represent a range of hypothesized stomata–environment interactions: Ball, Woodrow & Berry (1987), Leuning (1990, 1995) and Pitman (1996). Whereas each of these g modules, including the one in A–Season, assume a feedback effect of g on Ci (via Eqn 2), the Ball and Leuning models are the only ones with a feedback of photosynthetic rate (and thus Ci) on g (e.g. see Wong et al. 1979). The Pitman model (see Eqns 1–5 in Pitman 1996) follows the approach of Jarvis (1976), where Ψpd, T, PFD and VPD interact in a multiplicative fashion to affect g. When the A–Season model is modified by incorporating the alternative g formulations, the resultant photosynthesis models are termed A–Ball, A–Leuning and A–Pitman.

Model parameterization and validation

Field experiments

During June 1998 to June 1999 we performed an irrigation experiment with Larrea shrubs at the Jornada LTER (Long-Term Ecological Research) site in southern New Mexico, USA. Complete details of the general study site (located in Pasture no. 6), including soils and vegetation, are given in Reynolds et al. (1999). Climate summaries for the Jornada Basin are provided in Conley, Conley & Karl (1992), who characterize the semi-arid climate of the Jornada as having three distinct seasons: hot, dry springs (April–June); hot, moist summers (July–October); and cold, moderately dry winters (November–March). Total annual precipitation is about 230 mm, of which approximately 65% falls in the summer as localized showers associated with thunderstorms; approximately 25% falls in the winter as rain and snow associated with frontal storms; and approximately 10% occurs in the spring. The mean monthly maximum temperature is highest in June (36 °C) and lowest in January (13 °C). Night-time freezing temperatures occur frequently from late October to early April.

We selected 16 shrubs for study. Eight ‘watered’ shrubs were irrigated twice in summer 1998 and once in early spring 1999; eight ‘control’ shrubs received only ambient rainfall. During summer 1999 no shrubs were irrigated. During this period, we made diurnal measurements of gas exchange with an open-system infrared gas exchange analyser (LI-6400; Li-Cor, Lincoln, NE, USA) on four ‘target’ watered and four ‘target’ control shrubs for 11 d in 1998 and 5 d in 1999. Each day consisted of 8–11 gas exchange measurements on a cluster of 10–20 leaves per shrub. The same four watered and four control shrubs were used for all diurnal measurements throughout the study. On these same days, we recorded Ψpd of excised stems with a Scholander-type pressure bomb (Soil Moisture Equipment Corp., Santa Barbara, CA, USA) on the remaining four ‘alternate’ watered and four ‘alternate’ control shrubs to avoid excessive defoliation of the shrubs used for the diurnal measurements.

The use of the alternate shrubs is justified by Ψpd measurements made for all 16 shrubs on three different days at the end of the 1999 study period (i.e. 15, 22, 25 June). After accounting for treatment (watered versus control), alternate and target shrubs did not differ in their mean Ψpd values (P = 0·19, n = 48). Furthermore, there was no significant difference in mean canopy volume of alternative and target shrubs (P = 0·25, n = 16) and any two shrubs were within 60 m proximity.

Model fitting with summer 1998 data

We parameterized A–Season with data collected during summer 1998. Means of Ψpd and maximum observed g were calculated for each of the 11 measurement days by treatment group (watered versus control). We calculated Tgro, a running average of 24 h 30 min temperature records for 7 d prior to each measurement date. Non-linear regressions were conducted to fit the gmax model (Eqn 7) to obtain estimates for τ, ρ, Tmax and Tmin (PROC NLIN, SAS non-linear procedure; SAS Institute, Cary, NC, USA).

For each of the 8–11 measurement intervals during each diurnal period, instantaneous means were determined by treatment group for g, A, Ci, VPD, RH, T and PFD (n = 92 means per group per variable). We programmed Eqns 7 and 8 into the SAS NLINMIX macro (NonLINear MIXed model; created for SAS/STAT Version 8) to estimate the instantaneous g parameters (i.e. m and b0 in Eqn 8); the gmax parameters were fixed according to the gmax non-linear regression results. Finally, we estimated the remaining parameters needed to fully describe A (i.e. gcrit, Γ25, r1, r2 and a1) by programming Eqns 1–8 into the SAS NLINMIX macro; the gmax and g parameters were fixed according their respective non-linear fitting results. We employed the NLINMIX macro because it allowed us to account for correlated errors, which was important as the exponential covariance parameter was significant for both the g and A regressions (P < < 0·01). Specifically, the correlation structure was modelled with an exponential spatial covariance model (i.e. SP{pow}{time}), where it is assumed that correlation between errors decreases exponentially as time between measurements increases.

Model assessment with spring–summer 1999 data

To assess how well the A-Season model is able to predict future behaviour, we compared observed and predicted values of instantaneous A, g and Ci for the 1999 sampling period. These 1999 data represent a different set of conditions as compared to summer 1998. For example, spring 1999 data were collected during a cold period immediately following both natural rainfall and irrigation that ended a long dry spell; the summer 1999 data were collected during and after a series of record precipitation. This diversity of weather is reflected in the Ψpd and Tgro data: the values of Ψpd were lower in 1998 (range = −6·5 to −1·8 MPa) than in 1999 (−5·2 to −1·2 MPa) and 1998 was generally hotter (Tgro = 24–34 °C) than 1999 (Tgro = 10 °C (spring) to 26 °C (summer)).

We calculated a series of statistics to assess the performance of the A-Season model (e.g. Mayer & Butler 1993; Power 1993). These included: (1) a regression of observations versus model predictions and t-tests to determine if the slope (β0) differed from unity and the intercept (β1) differed from zero; (2) R2, the proportion of variation in observations explained by this fitted regression line; (3) mean error (ME), mean difference between observations and predictions; (4) mean absolute error (MAE), mean of the absolute values of the differences between observations and predictions; (5) mean absolute percentage error (MAPE), 100% × MAE divided by the mean of the observations; and (6) variance ratio (VR), the ratio of the observation variance to the prediction variance.


Alternative g models

The A–Season, A–Ball, A–Leuning and A–Pitman models all fit the 1998 photosynthesis (A) data equally well, observed versus predicted R2s ranging from 0·78 (A–Ball) to 0·80 (A–Pitman). However, A–Season and A–Pitman fit the 1998 conductance (g) data much better than the A–Ball and A–Leuning models (R2s = 0·63 and 0·67 versus 0·15 and 0·31, respectively). Overall, the predictive power of the A-Season model for A and g was far superior to the other three models, especially during the cool spring period in 1999 (Fig. 1). For this reason, we present results only for the A-Season model.

Figure 1.

Plots and R2 values for observed versus predicted photosynthesis (A) and stomatal conductance (g) for summer (d) and spring (▵) in 1999. Points are treatment (watered, control) means for each measurement period per day. Observed versus predicted g are shown for the: (a) A–Ball; (b) A–Leuning; (c) A–Pitman; and (d) A–Season models. Observed versus predicted A are shown for the: (e) A–Ball; (f) A–Leuning; (g) A–Pitman; and (h) A–Season models.

Summer 1998

Fits of the A-Season model to the 1998 A, g and Ci data are shown in Fig. 2a, c & e, respectively. The parameter values and goodness-of-fit statistics are given in Table 2. The R2 values for observed versus predicted A (R2 = 0·79; Fig. 2b) and g (R2 = 0·71; Fig. 2d) are relatively high. These predictions are unbiased, i.e. the regression intercepts (β0) and slopes (β1) do not differ from zero or unity, respectively (Table 2), which is expected because the parameter estimates were obtained by fitting the model to the 1998 A and g data. The association for Ci is weaker (R2 = 0·63; Fig. 2f), which is also expected because Ci data were not used in the fitting procedures. These predictions of Ci are biased (see β0 and β1 in Table 2) and A–Season tends to over-estimate Ci when Ci is low (Fig. 2e & f). Additionally, the VR values show that the A-Season model can adequately capture variations in observed A and g (i.e. VR values close to 1; Table 2), but tends to underestimate variation in Ci (i.e. VR @ 2, indicating that observations are two-times more variable than predictions).

Figure 2.

Plots of observed versus predicted photosynthesis (A), conductance (g) and internal CO2 (Ci) for 1998. Diurnal trends in observed (s) and predicted values (thick solid line) for: (a) A; (c) g; and (e) Ci. Plots of observed versus predicted for: (b) A; (d) g; and (f) Ci. For plots (a), (c) and (e), points are means for the control group (for clarity, the ‘watered’ group is not shown, but the results are similar); for plots (b), (d) and (f), means for the control and watered groups are shown.

Table 2.  Parameter estimates and goodness-of-fit statistics obtained from fitting A–Season to 1998 data
ParameterParameter estimates
EstimateaCV (%)b,c
Γ2579·962 7·03
r 5·96941·10
τ 0·18321·69
a1 3·81 × 10−5 9·56
b0 0·219 5·26
gcrit 0·14n/a
m−0·0837 9·33
r1 3·22914·95
r2 0·53323·32
Tmax36·999 4·98
Tmin 5·0n/a
StatisticdGoodness-of-fit statistics for each dependent variable
Internal CO2
  • a Units given in Table 1.

  • b

    CV, coefficient of variation = 100% 

  • ×

    SE/?estimate?; SE is the (asymptotic) standard error.

  • c NLIN and NLMIX would not converge if gcrit and Tmin were allowed to vary. Thus, several values were tried and the values given above resulted in the best fit. Because gcrit and Tmin were fixed in the fitting routines, they do not have SE and CV values.

  • d A regression of observations versus predictions was conducted (n = 184 treatment means); regression intercepts (β0) significantly different from zero and slopes (β1) significantly different from unity (i.e. P < 0·05) are indicated by *. R2, coefficient of determination; ME, mean error (same units as dependent variable); MAE, mean absolute error (same units as dependent variable); MAPE, mean absolute percentage error (%); VR, ratio of the observation variance to the prediction variance (unitless).

β0 0·087−85·073* 0·0014
β1 0·970 1·179* 0·981
R2 0·786 0·706 0·629
ME−0·044 35·666−6·22 × 10−4
MAE 0·638 44·630 0·012
MAPE29·00 18·5529·97
VR 1·198 1·968 1·529

Spring–summer 1999

Based on the 1998 parameterization, the A-Season model successfully captures Larrea's photosynthetic and stomatal behaviour during the spring and summer of 1999 (see Fig. 3a, c & e). Plots of observed versus predicted A for 1999 show that the predictions fall along the 1 : 1 line (R2 = 0·42; Fig. 3b). Although β1 differs from unity and β0 differs from zero, suggesting a bias in predicted A, this bias is trivial (see Fig. 3a & b). The A–Season model captures 1999 g dynamics (R2 = 0·69; Fig. 3d), with no statistically significant bias (Table 3). However, Fig. 3c shows that the model consistently over-estimates g on 6/15/99 and 6/25/99. Likewise, observed versus predicted Ci fall near the 1 : 1 line (R2 = 0·53; Fig. 3f), but a significant bias was found (β1 < 1; Table 3) and A–Season also tended to over-estimate Ci on these same days (Fig. 3e).

Figure 3.

Plots of observed versus predicted A, g and Ci for 1999. See Fig. 2 legend for explanation of plots, symbols, axes, etc.

Table 3.  Validation statistics for predicted A, g and Ci based on 1999 data
StatisticaValidation statistics for each dependent variable
Photosynthesis (A)Internal CO2
  1. a See Table 2 and text for description of statistics (n = 74 treatment means).

β0 0·447*−7·820−0·003
β1 0·804* 0·764* 0·871
R2 0·742 0·532 0·691
ME 0·01562·54−7·17 × 10−3
MAE 0·65069·90 0·011
VR 0·871 1·097 1·098

The VR statistics for A, g and Ci (Table 3) are close to one, suggesting that the A–Season model captures the range of variation in observations. The model is able to reproduce these seasonal dynamics because of the inclusion of a growing temperature (Tgro) effect on gmax (Eqn 7). Without this temperature effect, A–Season over-estimates A during the cool spring period of 1999 (Fig. 4a versus c). However, it is possible that these seasonal dynamics are also driven by changes in biochemistry. Given the present formulation of A–Season, the only biochemistry parameter that varies with Tgro is a1 (related to the dependence of carboxylation efficiency on PFD). When we allow a1 to vary with Tgro (and gmax independent of Tgro) predictions of A during 1999 improve relative to the model without a Tgro effect (Fig. 4a versus b). The inclusion of a Tgro effect on both gmax and a1 only slightly improves the agreement between observed and predicted A relative to the model with Tgro only affecting gmax (Fig. 4d versus c). Describing gmax as a function of Tgro appears essential, as not only does it improve simulated A, but it also dramatically improves predicted g (Fig. 5a versus b). Without this formulation, g is over-estimated during 1999, especially during the cool spring period.

Figure 5.

Plots of observed versus predicted conductance (g) for different assumptions regarding the effect of Tgro. (a) g is independent of Tgro, modified Eqn 7: gmax = τ · eρ·Ψpd; and (b) g depends on Tgro, kept original Eqn 7. Note that assumptions about the effect of Tgro on Ci do not alter predicted g. Spring 1999 data are shown by ▵ and summer 1999 data are d. The thick diagonal line is the 1 : 1 line.


Desert dogma revisited

We use the A–Season model to extrapolate the behaviour of Larrea A, g and Ci across a variety of environmental conditions. We couple these predictions with the field data to re-evaluate important dogma attributed to Larrea's success, including: temperature acclimation, stomatal control of photosynthesis under water stress and internal CO2 dynamics.

Temperature acclimation

It has been suggested that Larrea's ability to remain metabolically active year-round is partly due to photosynthetic temperature acclimation (e.g. Strain & Chase 1966; Strain 1969; Lange et al. 1974; Mooney et al. 1978; Downton, Berry & Seemann 1984). Furthermore, Mooney et al. (1978) and Lange et al. (1974) suggest that acclimation in Larrea is primarily a result of altered photosynthetic capacity and not stomatal activity. Here, our field and modelling results suggest significant seasonal differences in stomatal behaviour. That is, if we assume that Tgro alters the stomatal response (i.e. gmax, as in Eqn 7), then we are able to capture the seasonal dynamics in A and g (e.g. Figs 4c & 5b). We also modified A–Season to see if changes in biochemistry could account for the seasonal differences in A and g. In this scenario, we assumed that gmax was independent of Tgro and that the a1 parameter varied with Tgro. This modification improved predicted A, relative to the null model without any Tgro effect (Fig. 4a versus 3b). However, acclimation of the biochemistry parameter alone did not improve predicted g (Fig. 5a). These results suggest that seasonal changes in stomatal behaviour may have a more profound effect on net carbon gain in Larrea than previously recognized.

Maximum stomatal conductance

The idea that stomata may acclimate to the prevailing growth temperature is not unique to Larrea. This has been reported in various studies with herbaceous plants (Lösch 1977; Ivory & Whiteman 1978; Nobel 1980; Reddy, Reddy & Hodges 1998; Correia et al. 1999). Similar to our Tgro function in Eqn 7, Nobel (1980) and Reddy et al. (1998) noted a parabolic-like response of gmax to growing temperature, such that low and high growing temperatures effectively reduce gmax.

In Larrea we find that acclimation of gmax to growth temperature affects the relationship between gmax and Ψpd. Although numerous studies show that gmax is correlated with soil and/or plant water status, for both non-arid plants (e.g. Küppers, Küppers & Schulze 1988; Reich & Hinckley 1989; Fordyce, Duff & Eamus 1997; Myers et al. 1997) and semi-arid and arid species (largely Eucalyptus spp., e.g. van den Driessche, Connor & Tunstall 1971; Pereira, Tenhunen & Lange 1987; Tenhunen et al. 1994; Valladares & Pearcy 1997; Tezara et al. 1998; Thomas & Eamus 1999; Mielke et al. 2000; White, Turner & Galbraith 2000), Meinzer et al. (1988) reported large seasonal variation in gmax in Larrea in California that could not be explained by Ψpd. They suggest that the best predictor is an index of soil/plant hydraulic resistance. However, near our study site in New Mexico, Fanco et al. (1994) found that during the summer, gmax in Larrea is related to Ψpd. Although we found that gmax and Ψpd are correlated within a season, Ψpd alone cannot account for the large seasonal variation in gmax– this behaviour is sufficiently explained by adding a Tgro effect (e.g. see Eqn 7), which greatly improves diurnal simulations of instantaneous g (Fig. 5a versus b).

The lack of a Ψpd effect in the study by Meinzer et al. (1988) and the relatively high uncertainty associated with the Ψpd effect in this study (see CV for the ρ parameter, Table 2) could be due to pre-dawn disequilibrium. For example, gmax could be more strongly coupled to soil water than plant water potential (e.g. Gollan, Passioura & Munns 1986) and it is possible that Ψpd did not equilibrate with soil water potential and thus is not a good index of soil water status (Donovan et al. 1999). Regardless, our field and modelling results clearly demonstrate seasonal changes in stomatal behaviour. Thus, to develop a better mechanistic understanding of the seasonality of gmax (and thus A, g and Ci), it will be necessary to tease apart the effects of stomatal temperature acclimation, hydraulic resistance (Meinzer et al. 1988), pre-dawn disequilibrium (Donovan et al. 1999) and leaf age (e.g. Field 1987; Lajtha & Whitford 1989).

Instantaneous responses to atmospheric and soil water stress

It is well established that atmospheric and soil water status affect stomatal behaviour (e.g. Hall, Schulze & Lange 1976; Turner, Schulze & Gollan 1984, 1985; Schulze et al. 1987; Aphalo & Jarvis 1991; Turner 1991) and that there are strong interactions (e.g. Schulze & Küppers 1979; Schulze et al. 1987). In a study of several tropical tree species, Meinzer et al. (1993) demonstrated that if g is corrected for the ratio of leaf area to sapwood area, then a single non-linear function could be generalized. Thomas & Eamus (1999) and Franco et al. (1994) report a linear response of g to VPD in Eucalyptus tetrodonta and Larrea, respectively. However, this linearity may have resulted from the small VPD range examined (i.e. VPD changed by ≤ 2·5 kPa). In contrast, we measured and modelled g over values of VPD ranging from approximately 1·0–10·5 kPa and Larrea exhibits typical non-linear behaviour such that g decreases approximately exponentially with increasing VPD (Fig. 6).

Figure 6.

A–Season model predictions of conductance (g) as a function of VPD, based on fitting the g submodel (Eqns 7 & 8) to 1998 data. As indicated by the Ψpd isoclines, the model predicts that stomatal sensitivity to VPD decreases with increasing water stress (i.e. more negative Ψpd). Stomata are operating at their maximum for VPD < 1·54 kPa.

In Larrea, the response of instantaneous g to variations in VPD depends on Ψpd via its effect on gmax. In woody desert plants, the sensitivity of stomata to changes in VPD depends on plant and soil water status (Schulze et al. 1972; Schulze et al. 1975; Franco et al. 1994; de Soyza et al. 1996; Prior et al. 1997; Thomas & Eamus 1999) although there is no consensus on the direction of the response. Our work shows that in Larrea, stomatal sensitivity to VPD decreases with increasing water stress (Fig. 6; e.g. slope is flatter for Ψpd = −7 MPa than for −1 MPa). Ewers et al. (2001) found a similar response in loblolly pine (Pinus taeda) growing in North Carolina. However, the threshold-type equation (Eqn 8) in the A–Season model predicts that g is completely insensitive to changes in VPD, independent of Ψpd, for VPD < 1·54 kPa (Fig. 6). This type of behaviour has also been observed for wheat and sunflower (Turner et al. 1985; Gollan et al. 1986) and modelled and measured for several temperate–forest tree species (Bond & Kavanagh 1999). Yet, we are not aware of any photosynthesis models that have incorporated this type of stomatal response.

The stomatal behaviour that we observed and modelled in Larrea is in partial agreement with a biophysical model that assumes stomata operate in a manner that maintains constant leaf water potential (Oren et al. 1999). As observed in Larrea, the biophysical model also predicts a threshold response of g to VPD (Oren, personal communication). Additionally, the model of Oren et al. (1999) predicts that stomatal sensitivity to loge(VPD) should be proportional to gmax (i.e. –∂g/∂loge(VPD) @ 0·6·gmax). They surveyed 31 mesic tree species and found that all agreed with this proportionality. Consistent with data for Larrea from the Mojave Desert (unpublished results from Pataki cited in Oren et al. 1999), we find that –∂g/∂loge(VPD) @ 0·46·gmax. The shallower slope associated with Larrea agrees with the hypothesis that Larrea regulates leaf water potential to a lesser degree. Our field data supports this proposition, as diurnal measurements of leaf water potential varied by 1·5- to 3-times during a single day (data not shown).

Larrea's stomatal dynamics have implications for its photosynthetic behaviour. Unlike many mesic and xeric plants, Larrea has been reported to maintain active stomata and positive carbon balance under severe water stress (e.g. Ψpd < −5·6 MPa) (Odening et al. 1974; Hamerlynck et al. 2000a). The A–Season model predicts that under ‘typical’ summer growing temperatures (Tgro= 25 °C) and saturating light (2000 µmol m−2 s−1), Larrea can maintain positive photosynthesis. Figure 7 shows predicted A for three different TVPD combinations, chosen to represent varying degrees of environmental stress and shows that Larrea's photosynthetic rates at Ψpd = −10 MPa are as much as 20–25% of its maximum rates predicted at Ψpd = 0 MPa.

Figure 7.

A–Season model predictions of photosynthesis (A) as a function of Ψpd for several different VPD and T values. Larrea is predicted to maintain positive carbon balance for Ψpd exceeding −10 MPa.

Internal CO2 behaviour

The demand for CO2 under a diversity of environmental settings and temporal scales has not been thoroughly examined. Most studies that address variability in Ci are based on limited growth conditions. Wong et al. (1979) and Yoshie (1986) grew plants under near-optimal conditions and found that Ci was maintained at 220–270 p.p.m. across a variety of species. Tenhunen et al. (1984) measured Ci between 200 and 280 p.p.m. in well-watered field-grown Quercus suber. Conversely, Park & Furukawa (1999) reported that instantaneous Ci varied greatly in two evergreen temperate tree species (150–250 p.p.m) and in two tropical tree species (140–210 p.p.m) growing in a greenhouse. Although most controlled environment studies suggest that Ci is constant, instantaneous Ci may vary substantially when plants are exposed to suboptimal and variable conditions (see also Eamus & Cole 1997).

Even less is known about demand for CO2 in desert species. Mean daily Ci of field-grown Eucalyptus spp. can vary two-fold throughout the year (Mielke et al. 2000). Conversely, in a Mediterranean evergreen sclerophyll shrub, Beyschlag, Lange & Tenhunen (1987) estimated Ci at maximum daily A and found that it remained around 208 p.p.m. We also found that Larrea Ci varies little if we only look at it when g @ gmax, but over an entire day Ci can vary by an order of magnitude (Figs 2e & 3e). Whereas Herppich, Herppich & von Willert (1994) measured diurnal Ci/Ca ratios for a semi-arid fynbos shrub that ranged from 0·6 to 1·05, Larrea exhibits even greater variation (Ci/Ca = 0·14–1·39). These Ci dynamics can have profound consequences for Larrea's daily carbon balance because this shrub operates near maximum A for only a short period during early mid-mornings (Figs 2a & 3a).

Much of the seasonal and diurnal behaviour in Ci may be attributed to water availability, such that Ci on average is higher and less variable in wet than dry periods (e.g. Eamus & Cole 1997; Prior et al. 1997; Eamus et al. 1999). Additionally, the relationship between g and Ci depends on season (Eamus & Cole 1997) and time of day (Downton, Grant & Loveys 1987; Schulze et al. 1975). We found a similar pattern of hysteresis in Larrea. Stomatal conductance was typically positively correlated with Ci in the morning and negatively correlated with or independent of Ci later in the day (Fig. 8). Schulze et al. (1975) observed this pattern for Prunus armeniaca growing in the Negev Desert of Israel, and concluded that the lack of a unique relationship between g and Ci indicated that the two variables were operating independently. However, the A–Season model is able to reproduce this hysteresis (Fig. 8) using a simple non-linear relationship between Ci and g (Eqn 2). It appears that this hysteresis likely results from correlated diurnal changes in PFD, T and VPD.

Figure 8.

Predicted and observed diurnal courses of conductance (g) versus internal CO2 (Ci). Observation means for watered shrubs (open circles); numbers correspond to time (e.g. 1 = first measurement of the day). Predictions of the A–Season model (solid line) are based on 30-min averages of T, VPD and PFD obtained from a weather station located within the study site; arrows are placed near early morning and point in the direction of increasing time. Data are shown for 3 d for which modelled and observed Ci are in close agreement: (a) 28 July 1998, Ψpd = −1·9 MPa; (B) 31 July 1998, Ψpd = −2·6 MPa; and (c) 4 August 1998, Ψpd = −2·1 MPa. The model successfully captures the observed hysteresis patterns, such that the g versus Ci trajectory depends on time of day.


In general, our field studies and predictions from the A–Season model support dogma attributed to Larrea's success with regard to stomatal control of photosynthesis under a diverse array of water deficits. However, we suggest that seasonal changes in stomatal behaviour may be more important to photosynthetic temperature acclimation in Larrea than previously recognized. Moreover, our study sheds light on the current understanding of demand for CO2 in Larrea. Considerable variation in Ci can occur on a diurnal and seasonal scale and models that assume a constant Ci are inappropriate for Larrea, and possibly for other species.

The A–Season model presented here is successful at capturing the large diurnal and seasonal fluctuations in A, g and Ci in Larrea primarily because it incorporates an effect of average growing temperature on gmax. In addition, the g submodel is consistent with theoretical considerations of stomatal behaviour and the Ci submodel is based on a simplification of the ACi curve. Hence, A–Season's relatively simple, semi-mechanistic formulation makes it attractive for modelling responses of other species to environmental change, especially considering how well it describes Larrea's behaviour, a desert shrub that is adapted to a highly variable environment.


The authors thank Roberto Fernández, Sarah Bauer, Lisa Stano, Guy Telesnicki and David Tremmel for their able assistance in conducting the field experiment. Thanks also to John Anderson for logistical support in New Mexico and Jarrett Barber for statistical advice. Jeff Amthor, Ülo Niinemets, Rob Jackson, Ram Oren and Bill Schlesinger provided helpful comments on an earlier draft. This work was supported by NASA Headquarters under the Earth System Science Fellowship (Grant No. NGT5-30355), by the USDA (Grant No. 00-35101-9306) and is a contribution to the Jornada LTER (NSF grant No. DEB 94–11971).

Received 5 December 2001;received inrevised form 7 March 2002;accepted for publication 7 March 2002