Exposure of plants to salt stress is often accompanied by reductions in leaf photosynthesis and in stomatal and mesophyll conductances. To separate the effects of salt stress on these quantities, a model based on the hypothesis that carbon gain is maximized subject to a water loss cost is proposed. The optimization problem of adjusting stomatal aperture for maximizing carbon gain at a given water loss is solved for both a non-linear and a linear biochemical demand function. A key novel theoretical outcome of the optimality hypothesis is an explicit relationship between the stomatal and mesophyll conductances that can be evaluated against published measurements. The approaches here successfully describe gas-exchange measurements reported for olive trees (Olea europea L.) and spinach (Spinacia oleraceaL.) in fresh water and in salt-stressed conditions. Salt stress affected both stomatal and mesophyll conductances and photosynthetic efficiency of both species. The fresh water/salt water comparisons show that the photosynthetic capacity is directly reduced by 30%–40%, indicating that reductions in photosynthetic rates under increased salt stress are not due only to a limitation of CO2diffusion. An increase in salt stress causes an increase in the cost of water parameter (or marginal water use efficiency) exceeding 100%, analogous in magnitude to findings from extreme drought stress studies. The proposed leaf-level approach can be incorporated into physically based models of the soil-plant-atmosphere system to assess how saline conditions and elevated atmospheric CO2 jointly impact transpiration and photosynthesis.
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 Exposure to salt stress involves complex changes in plant morphology, physiology, and metabolism, and a large number of studies have focused on salt-stress effects on plant growth, leaf photosynthetic rates, CO2 fixation capacity, and leaf stomatal conductance [Yeo et al., 1985; Munns and Tester, 2008; Chaves et al., 2009]. The compass of this work is to develop an optimization model to address how salt stress impacts the linkages between leaf photosynthesis, conductance, and transpiration rates. More specifically, the trade-offs between leaf carbon gains and water losses are explored when salt stress is increased.
 Models describing leaf photosynthesis and water uptake under water limitations and, to a lesser extent, salt stresses, are numerous but can be grouped into three main categories. The first category includes detailed hydromechanical descriptions of stomatal movement [Dewar, 2002; Buckley et al., 2003], requiring the specification of a set of parameters rarely accessible in practical hydrologic and biogeochemical applications. The second category is composed of semi-empirical models that reduce stomatal conductance according to a stress level [Jarvis, 1976], or relate stomatal conductance to photosynthesis through a humidity index [Collatz et al., 1991; Leuning, 1995]. The third category, which is extended here to the case of salinity stress, retains the key physiological mechanisms employed by the previous two model categories, but replaces precise hydraulic and biochemical descriptions of stomatal aperture with an optimization hypothesis [Givnish and Vermeij, 1976; Cowan and Farquhar, 1977; Hari et al., 1986].
 This evidence is often presented as leaf-level CO2 flux (fc) against ci and cc when inferred separately from ci. For the fc − ci relationship, the initial slope is significantly affected by salinity, whereas in the fc − cc case, the initial slope is not [Ball and Farquhar, 1984; Brugnoli and Lauteri, 1991; Delfine et al., 1998]. Moreover, the cc/ci is relatively invariant to increasing fc in control leaves, while it decreases with increasing fcin salt-stressed conditions. This decline incc/ci emphasizes the role of reduced mesophyll conductance in saline conditions. Changes in the stomatal and mesophyll conductances, rather than in the stomatal conductance alone, are thus jointly responsible for changes in fc and cc (Figure 1).
 The possible compound effects of salinity and elevated ambient CO2concentrations on gas-exchange rates have not been extensively explored in earlier studies.Nicolas et al.  and Geissler et al.  do report some experimental results, which suggest a positive compensation effect with elevated atmospheric CO2concentrations with respect to salt stress. The quantification of the magnitude of such compensation mechanism is of interest for climate-change scenarios in saline environments.
 The direct effects of salt stress on the photosynthetic machinery are also not fully established and are seldom included in plant-atmosphere gas-exchange models [Flexas et al., 2004; Geissler et al., 2009] even though some studies do point out to significant changes in the photosynthetic capacity [Ball and Farquhar, 1984; Seemann and Sharkey, 1986; Bongi and Loreto, 1989; Paranychianakis and Chartzoulakis, 2005] associated with increased salinity. Hence, salt stress simultaneously affects stomatal and mesophyll conductances as well as photosynthetic efficiency, and their interrelations must be accounted for in quantitative models of plant responses to salinity. Quantifying these interrelationships frames the scope of the present work. To progress on these issues, this work addresses three interrelated questions:
 1. What are the effects of saline stress on photosynthesis and how can these effects be partitioned among stomatal conductance, mesophyll conductance, and photosynthetic capacity if the stomatal aperture is regulated so as to maximize carbon gain at a given water loss?
 2. Is this proposed model able to describe gas-exchange experiments in general and the relationship between stomatal and mesophyll conductances in particular?
 3. What hypotheses can be generated from such a model about the joint effects of salinity and elevated atmospheric CO2 on photosynthesis and stomatal conductance?
 To address these questions, a stomatal optimization approach that maximizes carbon gain at a given water loss to describe stomatal operation under saline conditions is extended by accounting for the mesophyll conductance. The resulting model explicitly predicts the functional relationship between stomatal and mesophyll conductances in response to changes in salinity thereby allowing direct evaluation against published data sets. The findings from this work can be imminently incorporated into soil-plant-atmosphere models dealing with salinity effects on land-surface fluxes of CO2 and water vapor.
 Basic definitions employed in stomatal optimization theories that maximize carbon gain for a given water vapor loss are first reviewed. Next, how salt stress modifies this conventional picture is described. Published gas-exchange experiments on two C3 species with mild to intermediate salt tolerance are then used to explore the proposed modifications. The overall aim here is to disentangle salinity effects on photosynthetic properties versus gas diffusional limitations arising from reduced stomatal and mesophyll conductances.
2.1. Extending Stomatal Optimization Theories to Saline Environments
 The bulk transfer rates of CO2 and water vapor across the leaf stomata are given as
where fc (μmol m−2 s−1) and fe (mol m−2 s−1kPa) are the leaf-level CO2 and water vapor fluxes; gs is the CO2 stomatal conductance (mol m−2 s−1); ca and ci are the ambient and the intercellular CO2 concentrations (μmol mol−1 or ppm), respectively; a = 1.6 is the relative molecular diffusivity of water vapor with respect to carbon dioxide; VPD = [e*(Ta)(1 − RH)] is the vapor pressure deficit (kPa) assuming the leaf is well coupled to the atmosphere (as is the case for virtually all gas-exchange measurements);e*(Ta) is the saturation vapor pressure (a function of air temperature, Ta, given by the Clausius-Clapeyron equation); andRH is the mean air relative humidity, expressed as a fraction (Table 1). The VPD can also be expressed as a dimensionless fraction when normalized by the atmospheric pressure. In this dimensionless representation for VPD, the units of fe are altered accordingly.
The cost parameter, λ, is conventionally labeled as the marginal water use efficiency. With respect to the conventional definition of water use efficiency WUE = fc/fe, the marginal water use efficiency refers to the variations of the fluxes with respect to the variation in stomatal conductance (marginal WUE = λ = ).
 This formulation must now be modified to account for salt stress and, in particular, for the changes induced by salinity to the mesophyll conductance as well as to the photosynthetic efficiency. Because fc occurs inside the chloroplast, equation (1) describing the CO2 flux must be revised to explicitly consider cc and the mesophyll conductance, gm, characterizing CO2 transport from the intercellular space to the chloroplast (Figure 1). The effective conductance, geff, associated with the series of conductances, gm and gs, leading from the chloroplast to the atmosphere as shown in Figure 1 is given by
When leaf respiration is small compared to fc, fc can be approximated as the total biochemical demand for CO2 occurring in the chloroplast, which can be expressed as [Farquhar et al., 1980]
where cp is the CO2 compensation point and a1 and a2are physiological parameters, depending on whether the photosynthetic rate is restricted by electron transport or by Rubisco. Under light-saturated conditions,a1 = Vcmax, the maximum carboxylation capacity of Rubisco, and a2 = Kc(1 + Coa/Ko), where Kc and Ko are the Michaelis constants for CO2 fixation and oxygen inhibition, and Coa is the oxygen concentration in the atmosphere. When light is limiting, a1 = αpemQp = γQp and a2 = 2cp, where αp is the leaf absorptivity of photosynthetically active radiation (= Qp), em is the maximum quantum efficiency of leaves and γis the apparent quantum yield determined from empirical light-response curves. The parameters necessary to computecp and a2 were taken from Farquhar et al.  and adjusted for temperature according to Campbell and Norman [1998; equation (14.26) ff., pp. 240–241].
 By equating the transport rate of CO2 given by equation (5) to the biochemical demand in equation (6), an expression for the ratio (cc/ca) can be derived and is given as
When substituted back into equation (5), an expression for fc is obtained,
Using expressions (2) and (8), the maximization of the objective function (F from equation (3)) results in
which is in implicit form and the analytical solution is too unwieldy to report here. This equation can be readily solved numerically to obtain gsand, hereafter, we refer to this solution as the non-linear model because it accounts for all the non-linearities in the biochemical demand function.
2.2. A Linearized Model
 For more immediate interpretations of published gas-exchange measurements, and for simpler implementations in ecohydrologic models, a linearized analytical expression for conductance and photosynthesis is also developed here and compared with the non-linear model. This simpler analytical expression forgs can be obtained by simplifying the denominator of the biochemical demand function (equation (6)) as
where the variability in s = cc/ca is assumed to be small compared to the magnitude of a2 such that s can be treated as approximately constant [Katul et al., 2000, 2010]. It must be emphasized here that s is treated as a model constant only in equation (10), i.e., in the denominator of equation (6), while in equation (5) describing the rate of CO2 uptake, cc/ca is allowed to vary. This linearized biochemical demand is now given as
where, despite the linearization, fc retains the saturating behavior with increasing ca. By combining the rate of CO2 uptake (equation (5)) and the linearized biochemical demand function (equation (11)), the chloroplast concentration is given as
and by substituting into equation (5), fc is readily expressed as
which can now be used in defining the objective function F (equation (3)).
 Upon differentiation with respect to gs and by setting = 0, an analytical solution for gs can be derived as
By combining equation (14) with equation (13), an expression for the photosynthetic rate as a function of the mesophyll conductance is obtained:
Hereafter, we refer to this solution as the linear model.
 The use of equations (9) and (14) clearly requires either calibrating λ based on measurements (later described) or adopting independent estimates. Atmospheric CO2 concentration has been shown to affect the value of λ. A linear dependence may be assumed [Katul et al., 2010; Manzoni et al., 2011],
where co is a reference CO2 concentration for which λ = λo is known. If this linear expression for λ is adopted, and upon neglecting variations in cp compared to ca, the canonical form of the gs versus fc relationship reduces to
 This mathematical form is virtually identical to the Ball-Berry and Leuning semi-empirical models [Collatz et al., 1991; Leuning, 1995] with three exceptions: (1) this canonical form is an emergent property of the linear optimality model, not a prioriassumed as was the case in the Ball-Berry and Leuning models [Collatz et al., 1991; Leuning, 1995]; (2) the VPD−1/2 reduction function is also an emergent property of the optimization theory and is not empirically assumed as noted elsewhere [Hari et al., 1986; Katul et al., 2009]; and (3) the stomatal sensitivity parameter m1 = can be explicitly related to the marginal water use efficiency λo reflecting CO2 conditions during plant growth.
 Both the non-linear and the linear optimality models are used to interpret published gas-exchange measurements for salt-stressed plants. After a literature review, two studies were identified involving simultaneous measurements of the CO2flux and stomatal and mesophyll conductances for controlled and salt-stressed conditions.
 The first data set, published by Loreto et al.  and digitized by us for this study, refers to experiments in which olive trees (Olea europea) were irrigated with water while salinity was gradually increased (up to 200 mM, resulting in a water electrical conductivity of 24.6 dS m−1). Simultaneous gas-exchange and fluorescence field measurements were carried out on six different cultivars known to have moderate salt tolerance. The measurements were performed between 40 and 45 days after the beginning of the salt treatment and included stomatal conductance, photosynthesis and chlorophyll fluorescence under ambient air temperature (28°C–30°C), light intensity (800–1000μmol photons m−2 s−1, corresponding to saturating light conditions [Bongi and Loreto, 1989]), and VPD (<2 kPa).
 The second data set [Delfine et al., 1998, 1999] refers to irrigation experiments performed on spinach plants (Spinacia oleracea), displaying intermediate sensitivity to salt stress. The control setup was irrigation with freshwater, while a subset of the plants were irrigated with saline water (1% NaCl w/v = 200 mM). Plants were grown in a greenhouse under controlled temperature and light conditions. Sampling commenced 13 days after the first saline irrigation and continued once a week until flowering. The mean leaf temperature was 25°C and the light intensity was 1200 μmol quanta m−2 s−1, also in this case close to light saturation conditions [Calatayud et al., 2003; Yamori et al., 2005].
 The gas-exchange measurements considered here were performed well after the start of the salt treatment. It is safe to assume that the salt concentration in the tissues in all cases exceeded a threshold beyond which salinity induced significant physiological responses. The behavior of the two contrasting end-members sets (non-stressed and salt-stressed plants, indicated by subscriptsns and s, respectively) are considered for simplicity. Mesophyll conductances and chloroplast concentrations were retrieved using methods described elsewhere [Loreto et al., 1992; Harley et al., 1992]. Since both S. oleracea and O. europea are C3 species [Schnarrenberger et al., 1980; Camin et al., 2010], equation (6) can be used to model the biochemical demand for CO2. Light-saturated conditions were assumed in all cases, noting the high light intensity measured in the two experiments.
3.1. Model Calibration
 Following a sensitivity analysis (not shown for brevity), two parameters (a1 and λ) were identified as most significantly controlling the behavior of the non-linear and linear optimality models and serve as logical candidates for assessing how salinity affects their values. Any salt-stress effect ona1 is here interpreted as impacting the photosynthetic efficiency of the plant, while salinity effects on λare interpreted as impacting the stomatal regulation. Both parameters have been computed through non-linear fitting to the data of the linearized and non-linear model equations developed insection 2, as discussed next.
 In the non-linear model,a1was computed by fitting the non-linear model forfc (equation (8)) to the simultaneously measured values of fc, gs, and gm (the latter two are always combined in geff) using a Root Mean Square Error (RMSE) minimization between modeled and observed values of fc, which provided a satisfactory agreement both for the freshwater and the salt-stressed cases and for both data sets.
 For the olive trees data set, the optimized values for a1in the non-saline and in salt-stressed conditions were respectivelya1,ns = 61.55 μmol m−2 s−1 and a1,s = 38.21 μmol m−2 s−1 (recall subscripts ns and sindicate unstressed control and salt-stressed plants). Hence, salt stress reduceda1by some 40% from its non-saline value. In the case of the spinach data set:a1,ns = 127.25 μmol m−2 s−1 and a1,s = 87.36 μmol m−2 s−1, again suggestive of some 30% reduction due to salt stress. Hence, these model calculations show that the photosynthetic capacity is significantly reduced by salt stress in both cases.
 Using a numerical procedure based on the combination of two algorithms (the simplex search method of Lagarias et al. and the trust-region-reflective algorithm described inColeman and Li [1994, 1996]) to iteratively solve the non-linear objective function (equation (9)), the numerical value of λ was determined by minimizing the RMSE between measured and modeled gs. For the olive trees data set, the computed λfor the non-saline and the salt-stressed condition, were respectively:λns = 1.64 ppm/kPa and λs = 8.07 ppm/kPa. For the spinach data set, λns = 8.00 ppm/kPa and λs = 14.35 ppm/kPa. Again, in all cases, the results appear consistent with intuitive expectations: λ increases with increased salt stress, indicating that the cost per unit mass of water transpired increased with increased salinity (analogous to worsening plant water status during soil moisture stress). Figure 2 illustrates the dependence of fc on gs and gm using the observed values for gm, the values of gs obtained from the optimality model (equation (9)), and the values of fc determined from equation (8). The shape of the modeled relationships are remarkably consistent with the data set considered for gm. The relationship between fc and gs is almost linear for olives and spinach, while fcexhibits a non-linear dependence ongm with an asymptotic behavior.
 While the non-linear model retains all the non-linearities of the biochemical demand function, it lacks the analytical tractability of the linearized model and does not allow an immediate understanding of the scaling relationships between fluxes and biological and environmental parameters. The linear model is also attractive for the estimation ofa1 and λ, as discussed next.
 The value of the parameter s = cc/ca, which was employed in the linearization of the biochemical demand function (equations (10) and (11)), was retrieved for the two data sets from mean values of measured cc and ca. The inferred sfrom these data is higher for non-saline conditions (due to decreasedgm), ranging from 0.6 (non-saline) and 0.2 (salt-stress) forS. oleraceato 0.7 (non-saline) and 0.4 (salt-stress) forO. europea.
 The calibration of λ for the linearized model is performed by minimizing the RMSE for fc using the solution of the linearized model (equation (16)) (Figure 2). As earlier noted, the modeled relationship between fc and gs is approximately linear and consistent with the measurements, resulting in λns = 1.25 ppm/kPa for the olive trees, and λns = 8.33 ppm/kPa for spinach. As in the case of the non-linear model, the values ofλ increase with salinity in both cases (λs = 2.8 ppm/kPa, for olive trees, and λs = 14.34 ppm/kPa for spinach).
 Subsequently, using the expression for the photosynthetic rate as a function of the mesophyll conductance obtained from the linearized model (equation (15)), the value of a1 using the now determined value of λ was obtained. The resulting values of a1 also decreased with salinity for the olive trees (a1,ns = 59.33 μmol m−2 s−1, a1,s = 18.80 μmol m−2 s−1) and the spinach plants (a1,ns = 122.60 μmol m−2 s−1, a1,s = 81.01 μmol m−2 s−1). The modeled relations between fc and gm (Figure 2) captured the observed patterns as well as the non-linear model. The results of the model calibration are summarized inTable 2.
Table 2. Results of the Model Calibration for Non-saline and Saline Conditions, Linear and Non-linear Models, and Both Data Sets
λns (mol mol−1 kPa−1)
a1,ns (μmol m−2 s−1)
λs (mol mol−1 kPa−1)
a1,s (μmol m−2 s−1)
3.2. Parameter Uncertainty
 The values of a1 and λestimated using the linear and non-linear models are comparable for both species in the reference non-stressed cases. In the salt-stress case, however, the values ofλ and a1 vary between the two models for O. europea, possibly because of the narrow range of flux values, which did not constrain the regression parameters as well as in the other cases (Figures 2a and 2b).
 For both models, a bootstrap resampling technique [Efron, 1979] was employed to retrieve the frequency distribution of the parameters involved in the calibration. This analysis is performed to determine whether differences in parameter values from the non-stressed and stressed cases were statistically significant. The bootstrap procedure is based on randomly selecting data from the original data set (with replacement, i.e., potentially allowing the selection of the same data value multiple times), thereby generating a large number of new synthetic samples (here equal to 10,000) with the same size as the original one. The larger is the number of resamplings, the more precise is the frequency distribution obtained because the random sampling errors are reduced; but this choice must allow reasonable computational time. The model is then calibrated for each synthetic sample, thus providing numerous estimates (10,000 in our case) of the parameters and allowing the construction of their frequency distribution in a non-parametric manner. The obtained distributions (seeFigure 3for the linear model) display a marked separation, showing that indeed the differences between the values for control and salt-stressed treatments are statistically significant. The mean values of the distributions and the 95% confidence intervals for both the linear and non-linear models are reported in theauxiliary material as a summary table (Text S1).
 A model validation was also performed using a Leave-One-Out Cross-Validation technique [Wilks, 2006]. This procedure calibrates the model with all but one observation from the original sample, and uses the single one left for independent validation. This procedure is repeated such that each observation in the sample is used once for validation. The results of this analysis (shown in the auxiliary material(Text S2)) indicate no significant estimation bias, relatively modest dispersion between predicted and observed values, and no significant difference between the errors for the non-linear and the linear models. The two models perform equally well in predicting the photosynthesis and stomatal conductance in saline and salt-stressed conditions.
3.3. The Relative Role of Stomatal and Mesophyll Limitations
 The relative importance of the stomatal versus the mesophyll conductance in the overall effective conductance is presented in Figures 4a and 4c, where measured and modeled (equation (14)) conductances are compared. Figures 4a and 4c show that mesophyll conductance is far from infinite but rather comparable to the stomatal conductance, thus reinforcing the importance of accounting for mesophyll conductance in saline environments. Moreover, for a fixed gm, gsis larger in the fresh water case than in salt-stressed conditions, suggestive that stomata can open more freely in response to environmental factors such as light, temperature, and humidity, when they are not stressed by salinity.
 The same relationship can be explored in terms of resistances, r = 1/g, with the advantage of being able to more clearly separate stomatal and mesophyll effects in an additive manner, as reff = rs + rm (Figures 4b and 4d). The rs and rm give similar contributions to reff in the case of spinach plants. For olive trees, the stomatal resistance is always lower than the mesophyll resistance in the freshwater case, but rs and rmbecome comparable in salt-stressed conditions.
3.4. Effect of Elevated Atmospheric CO2 Concentration on Gas Exchange
 The model in equation (15), calibrated for the olive tree case, is now used to investigate the compound effect of salinity stress and elevated atmospheric CO2concentration. To this end, the two contrasting cases of fresh water irrigation and salt-stressed conditions are considered, with the respective values of the cost parameter and the photosynthetic efficiency fromTable 2. Two contrasting but typical values of gmare used to represent the saline and non-saline cases, as derived fromLoreto et al. . Namely, we adopted gm=0.12 mol m−2 s−1for the salt-stressed case (with salt concentration in the irrigation water of 200 mM, or 24.6 dS m−1), and gm = 0.23 mol m−2 s−1 for the fresh water case. While in trees a1 can be assumed to be independent of ambient ca [Ainsworth and Rogers, 2007; Ellsworth et al., 2011], the effects of CO2 concentration are accounted for by linearly scaling the value of the cost parameter λ, as described in equation (17) (where the reference ambient CO2 concentration was set to ca,0=380 ppm).
 Photosynthesis (fc) increases with ca (Figure 5a), thus partially compensating for the adverse effects of salinity. As salinity increases, however, the sensitivity of the gas-exchange rate tocadecreases significantly. In fact, to offset salt stress, and obtain the same photosynthesis as under non-stressed conditions, an increase of over 1000 ppm of CO2would be needed in the most severe salt-stress case considered here. However, future smaller increases in atmospheric CO2may be sufficient to compensate for less severe salt-stress conditions. Stomatal conductance, differently fromfc, decreases both in response to increased salinity and atmospheric CO2 (equation (14); Figure 5b). Moreover, increased atmospheric CO2concentration alters the relative effects of salinity, changing the ratio between the two contrasting cases (salt-stressed over non-stressed) for both photosynthesis and stomatal conductance (Figures 5c and 5d). Here, the ratio between photosynthesis (or stomatal conductance) in the salt-stressed case and increasingca over the unstressed value at ca,0 = 380 ppm is shown. In Figure 5c, as the ratio tends toward unity, the CO2 effect balances the salt stress, indicating that salinity is mitigated by the increase of CO2 concentration. In contrast, both elevated CO2 and salinity decrease stomatal conductance and hence leaf transpiration.
 The former represents the cost of water losses through transpiration [Cowan and Farquhar, 1977] and thus regulates the sensitivity of stomata to the environment. An increase in salt stress increases the cost of water, λ, analogous to theoretical and experimental findings from drought-stress studies [Mäkelä et al., 1996; Manzoni et al., 2011]. Plants in both experiments considered here were irrigated and hence do not suffer from soil moisture limitation per se. Hence, the increase in λ with salt stress represents a measure of leaf responses to adverse osmotic conditions. An increased salt concentration in the soil induces a restriction in transpiration that is beneficial to slow down further salt accumulation, and hence to prevent possible irreversible damages (at the expenses of lower carbon gains and plant growth).
 Parameter a1 reflects the intrinsic photosynthetic capacity of the leaf. For O. europea, Wullschleger  reports a Vcmax of 8–23 μmol m−2 s−1, much lower than 68–95 μmol m−2 s−1 reported for S. oleracea(both at 25°C). Consistent with this general pattern, our temperature-corrected estimates fora1 are larger for spinach than for olive trees. For O. europea, a1 = 43 μmol m−2 s−1, an intermediate value between the lower estimates by Wullschleger  and the higher by Díaz-Espejo et al.  (50–90 μmol m−2 s−1) and Nogués and Baker  (150 μmol m−2 s−1). These differences can be ascribed to different factors, ranging from growth conditions to leaf age. Light intensity also plays a role, as the values obtained from model calibration are lower if light limiting conditions are assumed. Moreover, the literature values of Vcmax do not take into account the effect of the mesophyll conductance, which is explicitly included in the model and hence the inference of a1. If, for instance, gm is assumed not to be limiting CO2 exchange, then the calibrated values of a1decrease significantly. In this case, and for non-stressed leaves,a1,ns ≈ 25 μmol m−2 s−1 for O. europea and a1,ns ≈ 88 μmol m−2s−1 for S. oleracea, in line with the values reported by Wullschleger . This consistency of a1 with independent estimates when gm/gs ≫ 1 lends support to the robustness of the proposed model.
 The fresh water/salt water comparisons further show that the photosynthetic capacity of the plant is directly impacted by increased salt stress, as evidenced by a statistically significant 30%–40% reduction in maximum carboxylation capacity. This shows that the reductions in photosynthetic rate observed under salt stress are not only due to a limitation of CO2 diffusion (associated with reduced mesophyll and stomatal conductances), but also caused by a direct negative effect on the metabolic apparatus of the plant, consistent with Ball and Farquhar ; Seemann and Sharkey ; Bongi and Loreto ; Paranychianakis and Chartzoulakis ; Egea et al. . Interestingly, the optimization framework also predicts a non-linear scaling between stomatal and mesophyll conductances (equation (14)) as salinity effects become more severe, which is consistent with observations (Figure 4). Such a relationship, together with the reduced photosynthetic capacity, allows disentangling the diffusive and biochemical limitation to CO2 uptake under salinity.
 Overall, these modeling results (increased λ and decreased a1) support the hypothesis that plant response to salinity and water stress are similar [Munns, 2002; Chaves et al., 2009; Lawlor and Tezara, 2009; Vico and Porporato, 2008]. The initial response to stress (i.e., reduced gsand leaf elongation) is analogous in saline and drought conditions. In the long term, however, salt-specific effects linked to the toxic effect of salt arise (e.g. reduction ina1 and mesophyll conductance). The osmotic stress induced by salinity reduces the water potential in the soils and thus plants tend to minimize the water loss by closing the stomata [Geissler et al., 2009], similar to drought responses.
 An interesting extension of the present study is to explore the compound effect of salt stress and elevated CO2 concentration in the atmosphere. In the halophyte Aster tripolium salinity reduced photosynthesis and stomatal conductance, although net photosynthesis was significantly ameliorated under elevated atmospheric CO2 concentrations, while intercellular CO2 concentration increased [Geissler et al., 2009]. Similar positive effects of elevated CO2 were found by Nicolas et al.  in wheat, but no significant effect was observed by Melgar et al.  in olive trees. Ainsworth and Rogers  also report a reduction in stomatal conductance and increased photosynthesis under elevated CO2 concentration for both C3 and C4 species. These effects are confirmed by the model results here that quantify the atmospheric CO2 concentration at which the photosynthetic reduction induced by salt stress may be offset.
 A model for leaf gas exchange based on the maximization of the carbon gain subject to unavoidable water losses is extended to include the effects of salt stress. The revised optimality model explicitly includes the mesophyll conductance and its dependence on water salinity. The optimization problem is solved numerically for a non-linear biochemical demand function, and analytically for a linearized biochemical demand function. Both models reproduced well gas-exchange measurements collected for olive trees and spinach plants in fresh water and in salt-stressed conditions. As a result of salt stress, the maximum carboxylation capacity was reduced by 30%–40%, while the parameter indicating the cost of water increased. The model scenarios simulating the compound effect of salinity stress and increasing atmospheric CO2 concentration showed that the reduction in stomatal conductance and the increase of photosynthesis under elevated CO2concentration are slightly affected by salinity stress. Given the agreement between the non-linear and linear models, the simpler linearized model can be readily incorporated into ecohydrological models of saline environments, providing a parsimonious (and analytical) description of transpiration and photosynthesis for salt-stressed conditions using well-established physiological principles. Up to this point, the skill of this proposed model is primarily ‘diagnostic’ and not yet ‘prognostic’, meaning that the model is able to describe the functional relationships betweenfc, gs, gm, cc, and ci provided a1 and λ are known. For prognostic purposes, it becomes necessary to describe mechanistically the variations of a1 and λ with leaf (or preferably soil) salinity, a logical next step here. Furthermore, the prognostic skills of the proposed approach can benefit from investigations that consider the joint effects of salt and soil moisture stress on a1 and λ in ambient and enriched CO2 environments.
 This work is an outcome of the Biogeodynamics and Earth System Sciences Summer School, held in Venice on 11–18 June 2010. The authors thank the Istituto Veneto di Scienze, Lettere, ed Arti for organizing the program. M. Marani and V. Volpe acknowledge the Progetto Strategico d'Ateneo of the University of Padua. G. Katul and S. Manzoni acknowledge support from the U.S. Department of Energy through the Office of Biological and Environmental Research (BER) Terrestrial Carbon Processes (TCP) program (NICCR DE-FC02-06ER64156), from the U.S. National Science Foundation (NSF-AGS-1102227, NSF-CBET 103347, NSF-EAR-10-13339), from the U.S. Department of Agriculture (2011-67003-30222), and from the Fulbright-Italy distinguished scholars program. The authors thank Danielle Way, two anonymous reviewers, and the Editor for their helpful suggestions and comments.