Increasing water use efficiency along the C3 to C4 evolutionary pathway: a stomatal optimization perspective

Summary Using a stomatal optimization model, an abrupt change is foundnd in the relationship between carbon and water fluxes along the evolutionary gradient from C3 to C4 photosynthetic types.


Introduction
While only 3% of the world's terrestrial plant species use the C 4 photosynthetic pathway, C 4 species are responsible for some 20% of global gross primary productivity (Sage et al., 2012). The high productivity of C 4 plants is due to their efficient photosynthetic physiology, which includes an additional yet spatially separated metabolic cycle, mediated by phosphoenolpyruvate carboxylase (PEPCase), to the conventional C 3 Calvin-Benson cycle. This additional cycle results in high CO 2 concentrations around Rubisco, thus suppressing the enzyme's oxygenase function and nearly eliminating photorespiration and the associated carbon and energetic costs.
C 4 photosynthesis has evolved independently at least 66 times in lineages throughout the plant kingdom and, in some of these lines, there are intermediate species that are neither C 3 nor fully C 4 (Sage et al., 2012). Phylogenetic analyses in some evolutionary groups where the full range of C 3 , C 3 -C 4 intermediates, and C 4 species are found (such as the genus Flaveria) have confirmed that C 3 photosynthesis is the basal state and C 4 photosynthesis is more derived; these analyses also place photosynthetic intermediate species as evolutionary intermediates to these two photosynthetic types (McKown et al., 2005). The C 3 -C 4 intermediates can be classified into three categories based on the degree to which they express C 4 traits: Type I intermediates show refixation of photorespiratory CO 2 by Rubisco in enlarged bundle sheath cells; Type II species have increased PEPCase activity and some C 4 cycle function; and C 4 -like species have an operational C 4 cycle, but have some residual Rubisco activity in their mesophyll cells (Edwards and Ku, 1987).
Despite extensive research, the role of environmental factors in driving the evolution of C 4 photosynthetic traits continues to draw significant attention (e.g. Osborne and Sack, 2012;Griffiths et al., 2013). Much work has focused on the importance of a drop in atmospheric CO 2 concentrations (c a ) from near 1000 ppm to ~400 ppm ~30 million years ago (mya), where the predominant benefit from a CO 2 -concentrating mechanism would have been enhanced net CO 2 fixation rates through suppression of photorespiration (Ehleringer et al., 1997;Sage, 2004;Christin et al., 2011;Sage et al., 2012). While low c a increases photorespiration, the effect is even greater when combined with high temperatures: very low c a conditions, such as those of the last glacial period (~180 μmol mol -1 ) (Lüthi et al., 2008), may have selected for traits in some C3 species to favour the capture and reassimilation of respired and photorespired CO 2 to offset this stress (Busch et al., 2013), but the detrimental effects of low c a conditions on C 3 species are further exacerbated at warmer temperatures (Campbell et al., 2005). The warm regions where C 4 species evolved therefore probably stimulated photorespiration considerably, but they also drove a concomitant increase in transpiration demand (Taylor et al., 2012). It has been known for decades that C 4 plants are more water use efficient than C 3 species under the same conditions (e.g. Rawson et al., 1977;Morison and Gifford, 1983); a spate of recent work has highlighted the role of other environmental variables that, along with low c a , may have contributed to the rise of C 4 photosynthesis, such as dry or saline conditions. These recent studies have emphasized the role of C 4 photosynthesis in improving plant water status and preventing hydraulic failure in these environments (Osborne and Sack, 2012;Griffiths et al., 2013).
Since C 4 species can maintain high photosynthetic rates even when stomatal conductance is low compared with their C 3 counterparts, it follows that C 4 photosynthesis promotes higher water use efficiencies (WUEs) than are found in C 3 species (e.g. Rawson et al., 1977;Morison and Gifford, 1983;Monson, 1989;Huxman and Monson, 2003;Kocacinar et al., 2008;Osborne and Sack, 2012 see Lloyd and Farquhar (1994); Vogan and Sage (2011); Manzoni et al. (2011); note that this definition of λ is consistent with that of Hari et al. (1986), but the inverse of the same symbol used by Cowan and Farquhar (1977)]. The marginal WUE λ can also be interpreted as the cost of losing water in carbon units. Thus, the higher λ of C 4 species implies that water loss is more costly for the carbon balance with respect to C 3 species, so that C 4 species operate at a relatively low E, but at comparable or higher A net . This finding is consistent with C 4 photosynthesis preventing hydraulic failure by means of a tight stomatal regulation of water loss (Osborne and Sack, 2012). Yet what controls the stomatal behaviour and WUE across the evolutionary continuum of C 3 to C 4 species remains a subject of research (Vogan and Sage, 2011;Way, 2012) and frames the scope of this work. Recent experiments have shown that instead of a gradual improvement in WUE from C 3 species, across the intermediate range and to a full C 4 pathway, the increase in WUE resembles a threshold effect: Type I and II intermediates have WUEs on a par with C 3 species, while C 4 -like species have a high WUE akin to C 4 plants (Kocacinar et al., 2008;Vogan and Sage, 2011). The development of the CO 2 -concentrating mechanism, which effectively pumps CO 2 from the substomatal cavity into the chloroplasts where the Calvin-Benson cycle occurs, is thought to be the primary mechanism by which C 4 plants enhance their WUE i . The present study therefore sought to investigate the connection between the evolutionary continuum of C 3 to C 4 photosynthesis and stomatal behaviour (which is a key factor in controlling WUE), by exploring the following questions.
(i)To what degree can stomatal optimization theories describe the WUE i patterns in species that have photosynthetic characteristics intermediate between C 3 and C 4 species? (ii)What are the relationships among the CO 2 -concentrating mechanism, λ, and WUE i in these C 3 -C 4 intermediates?
To address these questions, the genus Flaveria was used as a case study, since it contains species with C 3 photosynthesis, all three intermediate photosynthetic types, and C 4 photosynthesis (a system previously used by Huxman and Monson, 2003;Sage, 2004;McKown and Dengler, 2007;Kocacinar et al., 2008;Vogan and Sage, 2011;and others). Data on Flaveria are used to parameterize a stomatal optimization model and examine stomatal behaviour across the evolutionary range of C 3 to C 4 photosynthesis. By using a phylogenetically constrained system, the patterns of changes in the model parameters across the C 3 -C 4 photosynthetic continuum can be simultaneously explored while minimizing evolutionary differences between groups that might otherwise confound the analysis.

Theory
In the Farquhar et al. (1980) photosynthesis model, A net is determined by the minimum of two limitations: the Rubisco carboxylation rate (A C ) and ribulose-1,5-bisphosphate (RuBP) regeneration rate A J , and is commonly expressed as where R d is the daytime respiration rate (see Table 1 for symbols and definitions). Rubisco limitation occurs under saturating light or at low CO 2 concentrations at the site of Rubisco, while RuBP regeneration tends to limit photosynthesis when c a is high and light levels are low, resulting in a limited electron transport rate. The Rubisco-limited assimilation rate, A C , can be expressed as where V c,max is the maximum Rubisco carboxylation rate, c c is the CO 2 concentration at the photosynthetic site, Γ* is the CO 2 compensation point in the absence of mitochondrial respiration, and , with K c and K o being the Michaelis-Menten constants for Rubisco CO 2 fixation and oxygen inhibition, and O is the oxygen concentration in the air (21%). Conversely, the RuBP-limited assimilation rate is constrained by the rate of electron transport, J, and can be expressed as where the electron transport rate is given by J=α p ε m Q, and Q is the irradiance, α p is the leaf absorptivity, and ε m is the maximum photochemical efficiency (Genty et al., 1989). To avoid discontinuities in A net due to an abrupt transition from one limitation to another, the minimum function in Equation 1 has often been replaced by a quadratic function, at the cost of introducing an additional curvature parameter. An alternative approach is to approximate Equation 1 by a hyperbolic function ,

≈
When c k c / 2 is approximately unity, both Rubisco and RuBP regeneration rates exert comparable limitations on photosynthesis. Hereafter, this regime is referred to as the co-limitation regime. Under CO 2 -limited (or light-saturated) conditions in which k 1 =V c,max and k 2 =K cair , the optimal solution is identical to the one obtained by Katul et al. (2010) for non-linear photosynthetic kinetics without light limitation. Based on Equation 4, net photosynthesis is obtained as A net =A C,J -R d .
Although there are numerous physiological and anatomical traits that underlie the development of the CO 2concentrating mechanism in C 4 plants (e.g. McKown and Dengler, 2007;Sage et al., 2012), for modelling purposes, the simplest description of the effect of such a pump is to assume that the CO 2 concentration at the site where photosynthesis occurs is c c =ηc i , where η represent the strength of the CO 2concentrating pump. The value of η encompasses not only the development of C 4 biochemistry across the evolutionary gradient of species, but also biochemical and anatomical features that affect mesophyll conductance. In C 4 species, η>1 (Manzoni et al., 2011); while it is slightly smaller than unity in C 3 species due to the need to diffuse CO 2 through the mesophyll, the lack of specific data on mesophyll conductance meant this had to be neglected and η=1 was set for C 3 species.
In the following, the pump strength, η, is estimated from the slope of the A net (c i ) curve. Employing this simple description of the CO 2 -concentrating mechanism results in a simpler photosynthesis model than by considering explicitly PEPCase kinetics (Collatz et al., 1992;Laisk and Edwards, 2000;von Caemmerer, 2000von Caemmerer, , 2013Vico and Porporato, 2008), thereby allowing data sets collected across different experiments and conditions to be compared. Nevertheless, the parameter η can be linked to the kinetics of PEPCase. The CO 2 concentration in the stomatal cavity (c i ) is assumed to be transported by PEPCase activity and the shuttling of C 4 acids to the bundle sheath (the site of photosynthesis), where the CO 2 concentration reaches c bs . When PEPCase kinetics are assumed to be linear for illustration (but see von Caemmerer, 2000 for more detailed and non-linear models), then where α is the kinetic constant of the process. Setting V p =A net (from Equation 4) to guarantee continuity in the C fluxes from the stomatal cavity to the site of photosynthesis provides an equation to be solved for η, leading to Equation 6 shows that the pump efficiency η in principle depends on the photosynthetic parameters as well as c i . However, neglecting R d and assuming Γ*<<c i and αc i <<k 1 , it can be shown that η α = k k 2 1 / , which is a constant at a given temperature and light level. Therefore, when respiration is small and photosynthetic capacity is large, a constant efficiency η captures the main effect of the PEPCase on the photosynthetic rate. Outside these simplifications, the assumption of a constant η can only be regarded as a firstorder approximation.
The combination of the hyperbolic function in Equation 4 with the simplified description of the CO 2 pumping mechanism based on η (i.e. c c =ηc i ) provides a tool to describe CO 2 demand within a common framework valid across the C 3 to C 4 evolutionary continuum. Despite the inherent simplifications, this model is in good agreement with earlier, more complex photosynthesis models for C 3 -C 4 intermediates and C 4 species (von Caemmerer, 1989;Collatz et al., 1992) (data not shown; for an example of model comparison for C 3 species, see fig. 1 in Vico et al., 2013), thus lending support to the present approach.
The biochemical demand for CO 2 described by A C,J is met by CO 2 supplied by the atmosphere via Fickian diffusion at a rate given by where g s is the stomatal conductance and c a is the atmospheric CO 2 concentration. For a given c a , set of environmental conditions (such as Q and temperature), and physiological properties determining k 1 and k 2 , the atmospheric supply and biochemical demand for A C,J constitute two equations with three unknowns: g s , c a , and A net . Hence, one additional equation is needed to close this system of equations mathematically. This additional equation can take on the form of an optimality rule, whereby stomata are assumed to operate so as to maximize their carbon gain at a given water loss cost (Cowan and Farquhar, 1977;Hari et al., 1986). This hypothesis is equivalent to maximizing a Hamiltonian function H=A net -λE, where E=ag s D is the leaf transpiration rate (assuming a perfectly coupled canopy), and a=1.6 is the ratio of the molecular diffusivities of CO 2 to water vapour. Combining the biochemical demand with atmospheric supply so as to eliminate c i , and thereby expressing A C,J as a function of g s , inserting the outcome into the Hamiltonian, and setting ∂ ∂ H g s / =0, leads to a quadratic equation in g s . Solving this equation for g s results in a solution for optimal g s as a function of biochemical parameters (η, V c,max , K cair , R d , and Γ*), environmental conditions (c a and D), and the optimization parameter λ. The explicit functional form for optimal stomatal conductance is determined from the solution to the optimality problem as In Equations 9, 10, and 11, α 1 =k 2 +ηc a , α 2 =η(c a -γ), and γ=αλD. Therefore, the optimal stomatal conductance depends on λ, which by using the optimization condition can be shown to be equal to the definition of the marginal WUE, i.e.
Equation 12 provides a physical interpretation for λ, but does not give additional information (the optimization condition has already been used in Equation 8). Hence, λ needs to be determined to close the optimization problem mathematically. Although λ changes as a function of time when soil moisture declines during a dry period , under well-watered conditions or stable moisture levels, λ can be considered time-invariant. Before applying the proposed model, it is important to summarize its key assumptions and simplifications: (i) Photosynthetic kinetics are described by a hyperbolic function of c i bridging a CO 2 -limited regime (where A net scales linearly with c i ) and a light-limited regime (where A net depends solely on a light level). (ii) PEPCase kinetics are described by a single efficiency parameter η, which approximates more complex models well (Collatz et al., 1992;von Caemmerer, 2000) when respiration terms are small. Also mesophyll resistance is neglected, due to a lack of data across these species; this assumption implies that the estimated η could be inflated under dry conditions (though these are not the conditions considered when inferring the marginal WUE). (iii) Stomatal conductance is obtained from an optimization argument assuming that the marginal WUE is constanta reasonable approximation for experiments under controlled conditions and stable moisture levels . Thus, λ is used as a fitting parameter affecting the stomatal conductance in Equation 8.
Clearly, these assumptions could be relaxed, thereby improving realism. However, relaxing these assumptions reduces the ease of interpretation of the derived equations and the ability to compare across a wide range of data sets due to more required parameters. Once the optimal g s is determined, A C,J , E, and c i can then be computed. This model allows the quantification of A net and g s for C 3 , C 4 , and C 3 -C 4 intermediate species within a common framework and as a function of both environmental conditions (air temperature, Q, D, and c a ) and species-specific parameters (η, λ, V c,max , K cair , and Γ*)). As such, after showing that the modelled response of A net to changes in g s is well captured assuming optimal stomatal behaviour, the model is used to investigate how A net and WUE i are altered by changes in η, λ, and c a , thus following the steps of the hypothesized evolution of C 3 -C 4 intermediates and C 4 species from C 3 plants.  (Monson, 1989;Vogan and Sage, 2011). Environmental conditions (Q, D, c a , and leaf temperature) in model runs were matched to the measurement conditions described for the experimental data. The range in λ necessary to capture measured responses in gas exchange was explored in Flaveria species from all photosynthetic types.

Data availability and model parameterization
To parameterize the above model for Flaveria, V c,max values were derived for Rubisco from 15 Flaveria species that spanned C 3 to C 4 photosynthetic types using in vitro measurements of catalytic constants (or turnover numbers, k cat ) (Kubien et al., 2008) and Rubisco site concentrations from the same experiment (D. Kubien, personal communication) ( Table 2). The Michaelis-Menten constants K c and K o for Rubisco were also taken for each Flaveria species from Kubien et al. (2008). Rubisco kinetics were adjusted to 30 °C to match conditions in the carboxylation efficiency studies using correction equations and coefficients from Campbell and Norman (1998) (Table 2). K c and K o were temperature adjusted by multiplying their values at 25 °C by exp[q(T l -25)], where q is the temperature coefficient for that parameter (0.074 for K c and 0.015 for K o ) and T l is leaf temperature. where V c,max25 is the maximum carboxylation rate at 25 °C. The Γ* values for each of the five photosynthetic types were approximated using averaged values of Γ (the CO 2 compensation point) from Flaveria species in Ku et al. (1991), assuming that day respiration of mitochondria is small (R d =0.015V c,max ) and can be ignored (Table 2) The value for α p was set at 0.8 (based on values for C 3 and C 4 species in von Caemmerer, 2000 and Collatz et al., 1992, respectively), ε m was 0.1 mol mol -1 (similar to Norman and Campbell, 1998;Cheng et al., 2001;Taiz and Zeiger, 2010), and Q was set for the irradiance used in individual papers being modelled. Hence, α p ε m =0.08, resulting in α 1 =0.08Q when RuBP regeneration limits photosynthesis. This estimate is consistent with conventional values for C 3 species (Campbell and Norman, 1998; see table 14.1) though α p ε m may be more uncertain for C 4 species and C 3 -C 4 intermediates. For C 3 -C 4 intermediates, Monson (1989) and Monson and Jaeger (1991) report mid-day photosynthetic rates for several species including F. floridana between 15 μmol m -2 s -1 and 45 μmol m -2 s -1 at light levels ranging from Q=1500 μmol m -2 s -1 to 2000 μmol m -2 s -1 . Because A J J ≈ / 4 (assuming that Γ* is negligible in Equation 3), it follows that the measured A are consistent with the estimate J=0.08Q, which gives an A net of 40 μmol m -2 s -1 . This evidence supports the assumption that α p ε m is stable across photosynthetic types. A more rigorous parameterization would require direct observations of α p ε m or reliable V c,max -J max relationships across the C 3 -C 4 continuum.
Carboxylation efficiencies [CEs; i.e, the initial slope of the A net (c i ) curve] measured under saturating light for Flaveria species were taken from Krall et al. (1991) and Sudderth et al. (2007), citing Dai et al. (1996) , Therefore, knowledge of Γ, K cair , K c , and K o allowed an estimate of η for each Flaveria species.
Finally, the Vogan and Sage (2011) gas exchange data set was used to infer how λ changes across the evolutionary pathway from C 3 to C 4 species. In that study, a range of g s and A net values was obtained by altering the nitrogen availability for individuals of all photosynthetic types considered, while water was amply supplied, so λ can be considered time-invariant. As a consequence of different nutrient availability, a range of photosynthetic capacities and respiration rates were obtained. Since there is no way of knowing these biochemical parameters, a simplified but more robust approach to estimate λ was adopted that only requires gas exchange rates and photosynthetic type-averaged Γ and η (assuming λ is substantially unaltered by nutrient availability). For this step, instead of using the definition (Equation 12), which requires knowledge of all the photosynthetic parameters, the stomatal optimization model was simplified by selecting light-saturated conditions, so that R d ≈0 and the photosynthesis model is approximately linear. Following these simplifications, it can be shown that A g aD c net s a = − ( ) λ η Γ * / (Manzoni et al., 2011), which allows estimating λ through a linear least square regression of A net versus g s constrained through the origin for each photosynthetic type. In previous works on different species, this approach to estimate λ was compared with results obtained without these simplifications. Such comparison showed that the differences between the two approaches was rarely more than 20% across a wide range of environmental and physiological conditions (see fig. 4 in Katul et al., 2010), which is in the range of experimental variability [e.g. a mean standard deviation of 16% in light-saturated A net estimates across individuals in a range of C 3 , C 3 -C 4 intermediates, and C 4 species (Vogan et al., 2007)].
Gas exchange rates were also simulated under altered atmospheric CO 2 concentrations. In this analysis, all biochemical parameters were maintained constant, but the possibility was considered that the marginal WUE increases linearly with CO 2 concentrations (Manzoni et al., 2011). Simulations with constant λ estimated as described above were thus compared with simulations with λ(c a )=λ 400 (c a /400). Including CO 2 effects allows the robustness of the results to changes in λ to be tested.

Results and Discussion
Recent work has stimulated new interest in the role that transpiration demands may have played in the evolution of C 4 photosynthesis and traits associated with the C 4 syndrome (Taylor et al., 2011(Taylor et al., , 2012; Osborne and Sack, 2012; Griffiths References for values Sudderth et al. (2007), citing Dai et al. (1996 Kubien et al. (2008)  Data are taken from literature sources as outlined in the text (see also species-specific data points in Fig. 2 and Supplementary Table S1 at JXB online); λ and η are calculated values. et al., 2013). These studies have emphasized that C 4 photosynthesis not only benefits the carbon economy of a plant, but also has important implications for hydraulic traits, drought tolerance, and water use patterns, benefits that are maintained or enhanced when C 4 plants are exposed to the low c a conditions where C 4 photosynthesis evolved (Ripley et al., 2013). Here, λ is used as an 'index' of the cost of losing water in terms of carbon, and its variation along the evolutionary gradient from C 3 to C 4 photosynthesis is investigated.
Combining a stomatal optimization approach with measured biochemical parameters, realistic mean A net (c i ) curves for each photosynthetic pathway in Flaveria were computed ( Fig. 1A; Table 2). The corresponding estimated η values are reported in Fig. 1B. In the optimality model, recall that the parameter η represents an overall pump strength for the carbon-concentrating mechanism, which might naively have been expected to increase gradually from C 3 towards C 4 plants. Instead, the analysis here suggests that η was relatively stable and similar to that for C 3 species (η=1 or slightly above 1 due to unavoidable errors in the estimation) until reaching C 4 -like species. The relatively constant η between C 3 , Type I, and Type II Flaveria species occurred despite there being an increase in the initial slope of the A net (c i ) curve (e.g. the carboxylation efficiency) across these groups. Instead of being attributed to η, the steeper initial slopes in the Type I and Type II intermediates in comparison with the C 3 species were caused by higher V c,max values for Rubisco based on in vitro assays of the enzyme kinetic parameters (Table 2; Fig. 2A), consistent with positive selection on Rubisco across the C 3 to C 4 gradient (Kapralov et al., 2011). Thus, there was no increase in η until the C 4 -like species were reached; at this point, η values were about half-way between those of the full C 3 and C 4 photosynthetic groups. The greater variation in η estimates in species closer to the C 4 end of the spectrum is therefore probably due to the greater range of pump strengths possible as the carbon-concentrating mechanism is established and to the species-level diversity in V c,max values (Supplementary Table S1 at JXB online). While there were sharp changes in in vitro Rubisco V c,max between C 3 species and the Type I and Type II intermediates, the change in the K cair of Rubisco across the photosynthetic groups was more gradual until reaching the C 4 -like species (Fig. 2B), implying that these enzyme kinetic traits are not necessarily linked. The Γ* dropped sharply as η increased slightly above a value of 1 and then flattened (Fig. 2C).
While it might, a priori, seem reasonable to expect a steady increase in WUE i from C 3 species through the intermediate Flaveria species and to full C 4 plants, this was not borne out by the data, in agreement with published findings. Huxman and Monson (2003) showed that the WUE i s of C 3 -C 4 intermediates were similar to C 3 WUE i values, while C 4 WUE i values were considerably higher. Vogan and Sage (2011) also found no evidence for a gradual transition in the slope between A net and g s in C 3 -C 4 intermediates, but rather a sharp increase between Type II intermediates and C 4 -like intermediates. [Note that WUE i is a proxy for λ if a linear A net (c i ) curve is assumed.] In our re-analysis of the Vogan and Sage (2011) data set, the reported gas exchange data could be readily described with the optimality model for C 3 , and Type I and Type II intermediates using the estimated changes in η (as in Fig. 1B), but without significant changes in λ across photosynthetic pathways (Fig. 3). This result implies that there is little change in the relationship between carbon and water from that of a C 3 species in these early intermediate steps. However, in C 4 -like intermediates, a strong C 4 pump (i.e. η=8) was accompanied by a quadrupling of λ compared with that used to characterize the data for Type I and II intermediates. Thus, the stomatal optimization approach could be successfully used to capture key changes in the measured relationship between A net and g s across the C 3 -C 4 spectrum using the estimated η values, but only when the marginal WUE of the C 4 -like and C 4 species was modelled to be 4-fold greater than that of the C 3 species (Fig. 3). This increase in λ unambiguously indicates a higher carbon cost for losing water in the C 4 -like and C 4 species. In the optimization model, the long-term c i /c a dictates λ, because λ∞(1-c i /c a ) 2 . Therefore, the increase in λ is generated by a decline in c i (where c a is assumed to be 400 μmol mol -1 ). This finding suggests that the increase in C 4 WUE i values, the increase in λ, and the decline in c i (as expected by the presence of a C 4 pump) are all interconnected and predicted from the proposed stomatal optimization model. Since C 4 photosynthesis evolved under low c a , with the transition in Flaveria occurring within the last 3 million years (Sage et al., 2012), the effect of varying η and λ on A net and WUE i was further investigated under both current (400 μmol mol -1 ) and low CO 2 concentrations (280 μmol mol -1 ; Figs 4, 5), allowing V c,max , K cair , and Γ* to vary along with η as per the relationships in Figs 1 and 2, but keeping λ constant. In the results from both current and low c a levels, increases in η initially induce a sharp increase in A net , as more CO 2 is concentrated around Rubisco, with a diminishing response above a certain η (η=10 for 400 μmol mol -1 CO 2 ; Fig. 4A). Moreover, higher values of λ decrease A net in both environments, so that the slight changes in η and λ in Type I and II species compared with C 3 plants generate a similar A net in the three groups (Fig. 4A). Increased c a (from 280 μmol m -2 s -1 to 400 μmol mol -1 ) elevated A net in C 3 species by 80% due to greater substrate availability (Fig. 4B). Compared with a C 3 Flaveria at these low c a , C 3 -C 4 intermediates also have higher A net in modern CO 2 concentrations, with a gradual increase in the stimulation of A net with respect to C 3 values (Fig. 4B). In contrast to the A net results, increases in η have little impact on WUE i when λ is small, namely from C 3 species to Type I or II species (shown for 400 μmol mol -1 CO 2 in Fig. 5A). Moreover, while increases in c a have increased WUE i of C 3 species by 30%, there is no gradual rise in WUE i across the gradient of photosynthetic types, as there was with A net (Fig. 5B). Instead, compared with a C 3 Flaveria at 280 μmol mol -1 CO 2 , Type I and Type II intermediates have a similar 30% stimulation in WUE i , while C 4 -like and C 4 species show a more than tripling of their WUE i stimulation at modern CO 2 levels (Fig. 5B).
If the marginal WUE is assumed to increase with atmospheric CO 2 (e.g. Katul et al., 2010;Manzoni et al., 2011), the predicted g s at c a =280 μmol mol -1 increases. As a consequence, photosynthesis also increases and the ratios of net photosynthesis at c a =400 μmol m -2 s -1 and 280 μmol mol -1 therefore decrease (Fig. 4B). Because the positive effect of changes in λ is larger on transpiration than on net photosynthesis, the WUE i at the lower c a decreases. As a result, the ratio of WUE i at current and low CO 2 concentrations is higher than when assuming a constant λ (Fig. 5B).
The modelled changes in leaf-level performance between photosynthetic groups under low c a are shown in Fig. 6. This figure quantifies the advantages of the intermediate and C 4 species over the basal C 3 state. At low c a , the estimated changes in η and λ for intermediate species provide a continuous, smooth gradient of increasing carbon gain, over a C 3 Flaveria species (Fig. 6A). This trend is robust to changes in the λ(c a ) relationship, as indicated by minor differences between filled and open symbols. A Type I intermediate has a 15% higher A net than a C 3 species, which could provide a competitive edge to the intermediate in a low CO 2 environment; a similar jump in A net is seen for each photosynthetic group along the evolutionary trajectory, in agreement with a recently proposed smoothly increasing fitness landscape for C 4 evolution (Heckmann et al., 2013). However, the same pattern is not apparent in the WUE i results (Fig. 6B). There is no difference in the WUE i estimated at 280 μmol mol -1 CO 2 between C 3 , Type I and Type II Flaveria species. Instead, significant increases in WUE i are only achieved in C 4 -like and C 4 species, implying that the driving force for the initial steps ; and (C) the CO 2 compensation point in the absence of mitochondrial respiration (Γ*) for C 3 , C 4 , and C 3 -C 4 intermediate species. Solid lines are fit to data; vertical dotted lines indicate η=1. C 3 species, purple circles; Type I species, blue diamonds; Type II species, green triangles; C 4 -like species, yellow inverted triangles; C 4 species, red squares. Fig. 3. Relationships between stomatal conductance to CO 2 (g s ) and net CO 2 assimilation rate (A net ) in Flaveria species across the C 3 to C 4 photosynthetic range. Data points are from Vogan and Sage (2011); lines are obtained by analytical least-square fitting of the water use efficiency λ, employing a linearized version of the stomatal optimization model (Manzoni et al., 2011) for analytical tractability. Modelled relationships between net CO 2 assimilation rate (A net ), marginal water use efficiency (λ), and the CO 2 -concentrating pump strength (η) modelled at current CO 2 concentrations (400 μmol mol -1 ); V c,max , K cair , and Γ* vary with η according to the relationships in Fig. 2; vapour pressure deficit (D) was set to 1.5 kPa, leaf temperature to 30 °C, Q to 1500 μmol m -2 s -1 . Mean values of λ and η for each of the five photosynthetic types are indicated on the surface. (B) The ratio of A net at current atmospheric CO 2 levels versus A net of C 3 Flaveria at low atmospheric CO 2 concentrations (280 μmol mol -1 ) (A net , 400 /A net C3 , 280 ) for each photosynthetic group; means ±SE across species; filled symbols refer to constant λ, open symbols to λ increasing linearly with c a ; the dashed-dotted line indicates a ratio of 1. C 3 species, purple circle; Type I species, blue diamond; Type II species, green triangle; C 4 -like species, yellow inverted triangle; C 4 species, red square. Modelled relationships between instantaneous water use efficiency (WUE i , the ratio of A net to E), marginal WUE (λ), and the CO 2concentrating pump strength (η) modelled at current CO 2 concentrations (400 μmol mol -1 ); V c,max , K cair , and Γ* vary with η according to the relationships in Fig. 2; vapour pressure deficit (D) was set to 1.5 kPa, leaf temperature to 30 °C, Q to 1500 μmol m -2 s -1 . Mean values of λ and η for each of the five photosynthetic types are indicated on the surface. (B) The ratio of WUE i at current atmospheric CO 2 levels versus the WUE i of a C 3 Flaveria at low atmospheric CO 2 concentrations (280 μmol mol -1 ) (WUE i400 /WUE C3 i280 ) for each photosynthetic group; means ±SE across species; filled symbols refer to constant λ, open symbols to λ increasing linearly with c a ; the dashed-dotted line indicates a ratio of 1. C 3 species, purple circle; Type I species, blue diamond; Type II species, green triangle; C 4 -like species, yellow inverted triangle; C 4 species, red square. towards C 4 photosynthesis in this group was carbon based and not related to increasing WUE i .
Many of the features considered to pre-adapt a group to evolve C 4 photosynthesis are related to leaf hydraulics, including increased vein density and enlarged bundle sheath cell size (McKown et al., 2005;McKown and Dengler, 2007;Osborne and Sack, 2012;Sage et al., 2012;Griffiths et al., 2013). Stomatal anatomy also evolves along the transition from C 3 to C 4 photosynthesis, with C 4 species having lower maximum stomatal conductance (due to either lower stomatal density or smaller stomatal size) than C 3 congeners (Taylor et al., 2012). While changes in whole-plant physiology are outside the scope of this work, these findings have stimulated interest in the role of plant water relations in the evolution of C 4 photosynthesis. The results here indicate that while there is a gradual increase in carbon gain across the range from C 3 to C 4 , there is no corresponding transition in either WUE i or λ. Rather, increases in leaf-level WUE i are only seen between Type II intermediacy and C 4 -like species (as noted by Kocacinar et al., 2008;Vogan and Sage, 2011). However, this transition is accompanied by a rise in λ, indicating that a higher carbon cost is being incurred for water loss in C 4 -like and C 4 species than in C 3 , or Type I or Type II intermediate species of Flaveria. This corresponds to the coordinated set of changes to the hydraulic architecture of Flaveria species, including lower leaf specific hydraulic conductivity and greater cavitation resistance in C 4 and C 4 -like than C 3 species (Kocacinar et al., 2008), emphasizing the importance of the transition from having a functional C 4 cycle for both the carbon and water economies of the plant.

Conclusions
Using a stomatal optimization approach, the full range of C 3 , C 3 -C 4 intermediates. and C 4 gas exchange could be realistically modelled with the addition of a C 4 pump strength parameter η, describing the effects of the C 4 carbon-concentrating mechanism. The results here showed that, to capture the patterns apparent in measured gas exchange data, the carbon-based cost of losing water (λ) between C 3 , and Type I and Type II intermediates could be maintained constant, but λ had to be quadrupled to model C 4 -like and C 4 Flaveria (at least within the confines of the optimality assumption of stomata). When leaflevel fluxes were modelled at low CO 2 , there was no evidence for a greater WUE i in the C 3 -C 4 intermediates (compared with a C 3 Flaveria) until they developed a full C 4 cycle. However, the model results suggest a steady increase in net carbon fixation rates across the C 3 to C 4 photosynthetic range. While this implies that carbon, not water, was the main driving pressure for the early steps of C 4 evolution in this genus, the increase in λ indicates that there was a fundamental shift over the evolution of C 4 photosynthesis between the relative costs of carbon and water, resulting in higher carbon costs of water losses.

Supplementary data
Supplementary data are available at JXB online. Table S1. Parameter table. Fig. 6. Comparison of (A) modelled photosynthetic rates and (B) modelled WUE i among Flaveria species with different photosynthetic types at c a =280 μmol mol -1 , expressed as ratios over the mean A net and WUE i for C 3 species at c a =280 μmol mol -1 . Symbols represent means ±SE across species (for fixed C 3 A net and WUE i values); filled symbols refer to constant λ, open symbols to λ increasing linearly with c a ; the dashed-dotted line indicates a ratio of 1. Other parameters are as in Figs 4 and 5.