Evolution of C₄ plants: a new hypothesis for an interaction of CO₂ and water relations mediated by plant hydraulics

Abstract

C₄ photosynthesis has evolved more than 60 times as a carbon-concentrating mechanism to augment the ancestral C₃ photosynthetic pathway. The rate and the efficiency of photosynthesis are greater in the C₄ than C₃ type under atmospheric CO₂ depletion, high light and temperature, suggesting these factors as important selective agents. This hypothesis is consistent with comparative analyses of grasses, which indicate repeated evolutionary transitions from shaded forest to open habitats. However, such environmental transitions also impact strongly on plant–water relations. We hypothesize that excessive demand for water transport associated with low CO₂, high light and temperature would have selected for C₄ photosynthesis not only to increase the efficiency and rate of photosynthesis, but also as a water-conserving mechanism. Our proposal is supported by evidence from the literature and physiological models. The C₄ pathway allows high rates of photosynthesis at low stomatal conductance, even given low atmospheric CO₂. The resultant decrease in transpiration protects the hydraulic system, allowing stomata to remain open and photosynthesis to be sustained for longer under drying atmospheric and soil conditions. The evolution of C₄ photosynthesis therefore simultaneously improved plant carbon and water relations, conferring strong benefits as atmospheric CO₂ declined and ecological demand for water rose.

1. Photosynthetic conservatism and diversity

Photosynthesis has evolved only once, and every photoautotrophic organism on Earth uses the same ‘C₃ pathway’ [1]. This biochemical cycle employs the enzyme Rubisco to fix CO₂ into a five-carbon acceptor molecule, producing three-carbon organic acids, upon which ATP and NADPH produced from the light reactions are deployed to generate sugars and to regenerate the acceptor molecule. The pigments and proteins involved in C₃ photosynthesis are highly conserved across photosynthetic organisms, and this pathway operates unmodified in the majority of species, termed ‘C₃ plants’. However, the basic C₃ pathway has also been augmented by carbon-concentrating mechanisms (CCMs) in multiple lineages, many of which evolved during the Early Neogene following a massive depletion of atmospheric CO₂ [2–5].

‘C₄ photosynthesis’ is a collective term for CCMs which initially fix carbon into four-carbon organic acids via the enzyme phosphoenolpyruvate carboxylase (PEPC) [6], and then liberate CO₂ from these C₄ acids to feed the C₃ pathway within a compartment of the cell or leaf [7,8] (figure 1a). The compartment is isolated from the atmosphere and resists CO₂-leakage, so that CO₂ is enriched at the active site of Rubisco [12] (figure 1a). Coordination of C₄ and C₃ biochemical pathways requires complex changes to metabolism, and the compartmentation of these pathways usually relies on a specialized leaf anatomy (figure 1b). C₄ photosynthesis is therefore a complex trait based on the transcriptional regulation of hundreds of genes [13], coupled with post-transcriptional regulation [14] and the adaptation of protein-coding sequences [15].

Figure 1.

Mechanism of C₄ photosynthesis. (a) Simplified schematic of the C₄ syndrome, showing how the C₃ pathway is isolated from the atmosphere in most C₄ species within a specialized tissue composed of bundle sheath cells (BSC). The C₄ pathway captures CO₂ within mesophyll cells (MC) using the enzymes carbonic anyhdrase (CA) and phosphoenolpyruvate carboxylase (PEPC). It then transports fixed carbon to the BSC where decarboxylase enzymes (DC) liberate CO₂, which accumulates to high concentrations around Rubisco. (b) Transverse section of a C₄ leaf, showing the arrangement of MC and BSC. In this picture, the BSC are thicker walled, are stained darker and form rings surrounding the veins (adapted from Watson & Dallwitz [9]). Enlarged BSC relative to MC and close vein spacing are typical of C₄ leaves, and this pattern is referred to as ‘Kranz anatomy’. (c) Explanation of how variation in CO₂ and temperature favours C₃ or C₄ species [10,11]. The schematic shows the range of CO₂ partial pressures and temperatures predicted to favour the growth of either C₃ or C₄ species, based on the maximum quantum yield of photosynthesis. Quantum yield is a measure of photosynthetic efficiency, which declines in C₃ plants as photorespiration increases at low CO₂ and high temperature, (reproduced with permission from Edwards et al. [3], which was adapted from Ehleringer et al. [11]).

Despite the complexity of C₄ photosynthesis, it has been recorded in more than 60 plant lineages [16]. This striking evolutionary convergence probably arises because the pathway is constructed from numerous pre-existing gene networks [17], and altered levels and patterns of expression of enzymes that are already present in C₃ leaves [18–20]. Many of the known C₄ lineages occur in clusters, suggesting that they share early steps on the evolutionary trajectory towards C₄ photosynthesis, taking an independent path only during later stages of the process [21].

In recent years, evidence from genomics, molecular genetics, physiology, ecology, biogeography, evolutionary biology and geosciences has enriched our understanding of when, where and how C₄ photosynthesis evolved. Here, we extend previous work that focused on why the pathway evolved, based on the environmental conditions that drove natural selection. We begin by reviewing the well-established current hypothesis that atmospheric CO₂ depletion, high temperatures and open environments selected for the C₄ pathway as a means of directly improving photosynthetic rate and efficiency. Our main objective is to introduce a new dimension to these ideas, by proposing that these same environmental conditions—CO₂ depletion, high temperatures and open environments—as well as seasonal drought, would also select for C₄ photosynthesis for an additional reason; i.e. to compensate for the strain on the plant hydraulic system resulting from excessive demand for water transport. Our hypothesis is consistent with recent comparative analyses of ecological niche evolution and plant physiology, which suggest important effects of the C₄ pathway on plant–water relations. We support our proposal with evidence from the literature, and mechanistic models that integrate the latest understanding of how hydraulics, stomata and photosynthesis are coordinated within leaves. Our central focus is on grasses, but we complement our analysis with additional evidence from eudicots.

2. Environmental selection on photosynthetic efficiency

Atmospheric CO₂ depletion has long been advocated as the primary selection pressure for C₄ CCMs, through its differential effects on the efficiency of C₃ and C₄ photosynthesis [22]. This difference arises because the active site of Rubisco is unable to discriminate completely between CO₂ and O₂, and catalyses the fixation of both molecules [23,24]. The oxygenation reaction generates toxic intermediates that must be metabolized via photorespiration to render them harmless and to recover carbon. Oxygenation renders photosynthesis less efficient because it competes directly with carboxylation (CO₂-fixation), and because photorespiration consumes the products of photochemistry and liberates CO₂. In a C₃ plant, the ratio of carboxylation to oxygenation (and therefore photosynthetic efficiency) decreases rapidly with declining atmospheric CO₂, especially at high temperatures [25]. In contrast, by fixing the bicarbonate ion rather than CO₂, the C₄ pathway does not confuse CO₂ with O₂ (figure 1a). Furthermore, by isolating Rubisco from the atmosphere and concentrating CO₂ at its active site [26], it also minimizes oxygenation in the C₃ pathway. However, energy required to run the C₄ CCM imposes a cost on photosynthetic efficiency under all conditions [27,28]. This means that the efficiency of C₄ photosynthesis is only greater than the C₃ type under conditions that promote high rates of photorespiration [19]. Low atmospheric CO₂ and high temperatures are considered especially important in favouring C₄ photosynthesis, with a ‘crossover threshold’ for CO₂ of 35–55 Pa and temperatures of 25–30°C (figure 1c; [10,11]).

A further physiological difference between C₃ and C₄ species arises because the carboxylation reaction of Rubisco is strongly limited by its substrate when CO₂ falls below approximately 70 Pa at the active site [29]. Resistances to CO₂ diffusion from the atmosphere to the chloroplast mean that this limitation arises when atmospheric CO₂ levels fall below approximately 100 Pa. In contrast, significant CO₂-limitation only occurs in C₄ plants at atmospheric CO₂ levels of less than 20 Pa [30]. The CO₂-saturation of Rubisco in C₄ photosynthesis means that in high light environments the enzyme reaches its saturated catalytic rate, maximizing the photosynthetic difference between C₃ and C₄ species. As a consequence, in open habitats, the ‘crossover threshold’ is raised to higher CO₂ concentrations and lower temperatures [31]. Conversely, the cool shade of forest understorey environments offers little benefit for the C₄ pathway over the C₃ type [32], although once C₄ evolves in a lineage, descendent species may invade shaded habitats by modifying their tissue costs, allowing them to maintain an advantage in photosynthetic rate over co-occurring C₃ species [33].

Water relations have previously been proposed to influence the evolution of C₄ photosynthesis in an indirect way. For terrestrial vascular plants, the loss of water is an inevitable cost of photosynthesis, regulated by turgor-mediated decreases in the aperture of stomatal pores. The partial closure of stomata to conserve water in arid and saline soils or dry atmospheric conditions (characterized by high vapour pressure deficit (VPD)) has been hypothesized to select for the C₄ pathway via indirect effects on photosynthetic efficiency [34]. Thus, reduced stomatal aperture (i) restricts the CO₂ supply to photosynthesis and (ii) decreases transpiration, thereby reducing latent heat loss and raising leaf temperature. Both effects increase photorespiration, depressing the efficiency of C₃ photosynthesis, and favouring the C₄ type.

Therefore, the general expectation based on physiological evidence is that declining atmospheric CO₂ should select for C₄ photosynthesis in hot, open and dry or saline environments, where photorespiration is especially high in C₃ species [19].

3. Ecological drivers of c₄ pathway evolution

Recent data on the timing of C₄ origins and geological history have supported these ideas for the importance of low CO₂ and high temperature and irradiance, but also highlight the importance of aridity. First, the modelling of evolutionary transitions from C₃ to C₄ photosynthesis using time-calibrated molecular phylogenies indicated that C₄ origins have all occurred over the past 30 Myr, with no difference in timing between monocot and eudicot lineages (figure 2) [35–37]. Secondly, multiple geological proxies suggested that atmospheric CO₂ has remained below 60 Pa for most of this 30 Myr interval (figure 2), after a dramatic decline during the Oligocene (23–34 Ma) that corresponds to the onset of Antarctic glaciation [4]. Therefore, C₄ photosynthesis does seem to have evolved in a CO₂-depleted atmosphere, within the ranges of uncertainty that are inherent to phylogenetic and geological evidence [4,37].

Figure 2.

Geological history of atmospheric CO₂ and the estimated ages of C₄ evolutionary origins. The palaeo-atmospheric CO₂ history of the Cenozoic is reconstructed from multiple independent proxies (pale grey circles), with a smoothed line of best fit encompassing all of the evidence (reproduced with permission from Beerling & Royer [4]). The estimated ages of C₄ evolutionary origins in grasses (dark grey horizontal bars) and eudicots (black horizontal bars) were obtained using phylogenetic inference and calibration to fossils [35]. Thick bars represent uncertainty in the position of each C₄ evolutionary origin on the phylogeny, while thin bars indicate uncertainty in dating of the phylogeny (reproduced with permission from Christin et al. [35]).

The hypothesis that high temperatures select for C₄ photosynthesis has been supported for 30 years by invoking the observation that species richness of C₄ grasses increases along latitudinal and altitudinal temperature gradients [32,38,39]. However, phylogenetic comparative analyses have shown that C₄ species do not live in warmer environments than their closest C₃ relatives. First, Edwards & Still [40] showed that the absence of C₄ species from high altitudes in the predominantly exotic grass flora of Hawaii [39] is better explained by phylogenetic history than photosynthetic pathway. The exclusively C₃ lineage Pooideae is most speciose at cool, high elevations. However, species of the PACMAD lineage are most numerous in the warm lowlands, irrespective of whether they use C₃ or C₄ photosynthesis. Edwards & Smith [41] further investigated this pattern by reconstructing the evolution of temperature niche in the world's grasses. Their analysis indicated that grasses originated in the tropics. The C₃ and C₄ species of the PACMAD clade have remained predominantly in these warm environments, irrespective of photosynthetic pathway, while Pooideae have adapted to and radiated in low-temperature environments. Thus, C₄ photosynthesis did evolve at high temperatures, but the major innovation that caused ecological sorting of grasses along temperature gradients was the adaptation of certain C₃ lineages to cold conditions [41].

Comparative analyses also support the hypothesis that the C₄ pathway in grasses evolved in open environments. First, by modelling the rate of evolutionary transitions between C₃ and C₄ photosynthesis, and shaded and open habitats, Osborne & Freckleton [42] showed that C₄ origins were significantly more likely to have occurred in open than shaded environments. Secondly, Edwards & Smith [41] quantified the shift in environmental niche that is correlated with evolutionary transitions from C₃ to C₄ photosynthesis. The origins of C₄ photosynthesis were generally associated with migration from an aseasonal tropical niche into a seasonal, sub-tropical one, an ecological shift consistent with a transition from moist tropical forest to drier, more open woodland or savannah habitats [41]. These complementary analyses suggest that C₄ photosynthesis evolved in C₃ species that had migrated out of their ancestral niche in tropical forests, and invaded open sub-tropical woodland or savannah habitats. The C₄ pathway, therefore, seems to be a key adaptation to one of the most important ecological transitions in the evolutionary history of grasses [43], which ultimately enabled the assembly of the tropical grassland biome.

The proportion of C₄ species in eudicot floras increases along gradients of rising aridity [11]. Recent comparative analyses at the regional and global scales show that, in addition to preferring open habitats, C₄ grasses have also sorted into drier environmental niches than their C₃ relatives [40–42]. However, for grasses, there is no evidence that C₄ photosynthesis is more likely to evolve in xeric than mesic habitats [42]. Rather, the distribution of C₄ species in dry areas can be explained by two inferences from comparative analyses: (i) that C₄ origins were accompanied by shifts to a drier ecological niche within the humid sub-tropics [41] and (ii) a greater likelihood that C₄ than C₃ lineages will invade very dry (xeric) environments [42]. In some systems, C₄ grasses tolerate greater aridity than C₃ species of adjacent areas; for example, it has been argued that certain C₄ grasses of the Kalahari occur in areas too dry for the C₃ type to persist [44]. Water relations clearly play an important role in the ecology and biogeography of both C₄ monocots and C₄ eudicots.

A corpus of physiological work and comparative analyses therefore supports the theory of how low atmospheric CO₂ drove selection for improved photosynthetic rate and efficiency in hot and open environments over the last 30 Myr. What has been missing is an understanding of the importance of plant–water relations in differentiating photosynthetic types in such environments.

4. Strain on plant–water relations in a co₂-depleted atmosphere

Multiple strands of geological, ecological and physiological evidence indicate that a restriction in water supply and an increase in evaporative demand were important ecological factors during the evolution of C₄ species. First, permanent ice sheets of low CO₂ ‘icehouse’ climate intervals are known to reduce atmospheric moisture levels, with cool temperatures reducing the intensity of the hydrological cycle and increasing climatic seasonality [45]. As a consequence, the CO₂-depleted ‘icehouse’ climate of the last 30 Myr has caused the ecological availability of water to decline across large parts of the Earth's surface.

Paleontological evidence reveals that open woodland, savannah and grassland vegetation had begun to extend over large areas of the tropics and subtropics by the Miocene (24–6 Ma) [3,46]. By analogy with processes in the modern world, these open tropical and sub-tropical ecosystems are likely to have been generated by seasonal aridity, edaphic conditions that exclude trees (including high salinity), and disturbance by fire and large mammalian herbivores [3,47–49]. Low atmospheric CO₂ may interact with each of these processes by limiting tree growth [50–52]. In fire-prone environments, this limitation means that trees are less likely to become large enough to survive surface fires [51,53]. Indeed, in contemporary mesic savannahs, woody plant cover is apparently increasing in response to rising CO₂ [53]. C₄ plants are generally short-statured herbs, and only trees in exceptionally rare cases (several species of Hawaiian C₄ Euphorbia are fully trees, including rainforest as well as dry forest species; and Haloxylon trees of West Asia have C₄ photosynthetic stems). The central role of seasonal aridity in reducing forest cover therefore means that the early C₄ plants living in open tropical and sub-tropical environments may well have been subjected to fire events and/or episodes of soil drying.

The demand for water imposed by potential evapotranspiration (PET) is also significantly greater for plants in open habitats than in shaded understorey environments. This environmental contrast is caused by a suite of interrelated microclimatic effects associated with tree cover, illustrated in figure 3 using field observations and a model of leaf energy balance and evaporation (appendix A). Micrometeorological data are shown in figure 3a,b for transects crossing a rainforest edge into adjacent pasture in tropical (Mexico) and temperate (New Zealand) localities [54,55]. Closed forest canopies typically intercept greater than 95 per cent of incident shortwave radiation (figure 3a,b). A model of leaf energy balance shows that this markedly reduces the net radiation and therefore the energy available to drive evaporation (latent heat flux) at ground level (figure 3c,d). Shading of the land surface under a forest canopy also causes a decrease in the air temperature at ground level (from 28 to 25°C in the tropical example, and from 10 to 5°C in the temperate example; figure 3). Therefore, the vapour pressure gradient driving transpiration, as indicated by the VPD, also declines (figure 3a,b). Finally, windspeed is lower in forested compared with open environments (figure 3a,b). This reduces the leaf boundary layer conductance to water vapour (figure 3e,f) and further slows the modelled rate of evaporation. The overall effect of this micrometeorological gradient is a massive difference in the PET modelled for leaves in forested compared with open environments (figure 3e,f; appendix A). In the examples illustrated in figure 3, modelled PET is close to zero in the humid forest understorey, but exceeds 10 mmol H₂O m⁻² s⁻¹ in the adjacent open pasture for both tropical and temperate climates (figure 3e,f).

Figure 3.

Micrometeorological gradient spanning the transition from forested to open habitats. Data are shown for (a,c,e) pasture at the edge of tropical rainforest and (b,d,f) temperate rainforest, plotted against distance into the forest (negative values for distance = pasture; positive values = forest). Micrometeorological observations of photosynthetically active radiation (PAR), vapour pressure deficit (VPD) and surface windspeed are shown for (a) Mexico [54] and (b) New Zealand [55]. From these data, net radiation, latent and sensible heat fluxes are calculated using the model outlined in appendix A for the (c) tropical and (d) temperate forests. Calculated values of potential evapotranspiration (PET) and boundary layer conductance (g_a) are also shown for the same (e) tropical and (f) temperate localities.

In fact, the risk of colonizing exposed habits depends on the actual rate of leaf transpiration (E), which is lower than PET, being determined by the coupling of micrometeorological effects with the leaf stomatal conductance to water vapour (g_s). The g_s is controlled by changes in stomatal aperture, which are regulated by leaf water status, photosynthetic rate and chemical signals reflecting the soil water status transmitted from roots to leaves [56]. The g_s plays a pivotal role in leaf gas exchange, limiting both the efflux of water and influx of CO₂, and the C₄ CCM causes a large shift in this trade-off between carbon gain and water loss. For any given value of g_s, the net rate of leaf photosynthetic CO₂ uptake (A) is greater for C₄ than C₃ species. This contrast is illustrated in figure 4a for interspecific comparisons of closely related C₃ and C₄ PACMAD grass species. Measurements were made under modern atmospheric CO₂ levels, and in high light and temperature conditions representative of a warm, open environment. The contrast is also modelled in figure 4b using models of leaf gas exchange for idealized C₃ [59] and C₄ [29] species (see appendix B). In the interspecific comparison, photosynthesis at 30°C can span the same range in C₃ and C₄ species, with one exceptionally high value of A in the C₃ species exceeding the highest values observed in the C₄ species (figure 4a; [57]). However, high A for C₃ species comes at enormous cost in terms of g_s (figure 4a,b), and elevated rates of CO₂-fixation are therefore achieved with far greater water economy in C₄ than C₃ leaves (i.e. with greater water-use efficiency (WUE), defined as A relative to E). The ecological significance of this difference is underscored by the fact that the exceptionally high C₃ value of A in figure 4a was measured in the wetland species Phragmites australis, whereas the highest C₄ value was in the savannah species Eriachne aristidea [57].

Figure 4.

Illustration of the relationships of photosynthesis (A) to stomatal conductance (g_s) in C₃ and C₄ species [57,58]. (a) Interspecific comparison of PACMAD grass species under high light and the current ambient CO₂ level (filled symbols, C₃; open symbols, C₄; circles from Taylor et al. [58], photosynthetic photon flux density (PPFD) = 1300 µmol m⁻² s⁻¹, temperature = approx. 25°C, VPD = 1 kPa; triangles from Taylor et al. [57], PPFD = 2500 µmol m⁻² s⁻¹, temperature = 30°C, VPD = 0.8–1.5 kPa). Fitting a general linear model to these data showed that the slope of A on g_s was significantly steeper among C₄ than C₃ species (125 versus 29 µmol CO₂ mol⁻¹ H₂O, respectively; F_1,42 = 55.8, p < 0.0001), with a significant quadratic term that shows no interaction with photosynthetic pathway. (b) Intraspecific response simulated for a C₃ and a C₄ species by prescribing variation in g_s, and modelling A using the approach described in appendix B. Note the saturation response in C₃ and linear response in C₄, indicating the greater sensitivity of A to stomatal closure in C₄, despite achieving higher maximum A at its maximum g_s.

The greater WUE of C₄ compared with C₃ photosynthesis arises from both differences in stomatal aperture and the kinetic properties of the carboxylase enzymes employed by each pathway (figure 1a). PEPC in C₄ plants is able to fix carbon at a much higher rate than Rubisco in C₃ plants at in vivo substrate concentrations [29]. This allows the C₄ pathway to generate a much steeper air–leaf CO₂ gradient and higher rates of photosynthesis for a given value of g_s. The lower E and greater WUE of C₄ than C₃ plants was first recognized more than 40 years ago [60], although it is subject to ecological adaptation that can lead to significant interspecific variation and thus overlaps in the ranges of photosynthesis and transpiration for the two photosynthetic types [61]. However, recent work sampling multiple independent lineages of C₄ grasses from a range of different habitats showed that g_s is significantly lower in each lineage of C₄ species than in closely related lineages of C₃ grasses [57,58].

The need for a lower g_s to conserve water is especially strong when CO₂ levels fall and leaves tend to open stomata to maintain photosynthesis. Data compiled from five independent experiments demonstrate that g_s in both C₃ and C₄ plants increases dramatically in response to the depletion of atmospheric CO₂ to sub-ambient levels (figure 5). This negative relationship of g_s to CO₂ is apparently independent of the responsiveness of g_s to VPD [68], and partially or fully offsets the CO₂-limitation of photosynthesis at the cost of greater water use. A general linear model fitted to ln-transformed data shows a significant effect of photosynthetic pathway on the intercept of this relationship of g_s to CO₂ depletion, supporting the generality of higher g_s in C₃ than C₄ species (figure 5a). However, there is no difference in the slope of this relationship between C₃ and C₄ species (figure 5), indicating a similar relative increase in g_s with declining atmospheric CO₂ for C₃ and C₄ species. This finding is consistent with previous meta-analyses showing similar relative declines in g_s with CO₂ enrichment in C₃ and C₄ grasses [66,67]. Notably, because g_s is typically higher in C₃ than C₄ species, a similar relative response to CO₂ translates into a larger absolute effect (figure 5b). For example, for the model fitted in figure 5b, a depletion of atmospheric CO₂ from 100 to 30 Pa equivalent to the Oligocene CO₂ drop (figure 2) results in a rise in g_s from 0.23 to 0.61 mol H₂O m⁻² s⁻¹ in C₃, but only from 0.08 to 0.21 mol H₂O m⁻² s⁻¹ in C₄ species.

Figure 5.

Stomatal conductance (g_s) for the leaves of C₃ and C₄ plants grown and measured under a range of different CO₂ partial pressures, with an emphasis on experiments investigating the effects of CO₂ below the current ambient level of approximately 40 Pa (data sources: [30,62–65]; electronic supplementary material). The data compilation is based on literature searches for studies reporting the leaf gas exchange of plants under sub-ambient CO₂. However, values for elevated CO₂ were included when they were reported as part of the same CO₂-gradient studies. The fitted curve for the C₃ species is ln(g_s) = 2.16 − 0.78 ln(CO₂), and for the C₄ is ln(g_s) = 1.10 − 0.78 ln(CO₂). Data and curves are shown on (a) log and (b) linear plots to illustrate relative and absolute sensitivity to CO₂, respectively. The fitted curves produce effect sizes for g_s at elevated CO₂ in C₃ and C₄ grasses that fall within confidence intervals of previous meta-analyses [66,67]. Filled circles, C₃; open circles, C₄.

We explored the implications of these contrasting stomatal responses to CO₂ in C₃ and C₄ leaves by modelling leaf transpiration and energy balance (appendix A). Simulations with the model made the simplifying assumption that stomata respond only directly to CO₂, with no hydraulic or hormonal feedback on g_s. We compared the modelled response of E to CO₂ under four sets of micrometeorological conditions representing either an open pasture or a shaded rainforest understorey, in a humid tropical or temperate climate (using the data from figure 3). Our model simulations showed that falling atmospheric CO₂ drove larger increases of g_s and E in C₃ than C₄ species (figure 6a,b); this contrast was especially pronounced in open, tropical environments (figure 6a). For the simulations shown in figure 6a, we used a high relative humidity of 80 per cent (VPD = 0.6 kPa), which is typical of the moist tropics and the summer growing season in the humid subtropics (e.g. figure 3a). Under these conditions, simulated E in the C₃ species exceeded 6 mmol H₂O m⁻² s⁻¹ Mpa⁻¹ at a CO₂ level of less than 40 Pa (figure 6a). Assuming a leaf-specific whole- plant hydraulic conductance (K_plant) of 12 mmol H₂O m⁻² s⁻¹ in grasses, and a 50 per cent decline in K_plant under a soil–leaf water potential gradient of −1 MPa [69], this transpiration rate would be sufficient to cause 50 per cent failure of the hydraulic system. The threshold was not reached in a C₄ leaf under these conditions. In a drier atmosphere of 60 per cent relative humidity (VPD = 1.5 kPa), the threshold for 50 per cent hydraulic failure in the C₃ leaf was reached at CO₂ < 80 Pa, and in the C₄ at < 20 Pa (data not shown). The contrast was yet more pronounced at a VPD of 3.0 kPa, which is typical of hot, arid climates. Here, 50 per cent hydraulic failure occurred for the C₃ leaf at CO₂ < 150 Pa, and for the C₄ leaf at CO₂ < 50 Pa (data not shown).

Figure 6.

Modelled response of transpiration to CO₂ for C₃ and C₄ leaves in open (solid lines) and shaded rainforest understorey (dashed lines) conditions in either (a) humid tropical or (b) humid temperate climates. The model is described in appendix A. Horizontal dashed lines indicate the transpiration rate that would cause 50% hydraulic failure in the absence of feedbacks on stomatal conductance. Filled circles, C₃; open circles, C₄.

Thus, to avoid failure of the vascular system in open, tropical environments, hydraulic regulation of stomata, investment in hydraulic supply, or a reduction in leaf area [62], would be required at a considerably higher atmospheric CO₂ partial pressure in C₃ than C₄ species. Coupled with the inference that open tropical habitats selected for the C₄ pathway in grasses, this observation points strongly to plant–water relations as a potential driver of C₄ evolution.

5. Hypothesis for a central importance of hydraulics in c₄ evolution

The current consensus model for the evolution of C₄ photosynthesis has been developed over 25 years [19]. The evolutionary trajectory from C₃ to C₄ photosynthesis, via C₃–C₄ intermediates, is framed in terms of distinct phases for the sake of clarity; however, in reality, these are likely to overlap, and certain developments may occur earlier or later in the sequence. A simplified model of the phases is outlined in table 1, and Sage [19] provides both a comprehensive review of the evidence underpinning this model and the detailed mechanisms proposed. As with the evolution of any complex trait, each step must provide a selective advantage over the previous phase or be selectively neutral.

Table 1.

Hypothetical model for the evolution of C₄ photosynthesis, showing three phases that are each observed in extant C₃–C₄ intermediates. The scheme is a simplified version of that presented by Sage [19], incorporating new evidence [70].

phase 1. Evolution of ‘proto-Kranz anatomy’

A reduction in the distance between leaf veins and an enlargement in bundle sheath cells (BSC) (figure 1b) may evolve under dry environmental conditions to enhance leaf water status [19,71,72]. Since photosynthetic activity is limited in the BSC of most C3 leaves, increases in the number of chloroplasts may initially serve to maintain leaf light absorpance as the BSC occupy a larger fraction of the leaf. An increase in the numbers and asymmetric distribution of mitochondria in the BSC may establish a photorespiratory CO2 pump that shuttles glycine and refixes CO2within single BSC (see phase 2). This combination of traits has been termed ‘proto-Kranz anatomy’, and occurs in C3 species that are closely related to C3–C4 intermediates [70].

phase 2. Evolution of a photorespiratory CO2pump

Photorespiration liberates CO2 via a decarboxylation reaction catalysed by the enzyme glycine decarboxylase (GDC). The increasing localization of this enzyme in BSC mitochondria requires glycine to be shuttled between the mesophyll cells (MC) and the BSC, liberating CO2 in the BSC and allowing its refixation by Rubisco in this compartment (figure 1b). Efficiency of the glycine shuttle increases greatly if BSC walls are resistant to CO2 diffusion, thereby concentrating CO2 in the BSC. This type of photorespiratory CO2 pump is typical of C3–C4 intermediates [19].

phase 3. Evolution of the C4cycle

Increases in the PEPC activity of MC may occur initially to scavenge CO2 that leaks from the BSC, but eventually allows the fixation of CO2 from intercellular airspaces (figure 1a). Once this occurs, enhancement of decarboxylase enzyme activities in the BSC is needed to recover the acceptor molecule for carbon-fixation (figure 1a). As carbon-fixation by PEPC increases above that of Rubisco, the C3 cycle is increasingly confined to the BSC, and activities of the C4 and C3 cycles are coordinated. Finally, enzymes recruited into the C4 cycle adapt to their new catalytic environment via changes in turnover rate, substrate affinity and regulation. Changes in stomatal conductance occur during this phase [19].

We propose that atmospheric CO₂ depletion and open environments select indirectly for C₄ photosynthesis via plant–water relations at two points during the evolutionary sequence (table 1, phases 1 and 3). This mechanism acts in combination with the well-established effects of atmospheric CO₂ depletion and open environments on photorespiration. A direct role of water relations provides a clear explanation for many of the anatomical changes in the early evolution of C₃–C₄ intermediacy; these are observed in other lineages of C₃, C₄ and CAM species, which indicates that these steps are not rare or extraordinary events, but that C₄ evolution simply co-opts typical steps in adaptation to dry environments.

Evolution of ‘proto-Kranz anatomy’ (table 1, phase 1). Our hypothesized hydraulic mechanism is based on the vulnerability of C₃ leaves to desiccation and hydraulic failure under conditions of high evaporative demand in hot, open environments. Indeed, as described above, the hydraulic vulnerability of leaves would have increased dramatically as C₃ grass species migrated from the understorey of a tropical forest into more open tropical environments. If stomata close to protect the hydraulic system, the plant eventually faces carbon starvation through photorespiration and the depletion of carbon stores [73,74]. Carbon starvation is also exacerbated by atmospheric CO₂ depletion [75]. These conditions would select for greater hydraulic capacity in C₃ leaves, enabling greater g_s to achieve rapid rates of photosynthesis in periods when water is abundant, and reducing both the requirement for stomatal closure and the risk of hydraulic failure as stomata partially close in a drying soil or under increasing VPD.

Notably, the anatomical preconditioning required for C₄ is precisely that expected to evolve in C₃ plants under selection for greater tolerance of dry soil, open environments, high VPD and/or low CO₂. Previous studies of adaptation to these conditions within species or across closely related species within given lineages have shown increased vein densities, and thus shorter interveinal distances [76–79]. This higher vein density would permit greater g_s and higher A during periods with high water availability, to compensate for low CO₂. Indeed, the evolution of greater vein density in the early angiosperms may have allowed them to better cope with low CO₂, while avoiding stomatal closure, contributing to or driving their contemporary dominance of world vegetation [78,80]. The higher vein densities in C₄ than C₃ species may indicate an extension of that trend, i.e. an adaptation to the water deficit that accompanies higher demand from transpiration to maintain photosynthetic rate in low CO₂. In the same way that an increase in vein density may have enabled angiosperms to displace gymnosperms in dominating the world's forests, this trend in grasses may have provided a competitive advantage over grasses with lower vein densities, contributing to their dominance over large areas of the planet. The high vein densities in species with ‘proto-Kranz anatomy’ led to this feature being co-opted as an early part of the C₄ syndrome, providing enough tissue to later serve as the locus of sequestered C₃ metabolism (figure 1a,b) [19,71,72,81,82].

Similarly, the enlargement of bundle sheath during the early phase of C₄ evolution may have contributed water storage capacitance to the tissue [19,71]. Indeed, the evolution of such tissue in species with ‘proto-Kranz anatomy’ would be an extension of a frequently observed trend in certain plant lineages in which the species adapted to saline and drier climates have more strongly developed achlorophyllous, large-celled tissue. This tissue serves an apparent function for water storage either in the bundle sheath, mesophyll or hypodermal layers, and this trend of greater water storage with aridity is apparent within C₃ lineages with leaves [83,84] and phyllodes [85], but also within C₄ and CAM lineages [86,87] (M. J. Sporck & L. Sack 2011, unpublished data).

Evolution of the C₄ cycle (table 1, phase 3). The evolution of greater WUE is apparently an important step in C₄ evolution. It may be achieved in certain C₃–C₄ intermediates operating a photorespiratory pump (table 1, phase 2) through the enhancement of A for a given g_s (e.g. Heliotropium [88]). However, once the carboxylase activity of PEPC exceeds that of Rubisco (evolution of ‘C₄-like’ plants during phase 3, table 1), further improvements in WUE may occur through reduced g_s (e.g. Flaveria [89]). Thus, evolution towards C₄ probably first involved a suppression of photorespiration (table 1, phase 2) and then increased PEPC activity (table 1, phase 3), but only this last step enabled a reduction of g_s. These steps may even occur within C₃ species: populations of the grass Phragmites australis in hot, arid and saline environments show increasing investment in elements required for the C₄ cycle, including PEPC, decarboxylase enzymes and bundle sheath tissues, which may enhance both CO₂-fixation and WUE [90]. Thus, the engagement of CO₂-fixation via PEPC (table 1, phase 3) improves leaf–water relations, allowing a lower value of g_s for a given rate of photosynthesis, and thus a smaller absolute response of g_s to CO₂ depletion in C₄ leaves (figure 5b). This benefit would lead atmospheric CO₂ depletion and open environments to select for the C₄ cycle via plant–water relations, as well as via their effects on photosynthetic efficiency. Together, these physiological differences mean that leaves operating a fully integrated C₄ cycle are less prone than C₃ leaves to hydraulic failure or stomatal closure in hot, open environments. This contrast in sensitivity to water deficit increases dramatically under atmospheric CO₂ depletion.

A greater hydraulic conductance relative to demand, as would arise from the adaptation described, would result in a greater ability to maintain open stomata during soil drying events in C₄ than C₃ leaves, and a lower sensitivity of stomata to increases in VPD and to decreases in CO₂ (see §6). These improvements in water relations provide a plausible physiological basis for the greater likelihood for C₄ than C₃ grass lineages to invade xeric environments [42].

6. Hydraulic feedbacks on leaf physiology

Our hypothesis that C₄ evolved not only to improve photosynthetic efficiency per se, but also to reduce water stress by enabling low g_s, has additional implications that at first sight lead to inconsistency. While the C₄ species can achieve higher A for a given g_s, A declines more rapidly as g_s decreases (figure 4a,b). Because of this greater sensitivity of A to g_s, a C₄ plant must keep stomata open to maintain its advantage in A over C₃ plants. At first sight, this problem should render photosynthesis in C₄ plants particularly sensitive to soil drying owing to stomatal closure. As an initial test of our hypothesis for a hydraulics-mediated advantage of C₄ photosynthesis, and to further explore the physiological implications, we used a novel integrated model of leaf photosynthesis, stomatal and hydraulic systems to compare the physiological behaviour of C₃ and C₄ species (appendix B), with a particular focus on conditions of CO₂ depletion (low CO₂), atmospheric water vapour deficit (high VPD) and soil drying (low soil water potential). Given reasonable assumptions, these model simulations supported the hypothesis of a hydraulically based advantage of the C₄ syndrome under high VPD and low soil water potential, enabling stomata to remain open, and maintaining A at higher levels than C₃ species, with greatest differences at low CO₂.

We tested the role of hydraulic conductance in allowing g_s and A to be maintained during drought under varying VPD and atmospheric CO₂ in C₃ and C₄ species. We parametrized the model using data from the literature, and coupled this with photosynthesis models for C₃ and C₄ types (appendix B). Thus, we compared C₃ and C₄ species that differed in g_s (0.23 versus 0.10 mol m⁻² s⁻¹, respectively) but assumed the same responsiveness of g_s, and the same vulnerability of the hydraulic system, to declining leaf water potential. We tested three scenarios, with the C₄ species having: the same whole-plant hydraulic conductance (K_plant) as the C₃ species; double the K_plant; or half the K_plant (figures 7 and 8).

Figure 7.

Simulated response of mid-day operating stomatal conductance (as a percentage of maximum for hydrated leaves) and leaf water potential to drying soil at VPD of (a,b) 1 kPa and (c,d) 3 kPa, for a C₃ species and C₄ species with identical plant hydraulic conductance (K_plant), for a simulated C₄ species with double the K_plant, and for a simulated C₄ species with half the K_plant (corresponding to its value of g_s being approximately half that of the C₃ species). Note that the C₄ species maintains stomatal opening into drier soil and higher VPD than the C₃. Increasing the K_plant improves this ability in the C₄ species, whereas reducing the K_plant by half leads to very rapid decline of g_s at high VPD or in a dry soil. (a–d) Dashed line, C₃; black solid line, C₄; light grey solid line, C₄, 2 × K_plant; dark grey solid line, C₄, 0.5 × K_plant.

Figure 8.

Simulated response of light-saturated photosynthetic rate to a drying soil at low (20 Pa), ambient (40 Pa) or high CO₂ (80 Pa) and VPD of (a) 1 kPa or (b) 3 kPa, for a C₃ species and C₄ grass species with identical plant hydraulic conductance (K_plant), and for a simulated C₄ species with double the K_plant, and a simulated C₄ species with half the K_plant (corresponding to its value of g_s being approximately half that of the C₃ species). (a,b) Dashed line, C₃; black solid line, C₄; light grey solid line, C₄, 2 × K_plant; dark grey solid line, C₄, 0.5 × K_plant.

When the C₄ species had the same K_plant as the C₃, the C₄ was able to maintain g_s at a higher relative level (percentage of its maximum value) as the soil dried; this advantage over the C₃ was especially strong at higher VPD (figure 7). This result is consistent with an experimental comparison of PACMAD grasses under drought, which showed a more sensitive response of g_s to soil water deficits in C₃ species than in closely related C₄ species [57]. Model simulations also showed lower leaf water potential in the C₃ than C₄ species as soil dried, until the point of stomatal closure, where the leaves equilibrated with the soil (figure 7). This contrast is also broadly consistent with comparative experiments on closely related C₃ and C₄ PACMAD grasses, which showed a difference in leaf water potential under moist conditions that was diminished under chronic drought [57,68]. In our model simulations, this advantage was evidently owing to the higher K_plant relative to g_s for the C₄ over C₃ species. When the C₄ plant was given double the K_plant of the C₃ species, its advantage in maintaining open stomata during soil and atmospheric drought was increased, and when the C₄ plant was given half the K_plant of the C₃ species, its advantage was diminished.

The ability of a C₄ species with similar or higher K_plant to a C₃ species to maintain open stomata during drought also translated into an ability to maintain A at a higher level. This advantage went beyond compensating for the tendency of A to decline more precipitously with declining g_s in C₄ than C₃ species, described above (figure 4a,b), and typically provided C₄ species with an ability to maintain higher A during mild drought, especially at higher VPD (notably, simulations at yet higher VPDs led to even stronger differences between photosynthetic types). When the C₃ and C₄ species had the same K_plant, A was higher in the C₄ than the C₃ under low CO₂, but the rank was reversed under high CO₂ (figure 8). Doubling the value of K_plant in C₄ compared with C₃ species gave an advantage in A, and the ability to maintain photosynthesis during drought. This finding is broadly consistent with an early demonstration that, during the dry season in the Negev desert, the C₄ species Hammada scoparia showed a shallower decline of A with declining leaf water potential than three C₃ species (Prunus armeniaca, Artemisia herba-alba and Zygophyllum dumosum). At a leaf water potential of −6 MPa, H. scoparia (C₄) had twice the A of these C₃ species [91]. In contrast, when the C₄ species in our model simulations had reduced K_plant, this led to a much reduced value of A, and the C₃ species showed an advantage of A across all CO₂ levels as soil dried minimally (figure 8). These findings indicate that, theoretically, a reduced K_plant in C₄ species would annul any advantage of the C₄ pathway for photosynthesis under drought or low CO₂ in open environments. However, an equal or higher K_plant in these conditions would provide an advantage not only in maintaining open stomata, but also in maintaining a high A, providing a strong benefit to C₄ species.

What evidence is there that K_plant is high relative to g_s in C₄ compared with C₃ species? To-date, no studies have made the necessary direct experimental comparisons. Nonetheless, the two comparative studies of five C₃ and eight C₄ lineages of PACMAD grasses presented in figure 4a (a total of 40 different species) found that C₄ grasses generated a lower soil to leaf gradient in water potential (ΔΨ) during typical diurnal transpiration than closely related C₃ species [57,58]. Similar patterns have been observed for the C₃ and C₄ subspecies of Alloteropsis semialata in common garden plots at high irradiance and temperature [92]. This finding is consistent with the hypothesis of a higher ratio of hydraulic supply to demand, i.e. a greater K_plant/g_s in C₄ than C₃ grass species.

Notably, several studies of C₄ woody eudicots have suggested the opposite situation, measuring reduced stem hydraulic conductance per supplied leaf area (K_stem) relative to C₃ species [93–95]. This was hypothesized to evolve in the final stages of C₄ evolution after WUE has increased (table 1, phase 3). A reduced K_stem would not necessitate a reduction of g_s under well-watered conditions or mild drought. On the other hand, it would likely reduce xylem construction costs, and also possibly reduce the vulnerability to cavitation of stems, and thus their longevity [93–95]. Such adaptation would be especially important for the economics and protection of long-lived woody parts [93]. However, we note that a lower K_stem does not necessarily imply a lower K_plant; indeed, a higher leaf hydraulic conductance (K_leaf) can easily compensate. Recent work has shown the leaf is a critical bottleneck in the whole-plant hydraulic pathway, accounting for greater than 30 per cent of whole plant resistance, and that leaves have steeper hydraulic vulnerability curves than stem [96]. Consequently, K_leaf is a strong determinant of K_plant, especially when leaves begin to dehydrate during transpiration or incipient drought [97–101]. Such an importance of K_leaf in the whole plant pathway is thus consistent with a reduction of K_stem in woody dicot C₄ species. It is also consistent with the evolution of high vein density in C₃ species under drier climates (table 1, phase 1), which would serve to increase K_leaf and maintain or increase K_plant, while the evolution of higher water storage capacitance would buffer changes in leaf water potential during high VPD or drought [77,96,102,103]. These modifications would then be co-opted for further evolution of C₃–C₄ intermediates and C₄ species (table 1).

In §5, we argued that the low values of g_s in C₄ species save the hydraulic system from embolism, especially as leaves are heated in open environments, and as stomata are stimulated to open under low CO₂. Our model findings further show that the low values of g_s in C₄ species also reduce stomatal sensitivity to hydraulic feedbacks, allowing stomata to remain open during drought, and photosynthesis to continue, but only if C₄ species have similar or higher K_plant than C₃ species, and thus a high hydraulic supply relative to demand. A lower K_plant would serve to make C₄ species more sensitive to soil drought, especially under high VPD and low CO₂. The circumstantial evidence we have presented for grass species is consistent with our hypothesis for a high hydraulic supply relative to demand in C₄ species. However, to our knowledge, there are no published data comparing K_leaf for C₃ and C₄ plants in general, or for grasses specifically. Such data are essential to test our hypothesis.

7. Metabolic limitation of photosynthesis during severe drought

We hypothesized that the evolution of the C₄ pathway provides significant physiological benefits for carbon-fixation and water conservation in well-watered soil, during the early stages of soil drought, or during transient drought events. However, there is no a priori reason to expect a greater tolerance of severe desiccation in C₄ than C₃ species [104]. In fact, recent comparative analyses of closely related C₃ and C₄ PACMAD grasses suggests the converse; that the C₄ photosynthetic system may be more prone to greater metabolic inhibition under chronic and severe drought events. Experimental evidence from controlled environment, common garden and field investigations all indicate that photosynthetic capacity declines to a greater extent with leaf water potential in C₄ than C₃ grass species after weeks of soil drying, or at very high VPD [57,92,105,106]. Chronic or severe drought may thus diminish, eliminate or even reverse the WUE advantage of C₄ over C₃ species. In the extreme case, photosynthetic capacity is significantly slower to recover after the end of the drought event [106]. Experimental evidence therefore suggests that metabolic limitation of photosynthesis will eventually offset hydraulic benefits of the C₄ syndrome during acute or prolonged drought events. For tolerance of severe drought, tight stomatal control and tissue water storage, as is strongly developed in CAM species, or desiccation-tolerant tissue, are far superior to C₄ metabolism. However, for tolerance of repeated transient droughts in the growing season, C₄ metabolism carries strong advantages, particularly under low CO₂.

8. Conclusions

We hypothesized that atmospheric CO₂ depletion coupled with high temperatures, open habitat and seasonally dry subtropical environments caused excessive demand for water transport, and selected for C₄ photosynthesis to enable lower stomatal conductance as a water-conserving mechanism. C₄ photosynthesis allowed high rates of carbon-fixation to be maintained at low stomatal conductance, and reduced stomatal opening in response to low atmospheric CO₂. These mechanisms served to reduce strain on the hydraulic system. Maintaining a high hydraulic conductance enabled stomatal conductance and photosynthesis to be sustained for longer during drought events. The evolution of C₄ photosynthesis, therefore, rebalanced the fundamental trade-off between plant carbon and water relations, as atmospheric CO₂ declined in the geological past, and as ecological transitions drove increasing demand for water.

Our hypothesis adds the evolution of C₄ photosynthesis to the list of exceptional innovations based on the plant hydraulic system that arose during periods of low CO₂ that have impacted on plant life history, biogeography and the distribution of ecosystems in the deep past, present and future [107]. Previously hypothesized modifications of the water transport system and associated plant features driven by low CO₂ include the evolution of xylem vessels and stomata [108], and the planate leaf [109,110] with high vein density [78]. These innovations permitted more rapid growth and diversification, leading to the succession of dominance from pteridophytes to gymnosperms to angiosperms [78,80,111,112]. The evolution of C₄ photosynthesis, for improved performance in exposed, seasonally dry habitats in low CO₂, thus joins a long line of hydraulic innovations driven by low CO₂ that changed plants and the world.

Appendix A

(a). Model of evaporation from a leaf in a forest understorey or in open pasture

The net radiation balance at the leaf surface (Φ_n) is a function of shortwave (S) and longwave (L) radiation fluxes (both W m⁻²):

A1

where 2L_l represents longwave radiation emitted upwards and downwards from the leaf, L_s the upwards emission from soil and L_d the downwards emission from the sky or forest canopy, depending on tree cover. Values of L were calculated according to Stefan's Law, tracking the temperatures of leaf, soil, tree canopy and sky, by assuming that the lowest layer of leaves in the forest canopy is approximately at air temperature, and the apparent temperature of the clear sky is 20 K lower than that of surface air [113,114]. Heat storage by the leaf was assumed to be negligible, such that Φ_n is dissipated entirely via latent and sensible heat fluxes (λE and H, respectively)

A2

Evaporation from the leaf surface (E, mol H₂O m⁻² s⁻¹) was modelled using two variants of the Penman–Monteith equation [115,116]. For the simulations shown in figure 3, we were interested in the potential for evapotranspiration in the absence of any limitation imposed by stomata, and used the original form [115]

A3a

where Φ_n is net radiation at the leaf surface (W m⁻²), VPD is the atmospheric VPD (Pa), g_a is the leaf boundary layer conductance (m s⁻¹) and the remaining parameters are physical properties of air and water: s, the rate of change of saturation vapour pressure with temperature (Pa K⁻¹), ρ_a, the density of dry air (kg m⁻³), c_p, the specific heat capacity of water (J kg⁻¹ K⁻¹), γ, the psychrometer constant (Pa K⁻¹) and λ, the latent heat of evaporation for water (J mol⁻¹). The values of s, γ, ρ_a and λ were corrected for temperature following Friend [117]. We made the simplifying assumption that the leaf boundary layer conductance is approximately equal for heat and water.

For the simulations shown in figure 6, we were interested in the regulation of E by stomata, and used the modification by Monteith [116]:

A3b

where g_W is the total leaf conductance for water:

A4

and g_a is a function of leaf width (d = 0.01 m), and wind speed (u, m s⁻¹):

A5

Values of g_s were prescribed for these simulations as a function of atmospheric CO₂, using the equations derived for C₃ and C₄ leaves in figure 5.

The sensible heat flux is given by:

A6

where T_l is the leaf temperature and T_a the air temperature (both K). To solve the leaf energy balance, equation (A 2) must be rearranged to give H, and equation (A 6) to give T_l:

A7

and

A8

Equations (A 1), (A 3), (A 7) and (A 8) are then solved simultaneously using iteration in R (The R foundation for Statistical Computing) to yield values for Φ_n, E, H and T_l.

Appendix B

(a). Modelling of hydraulic-stomatal limitation on photosynthesis in C₃ and C₄ species

A model based on a few simplifying assumptions was used to determine the response of operating g_s and leaf water potential (Ψ_leaf) to declining soil water potential (Ψ_soil) and increasing vapour pressure deficit (VPD). The g_s was then used to estimate photosynthesis from a diffusion-biochemistry model (see appendix B). The hydraulic-stomatal model determines Ψ_leaf, plant hydraulic conductance (K_plant) and g_s at a given Ψ_soil and VPD. First, Ψ_leaf is determined based on steady-state water transport according to the Ohm's Law analogy [118,119]:

B1

Secondly, a hydraulic response function modelled the vulnerability of K_plant to declining Ψ_leaf. This used a linear function to approximate observations between full hydration and turgor loss, as reported for the leaves of grasses and several other taxa [69,120,121]:

B2

where K_max and a are constants for given species. We assumed that K_plant showed a similar vulnerability response to leaves [69,99], calculating K_plant = 80% × leaf hydraulic conductance, based on the range shown in previous work on grasses (65% to over 80% of plant resistance in the leaf [69,101,118]). Changing these assumptions would not affect the comparative findings of our simulations.

Thirdly, we simulated the decline in g_s with more negative Ψ_leaf as a sigmoidal function:

B3

where g* is the maximum value of g_s at Ψ_leaf = 0, and b is the Ψ_leaf at 50 per cent stomatal closure. The constant c defines the shape of the sigmoidal curve.

For given Ψ_soil and VPD, equations (B 1–B 3) were solved simultaneously, minimizing the implicit forms by iteration [122] (Microsoft Visual Basic; Microsoft, Redmond, WA, USA). Using this model, we simulated the response of g_s to Ψ_soil for C₃ and C₄ species, from 0 to −2 MPa, and at VPD of 1 and 3 kPa, using parameters for equations (B 1–B 3) from the literature, as available (table 2). We also tested scenarios for C₄ species with double the K_plant and half the K_plant of the C₃ species.

Table 2.

Parameters used for hydraulic-stomatal-photosynthesis modelling.

parameter	units	C3, C4 values	source
leaf Kmax	mmol m−2 s−1 MPa−1	15, 15	[69]
a	mmol m−2 s−1 MPa−2	−7.5, −7.5	[69]
g*	mol m−2 s−1	0.25, 0.10	[58]
b	MPa	−1.0, −1.0	[69]
c	MPa	0.1, 0.1	[69,123]
Vc, max	µmol m−2 s−1	83, 39	[124]
Γ*	µmol mol−1	46, 10	[124]
Kc	µmol mol−1	302, 302	[124]
Ko	µmol mol−1	256, 256	[124]
O	mol mol−1	0.210, 0.210	[124]
Jmax	µmol m−2 s−1	132, 180	[124]
Rd	µmol m−2 s−1	1.66, 0.78	[124]
Vp,max	µmol m−2 s−1	n.a., 120	[124]
Kp	µmol mol−1	n.a., 80	[124]
Vpr	µmol m−2 s−1	n.a., 80	[124]

(b). Modelling of photosynthetic rate from diffusion-biochemical limitations for C₃ and C₄ species during drought under varying vapour pressure deficit and atmospheric CO₂

We simulated photosynthetic rate (A) and its response to CO₂, by first modelling a direct response of g_s to CO₂, and then inputting the adjusted g_s values into equations for C₃ and C₄ photosynthesis.

First, for low and high CO₂ we multiplied the g_s values by a factor corresponding to 20 or 80 Pa (1.72 and 0.58, respectively) based on the data and fitted equations of figure 5. This multiplicative adjustment of g_s for CO₂ level was applied independently of the g_s response to water status (from which g_s was determined from equations (B 1–B 3) above). Thus, the model considers a simplified scenario in which the response of stomata to VPD and soil drought on one hand, and to CO₂ on the other, is independent and multiplicative, with no hydraulic or hormonal feedback on g_s. The assumption is consistent with previous work measuring the effects of CO₂ and VPD on g_s in C₃ and C₄ species [68]. This independence of the responses would put plants in low CO₂ at risk of severe leaf dehydration if stomata open strongly when VPD is low, and, indeed, such dehydration has been observed [125]. However, there is evidence that declining soil water availability can interact with the CO₂ response, resulting in greater sensitivity of stomata to CO₂, to a varying degree across different C₃ and C₄ species, in part modulated by abscisic acid responsiveness [126,127]. More work is needed to resolve and to explicitly model the potential interactions of stomatal responses to different factors in C₃ and C₄ species. For example, the interaction with falling soil water potential during drought would be expected to produce a stronger decline of g_s and of A.

In our model, the g_s, now adjusted for CO₂, was used to predict A based on the equations for C₃ and C₄ photosynthesis provided by von Caemmerer [29], using parameters from Vico & Porporato [124] (table 2). We assumed that the impact of Ψ_leaf on A was mediated by g_s without any separate, direct impacts on mesophyll conductance or on metabolism itself; these impacts could be added but, without detailed information of differential impacts on C₃ and C₄ species, would not change the outcome of our scenarios [124].

Thus, for C₃ species, A was determined as

B4

where A_c is the Rubisco-limited rate of photosynthesis, A_j is the rate of RuBP-limited CO₂ assimilation and R_d is the total mitochondrial rate of respiration. In turn,

B5

where V_c,max is the maximum catalytic activity of Rubisco at current leaf temperature (here considered as optimal); C_m is the CO₂ concentration at the site of photosynthesis in the mesophyll cell (MC); Γ* is the equilibrium CO₂ compensation point for gross photosynthesis; K_c and K_o are the coefficients for CO₂ and O₂ of the Michaelis–Menten kinetics, accounting for competitive inhibition by O₂; and O is the O₂ concentration at the site of photosynthesis.

B6

where J_max is the maximum potential rate of electron transport. To determine A, the equations (B 5) and (B 6) were each equated separately with the diffusion equation:

B7

where C_a is the atmospheric CO₂ concentration. The value of g_t was determined as the conductance to CO₂ from the atmosphere to the intercellular space (stomatal conductance to CO₂, g_s,CO2) and from the intercellular space to the chloroplast (mesophyll conductance, g_m) in series:

B8

where g_s,CO2 was determined as g_s/1.6 and g_m as g_s × 1.65 [124]. In each case (equations B 6 = B 8, and equations B 7 = B 8), the equations were solved for a given g_s and C_a, to determine C_m using the quadratic equation. The values of C_m were inserted into equations (B 5) and (B 6), respectively, to determine A_c and A_j, before applying equation (B 4) to determine A.

For the C₄ species, a similar approach was used, but the first step involved determining the PEP carboxylation rate (V_p):

B9

where V_p,max is the maximum rate of PEP carboxylation, V_pr is an upper bound set by PEP regeneration rate and K_p is the Michaelis–Menten coefficient of PEPC. The C_m was determined by equating equation (B 9) with equation (B 7) for a given C_a and g_s. We then used the C_m and V_p to determine the A, by combining two equations:

B10

where L_bs is bundle sheath leakage, given by:

B11

and C_bs is the CO₂ concentration in the bundle sheath. Substituting equation (B 11) into equation (B 10), and making this equation equal to each of equations (B 5) and (B 6) separately (substituting C_bs for C_m in those equations), allowed them to be solved for C_bs. Equations (B 5) and (B 6) were then used to determine A_c and A_j, and equation (B 4) to determine A.

Glossary

A

net rate of leaf photosynthetic CO₂ assimilation

BSC

bundle sheath cells

CA

carbonic anhydrase

CAM

crassulacean acid metabolism

CCM

carbon-concentrating mechanism

DC

decarboxylase enzymes

E

actual rate of leaf transpiration

g_s

leaf stomatal conductance to water vapour

K_leaf

hydraulic conductance of leaves

K_plant

whole-plant hydraulic conductance

K_stem

stem hydraulic conductance

MC

mesophyll cells

PACMAD

acronym for the lineage of grasses comprising the subfamilies Panicoideae, Arundinoideae, Chloridoideae, Micrairoideae, Aristidoideae and Danthonioideae

PAR

photosynthetically active radiation

PEPC

phosphoenolpyruvate carboxylase

PET

potential evapotranspiration

PPFD

photosynthetic photon flux density

RH

relative humidity

Rubisco

ribulose-1,5-bisphosphate carboxylase/oxygenase

VPD

vapour pressure deficit

WUE

leaf water-use efficiency (A/E)

Ψ_leaf

leaf water potential