C₄ photosynthesis and climate through the lens of optimality

Significance

We use a coupled photosynthesis–hydraulic optimal physiology model in conjunction with paleoclimate modeling to examine the primary selective pressures along the ecological trajectory of C₄ photosynthesis and to confirm and revise likely geographical points of dominance and expansion. Water limitation was the primary driver for the initial ecological advantage of C₄ over C₃ in the mid-Oligocene until CO₂ became low enough to, along with light intensity, drive the global expansion of C₄ in the Miocene. Our integrated modeling framework also predicts C₄ evolution should be followed by a decrease in hydraulic conductance, an increase in the leaf–turgor-loss point, and CO₂-dependent reallocation of nitrogen between dark and light reactions.

Abstract

CO₂, temperature, water availability, and light intensity were all potential selective pressures that determined the competitive advantage and expansion of the C₄ photosynthetic carbon-concentrating mechanism over the last ∼30 My. To tease apart how selective pressures varied along the ecological trajectory of C₄ expansion and dominance, we coupled hydraulics to photosynthesis models while optimizing photosynthesis over stomatal resistance and leaf/fine-root allocation. We further examined the importance of nitrogen reallocation from the dark to the light reactions. We show here that the primary selective pressures favoring C₄ dominance changed through the course of C₄ evolution. The higher stomatal resistance and leaf-to-root ratios enabled by C₄ led to an advantage without any initial difference in hydraulic properties. We further predict a reorganization of the hydraulic system leading to higher turgor-loss points and possibly lower hydraulic conductance. Selection on nitrogen reallocation varied with CO₂ concentration. Through paleoclimate model simulations, we find that water limitation was the primary driver for a C₄ advantage, with atmospheric CO₂ as high as 600 ppm, thus confirming molecular-based estimates for C₄ evolution in the Oligocene. Under these high-CO₂ conditions, nitrogen reallocation was necessary. Low CO₂ and high light, but not nitrogen reallocation, were the primary drivers for the mid- to late-Miocene global expansion of C₄. We also predicted the timing and spatial distribution for origins of C₄ ecological dominance. The predicted origins are broadly consistent with prior estimates, but expand upon them to include a center of origin in northwest Africa and a Miocene-long origin in Australia.

The evolution of the C₄ photosynthetic pathway enabled the concentration of CO₂ around Rubisco, the enzyme responsible for the first major step of carbon fixation in the C₃ photosynthetic pathway, thus reducing photorespiration. C₃ photosynthesis is present in all plants, but within C₄ plants, the C₃ pathway is typically ensconced within specialized bundle sheath cells that surround leaf veins. CO₂ that diffuses into a leaf is shuttled from adjacent mesophyll cells to the bundle sheath via a four-carbon pump, the energetic cost of which is remunerated by ATP derived from the light reactions (1, 2). As a whole, the C₄ pathway reduces photorespiration, a process that can dramatically reduce photosynthesis and begins with the assimilation of O₂, instead of CO₂, by Rubisco. Over the last 30 My, the reduction in C₃ photosynthesis by photorespiration was large and broad enough to select for the independent evolution of the C₄ pathway more than 60 times across the terrestrial plants (3). The diversity of plant families with C₄ is greatest in the eudicots (1,200 species) and the Poaceae, the monocot family containing the grasses (4,500 species) (2), which accounts for nearly 25% of terrestrial plant productivity and several important agricultural species (4).

While increased photorespiration was central to the evolution of the C₄ carbon concentrating mechanism (CCM), the relative ecological importance of different environmental drivers of the photorespiratory increase is not as clear (5, 6). Lower CO₂ and higher temperature lead to higher rates of photorespiration, which selected for the evolution of C_3–C₄ intermediates and ultimately C₄. Past physiological models, therefore, focused on temperature and CO₂ concentration as selective pressures for C₄ evolution and expansion (7, 8). Under warmer temperatures and low CO₂, C₄ photosynthesis has greater carbon gain than C₃, but under cooler temperatures and high CO₂, the metabolic costs of the C₄ pathway and lower photorespiration in C₃ leads to greater carbon gain in C₃. Alternatively, water availability has been proposed as the impetus for C₄ evolution in eudicots (2), and recent phylogenetic analyses have suggested the same in grasses (6). Water availability should have an impact on C₄ evolution that could work independently or in concert with changes in CO₂ and temperature. First, water deficits indirectly increase photorespiration in C₃ plants by forcing stomatal closure to reduce leaf water loss, consequently decreasing the flux of CO₂ into the leaf and the availability of CO₂ for Rubisco (9). Second, the C₄ CCM allows for the maintenance of lower stomatal conductance, and therefore lower water loss, for a given assimilation rate, leading to a higher water-use efficiency (WUE) than C₃ (10).

The different environmental drivers of the photorespiratory increase in C₄ progenitors—atmospheric CO₂ concentration, temperature, and water availability—changed dramatically over the period of C₄ diversification and expansion. Although there is uncertainty of CO₂ concentration from different proxies (11), atmospheric CO₂ generally decreased from the mid-Oligocene (∼600 ppm) to the ∼400 ppm in the midearly Miocene (12, 13) but with significant variability (±100 ppm; refs. 13 and 14), after which it reduced to values of less than ∼300 ppm in the Pliocene (13). Physiological models that focused on temperature and CO₂ implied that C₄ evolved, in both grasses and eudicots, at the low end of this CO₂ range in the mid-Miocene to the Pliocene (2, 7, 8, 15). Isotopic and fossil evidence shows that C₄ grasses became a major component of grassland biomes—in terms of biomass, C₄ lineage diversity, or herbivore dietary components—in the mid-Miocene, but molecular evidence suggests that C₄ photosynthesis may have arisen in the grasses as early as the mid-Oligocene, more than 30 Mya (11). Similarly, phylogenetic reconstructions provide evidence that some eudicots evolved C₄ as early as the monocots and also saw the greatest rate of C₄ diversification and expansion in the late Miocene (16, 17). The error associated with these molecular dating techniques is large, however, and the uncertainty range for even the oldest C₄ lineages overlaps with the mid-Miocene estimates for C₄ evolution and expansion. Along with CO₂, precipitation declined over the period of C₄ diversification and expansion, leading to vast terrestrial areas where low or highly seasonal precipitation inputs led to the loss of forests and, consequently, the evolution of the world’s first grasslands (18). The spread of grasslands indicates a habitat change with larger surface radiation loads, higher surface temperatures, and increased potential for plant water loss (5, 19). Therefore, if the early evolution of C₄ suggested by molecular-dating approaches are correct, then water availability played an important role for both C₄ grasses and eudicots, while CO₂ was still relatively high (5, 16, 19, 20). The potentially interacting roles of water availability, changes in radiation, and CO₂ along the ecological trajectory of C₄ photosynthesis have not been fully investigated within comprehensive physiological and paleoclimate models.

A related but largely unstudied physiological change during the divergence of C₄ photosynthesis from C₃ is the allocation of nitrogen between the dark reactions and the light reactions. C₄ plants might allocate a greater proportion of N to light reactions than to dark reactions compared with C₃ because of the extra ATP cost of the CCM (21, 22). We propose that the reallocation of N between dark and light reactions provides a further advantage for C₄ above the CCM alone and that different environmental conditions can select for a shift in the degree of reallocation both through evolutionary time and across species in extant plants.

Our goal is to integrate several ecologically relevant selective pressures that determined the competitive advantage and expansion of the C₄ pathway from the mid-Oligocene through to the late Miocene. C₄ evolved via C₃–C₄ intermediates that display a number of successive biochemical and anatomical traits that reduce photorespiration compared with C₃ plants, but further reductions in photorespiration, enhanced WUE and nitrogen-use efficiency, and increases in ecological niche space did not occur until the evolution of the full C₄ CCM (23, 24). We therefore assume that C₃ plants, and not C₃–C₄ intermediates, were the major ecological competitors of C₄ plants. We examine how changes in selective pressures augmented the relative advantage of these two evolutionarily stable states within the framework of an optimality model in which the plant makes allocation “decisions” to maximize photosynthetic assimilation rate. We advance our understanding of C₄ photosynthesis in five ways. First, we revisit the temperature–CO₂ crossover approach and integrate the effects of water limitation, light, optimal allocation decisions, and the interactions between these in a single model. Second, we formalize the hypothesis that C₄ photosynthesis has a higher WUE than C₃, using an optimality argument to balance carbon gain and water loss. Specifically, we let both stomatal conductance and leaf/fine-root allocation emerge endogenously, rather than assuming a priori that C₄ grasses have lower stomatal conductance. This allows us to elucidate the previously unexplored role of optimal stomatal conductance (but see ref. 15) and resource allocation in mediating ecological success due to water limitation and to predict further divergence of hydraulic properties. Third, we explicitly include the additional ATP cost of the C₄ pathway with a mechanistic model (1, 25), which previous modeling analysis did not explicitly consider (7, 8, 19). Fourth, we consider reallocation of nitrogen from the dark reactions to the light reactions, which can change tradeoffs between photosynthesis and water use by C₄. Finally, we drive the optimality model under three CO₂ scenarios with outputs from a fully coupled general circulation model for Miocene/Oligocene climate to examine regions and timing of C₄ ecological advantage as a proxy for potential evolutionary origins.

Results

We validated our optimality model through comparisons with previous models and empirical data from closely related C₃ and C₄ species measured under similar conditions (26) (SI Appendix, Fig. S1). Model outputs were consistent with observed patterns of C₃ versus C₄ for stomatal resistance, biomass allocation, photosynthesis, and leaf water potential. Leaf water potential predictions matched observed values, while predicted values for other measures were slightly higher. We incorporated our stomatal resistance and biomass outputs into a Penman–Monteith model to determine if we could replicate the observed ecosystem-level water balance of C₃–C₄ mixed grasslands (27) (SI Appendix, Supporting Information SI3). Our model confirmed that increasing the C₄ grass component reduces desiccation under higher temperatures and CO₂ (SI Appendix, Fig. S2 and Table S3). We further predicted that local desiccation would occur in pure C₃ grasslands due to warming, even with CO₂ increasing from 400 ppm to 600 ppm (SI Appendix, Fig. S3). In contrast, local desiccation would be mitigated in pure C₄ grasslands.

Assimilation-based crossover temperatures, defined as the temperature at which assimilation by the C₄ pathway exceeds that of the C₃ pathway, decrease as water limitation increases and light intensity increases across all CO₂ concentrations (Fig. 1 and SI Appendix, Fig. S4). Without water stress (solid black line in Fig. 1), our model predicts a C₃/C₄ crossover temperature of 23 °C under 380 ppm, a result similar to previous data and/or models (7, 8). The model results in Fig. 1 were all under the light intensity of 1,400 μmol⋅m⁻²⋅s⁻¹ and with a C₄ J_max/V_cmax ratio of 4.5, which corresponds to a reallocation of nitrogen from dark to light reactions. Model results for a C₄ J_max/V_cmax ratio of 2.1 (no reallocation) were similar (SI Appendix, Fig. S4A), with the exception of low CO₂ and low water availability. Crossover temperatures are higher with J_max/V_cmax = 4.5, showing that nitrogen reallocation decreases the C₄ advantage under water limitation and low CO₂. Under saturated soil and low vapour pressure deficit (VPD), crossover temperatures decrease along with increasing light intensity (SI Appendix, Fig. S4 C and D). An increase in light intensity provides a larger relative benefit for C₄ at low CO₂, because C₃ photosynthesis remains CO₂-limited throughout, while C₄ light limitations lessen as light increases. Photosynthetic limitation states were examined under multiple environmental scenarios, using J_max/V_cmax = 2.1 or 4.5 for C₄. With J_max/V_cmax = 2.1, C₄ is light-limited in most conditions (SI Appendix, Fig. S5 A and C). With J_max/V_cmax = 4.5, or when CO₂ decreases to 200 ppm, C₄ becomes limited by CO₂ under low temperatures and by light under high temperatures (SI Appendix, Fig. S5 B and D–F).

Fig. 1.

Crossover temperatures of photosynthesis for C₃ and C₄ with the change of CO₂ concentration under different water conditions. Light intensity was 1,400 μmol⋅m⁻²⋅s⁻¹ for all model runs. J_max/V_cmax = 2.1 for C₃ and J_max/V_cmax = 4.5 for C₄. Solid black line: VPD = 0.1 kPa, ψ_s = 0 MPa; dashed black line: VPD = 0.625 kPa, ψ_s = −0.5 MPa; dot-dashed black line: VPD = 1.25 kPa, ψ_s = −1 MPa; dotted black line: VPD = 1.875 kPa, ψ_s = −1.5 MPa. The circle and error bars indicated the average and confidence intervals of crossover temperature in Collatz (8).

To provide a more quantitative measure of C₄ advantage, we calculated the net assimilation rate difference between C₄ and C₃, $\mathrm{\Delta }$A_n (net assimilation of C₄ minus that of C₃), through all environmental variations (Fig. 2 and SI Appendix, Fig. S6). The positive contour space ($\mathrm{\Delta }$A_n > 0) means that C₄ outcompetes C₃ within given environmental dimensions, and the higher the $\mathrm{\Delta }$A_n, the greater the advantage of C₄. In Fig. 2, the light intensity of 1,400 μmol⋅m⁻²⋅s⁻¹ is fixed for all model runs. Under CO₂ = 200 ppm, $\mathrm{\Delta }$A_n is higher under moist conditions than water-limited conditions (Fig. 2 A and B). In contrast, under higher CO₂ (400 and 600 ppm), C₄ has the greatest advantage only in water-limited conditions, leaving a relatively small environmental envelope for C₄ (Fig. 2 C–F). This is because C₃ photosynthesis has a greater proportional increase in assimilation from 200 to 400 or 600 ppm CO₂. Across all scenarios, increasing J_max/V_cmax increases both the $\mathrm{\Delta }$A_n and space for C₄ advantage (Fig. 2 B, D, and F). Light responses were examined under saturated soils (SI Appendix, Fig. S6) and at low CO₂. $\mathrm{\Delta }$A_n increases strongly as light increases, whereas there is a much smaller light effect at 400 ppm CO₂ and higher, and a high J_max/V_cmax was required for a C₄ advantage ($\mathrm{\Delta }$A_n > 0).

Fig. 2.

The total difference in CO₂ assimilation between C₄ and C₃ [A_n(C₄)–A_n(C₃)] under various CO₂ (200 ppm, 400 ppm, and 600 ppm) and water conditions under light intensity (1,400 μmol⋅m⁻²⋅s⁻¹). J_max/V_cmax = 2.1 for C₃ and C₄ (A, C, and E) and J_max/V_cmax = 2.1 for C₃ and J_max/V_cmax = 4.5 for C₄ (B, D, and F). Water limitation intensity is as follows: 1, VPD = 0.1 kPa, ψ_s = 0 MPa; 2, 0.625 kPa, −0.5 MPa; 3: 1.25 kPa, and −1 MPa; 4, 1.875 kPa, −1.5 MPa; 5: 2.5 kPa, and −2 MPa.

By driving the optimality model with outputs from the paleoclimate model, we can predict the geographic centers for C₄ ecological dominance as a proxy for C₄ origins. Areas of central Asia, southwest Asia, and northern Africa/Arabia would strongly select for C₄ at 600 ppm CO₂ because of the warm temperatures and arid conditions simulated there (Fig. 3A). Southwestern Australia also has a significant land area that would support C₄, and to a lesser extent, so does southwestern North America. As CO₂ decreased to 400 and 270 ppm, the areas mentioned above expanded to strongly support a C₄ ecological advantage with the addition of southern Africa and southern South America (Fig. 3 B and C). As CO₂ decreased, C₄ favorability maintained a foothold in the semiarid sites and moved into wetter regions, while still requiring warm temperatures for an advantage. At both 400 and 600 ppm, a higher J_max/V_cmax ratio was required for C₄ to maintain a higher advantage over C₃ (Fig. 3 A and B and SI Appendix, Fig. S7 A and B). At 270 ppm, C₄ had a broad advantage over C₃ with a lower J_max/V_cmax ratio (Fig. 3C and SI Appendix, Fig. S7C).

Fig. 3.

The regional distributions of C₃ or C₄ ecological dominance under Oligocene/Miocene climate and different CO₂. Dominance is determined by the assimilation difference [A_n(C₄)–A_n(C₃); μmol⋅m⁻²⋅s⁻¹] with the thresholds as follows: >3, C₄ dominant; between 1 and 3, C₄ slightly dominant; between −1 and 1, equal dominance; between −3 and −1, C₃ slightly dominant; < −3, C₃ dominant. For each grid cell, the optimality model was driven with outputs from the Community Land Model (CLM4.5) in the CESM: (A) 600 ppm CO₂ and (B) 400 ppm CO₂, both with C₃ J_max/V_cmax ratio = 2.1 and C₄ J_max/V_cmax ratio = 4.5, (C) 270 ppm CO₂, C₃ J_max/V_cmax ratio = 2.1 and C₄ J_max/V_cmax ratio = 2.1. Circles superimposed on figures indicate evolutionary origins from previous studies (23) and numbers within the circles indicate cumulative lineages within which C₄ evolved by a given time period for (A) late Oligocene/early Miocene, (B) mid-Miocene, and (C) late Miocene/Pliocene.

We calculated the photosynthesis rates of the two pathways by only varying the J_max/V_cmax for C₄ to further examine the pure effect of nitrogen reallocation (Fig. 4). With J_max/V_cmax = 2.1 for both C₃ (solid black line) and C₄ (dashed line), the C₄ assimilation rate is rarely higher than C₃, which indicates C₄ does not have an obvious advantage under current CO₂. However, with J_max/V_cmax = 4.5 for C₄ (dotted line), C₄ has an advantage over C₃ at higher temperatures.

Fig. 4.

Assimilation rates of C₃ with J_max/V_cmax = 2.1 (solid black line), C₄ with J_max/V_cmax = 2.1 (dashed black line), and C₄ with J_max/V_cmax = 4.5 (dotted black line) (other parameters are maintained the same for C₃ and C₄) under light intensity of 1,400 μmol⋅m⁻²⋅s⁻¹, CO₂ of 400 ppm, and different water limitation conditions. (A) VPD = 0.625 kPa, ψ_s = −0.5 MPa; (B) 1.25 kPa, −1 MPa.

Under all environmental and nitrogen allocation scenarios, optimal stomatal resistance (r_s) and leaf biomass/total biomass of leaf and fine-root allocation (f) are higher in C₄ plants than C₃ plants, and response patterns were similar across CO₂ concentrations (SI Appendix, Fig. S8). In addition, f decreases and r_s increases as the intensity of water limitation increases. Results are consistent for C₄ with a J_max/V_cmax of 2.1 and J_max/V_cmax of 4.5. The higher r_s in C₄ plants led to a consistently higher water potential than C₃ plants in all simulated conditions (SI Appendix, Fig. S1B). We also predicted that C₄ plants should have a higher leaf–turgor-loss point than closely related C₃ plants, and we found empirical support for this prediction across four closely related C₃–C₄ clusters (Fig. 5).

Fig. 5.

Measured leaf–turgor-loss points in four closely related groups of C₃ and C₄ species (white bars: C₃ species; gray bars: C₄ species). Error bars show SEs. Different letters denote a significant difference within a group.

Discussion

Based on the conditions under which C₄ plants have the ecological advantage over C₃, our results offer physiological and climatological support for a potential Oligocene ecological dominance of C₄. This finding is in concert with the early ranges of C₄ evolution from molecular-based approaches (16, 17), and we use this ecological dominance as a proxy to identify the regions where C₄ would likely emerge. Isotopic and fossil evidence suggest that C₄ photosynthesis first arose in the mid-Miocene, whereas molecular and phylogenetic approaches suggest that C₄ first arose anywhere from the mid-Miocene to mid-Oligocene (11). Our paleoclimate model broadly represents the environmental conditions for Oligocene to mid-Miocene (12, 28, 29), with high CO₂ conditions representing the mid-Oligocene, and low CO₂ mid-Miocene. We find that environmental conditions favored C₄ plants during the mid-Oligocene (∼30 Mya) at warm, arid sites where water limitation acted as the primary selective pressure to increase photorespiration when CO₂ was as high as 600 ppm. The geographic origins predicted by our model and those proposed by others (23) tend to agree, which lends general support to our approach. At the same time, there are important differences that impact both the location and potential age for the evolution of C₄ (Fig. 3). Notably, we find a greatly expanded region of potential origin in northern Africa. Under Oligocene/Miocene climate, northern Africa was arid, but the Tethys sea had not yet closed, and the northwest and the northeast were consequently just wet enough to ecologically favor C₄ over C₃ plants. Likewise, Australia is thought to have developed conditions favorable for the evolution and expansion of C₄ only within the last 9 Mya (23), yet we show it slightly favoring C₄ under Oligocene CO₂ and strongly favoring C₄ by the mid-Miocene. Climate simulations suggest that both northern Africa and southwestern Australia had wetter summers than the current Mediterranean-type climate.

As CO₂ decreased through the Miocene, warm temperatures remained a strong selective force, but the primary selective force for a C₄ advantage over C₃ shifted from water limitation to low CO₂ and, to a lesser extent, light intensity. However, as increased light intensity alone could not lead to an advantage of C₄ under high CO₂ (SI Appendix, Fig. S6C), it seems likely that C₄ could not dominate except in locally arid areas while CO₂ was high. Thus, after its emergence, C₄ radiation likely idled in small pockets of selective favorability as CO₂ concentrations declined through the Miocene (13), similar to the “edaphic ghetto” hypothesis (30). Furthermore, given that CO₂ may have been rapidly cycling on orbital time scales between 500 ppm and 300 ppm (14), the transition to widespread C₄ could have exhibited hysteresis and occurred through fits and starts. Such shifts in primary selective pressures on C₄ photosynthesis over evolutionary time are consistent with the isotopic evidence (31, 32).

Consistent with previous studies, our model predicts that low CO₂ (200–300 ppm) strongly favors C₄ over C₃ photosynthesis (e.g., refs. 7 and 15). We further show that low CO₂ provides a clear C₄ advantage under a large range of water availability and light intensity regimes. Under low CO₂, the greatest C₄ advantage occurs in relatively moist and mildly water-limited conditions, opposite to that which is seen under high CO₂. Under low CO₂, new C₄ species evolved in multiple lineages and together with the earlier C₄ species started to increase their biomass to occupy open sites (11). The environmental conditions that led to the largest C₄ advantage within our model, therefore, parallel those documented in extant C₄-dominated grasslands: highly seasonal precipitation that occurs chiefly within a warm growing season (33, 34). These are also similar to the conditions that led to the large-scale expansion of C₄ grasslands in the Miocene—for example, the onset of summer monsoons and subsequent C₄ grassland expansion in the Indian subcontinent (35).

The role of water limitation in C₄ grass evolution has sparked interest in grass hydraulics and the anatomical shifts in C₃ grasses that were prerequisites to C₄ evolution (19, 20), and we further propose that the evolution of C₄ photosynthesis leads to a reorganization of the hydraulic system. A lower leaf–turgor-loss point is typically a strong indicator of drought tolerance across species (36). On the contrary, we predict that the higher stomatal resistance of the C₄ CCM leads to a higher leaf water potential than C₃ in all water-limited conditions; thus, there is no need for C₄ to maintain a lower leaf–turgor-loss point. We confirmed this prediction in four closely related C₃–C₄ clusters (Fig. 5). It is thought that the higher vein density of C₄ grasses should lead to greater hydraulic conductance (19, 20), but we found a clear C₄ advantage solely by allowing for optimal leaf:fine-root allocation and stomatal conductance. We also find that increasing hydraulic conductance had little impact on the C₄ advantage (SI Appendix, Fig. S9), indicating that the C₄ CCM itself is enough to result in greater carbon gain under water stress. These results do not contradict the idea that larger bundle sheaths and smaller interveinal distance—which were clear prerequisites for C₄ evolution (20, 37)—led to greater hydraulic conductance and drought tolerance among C₄ progenitors (20). They do, however, suggest that greater hydraulic conductance is not necessary to give C₄ plants an advantage once the CCM evolved. We hypothesize that once C₄ evolves in a lineage, selection on increased hydraulic conductance would not only lessen but invert, leading to the development of even narrower xylem conduits and greater drought resistance. There is empirical support for such a prediction in eudicots (38).

Different environmental conditions can select for a shift in the degree of nitrogen allocation across the light and dark reactions separately from the C₄ CCM (assessed here by a change in J_max/V_cmax). In general, CCMs allow for less investment in nitrogen-rich Rubisco (39), and the nitrogen not used for Rubisco could be either reinvested in light-harvesting machinery or simply not used at all, thus reducing the total nitrogen requirement. Modeling studies have long assumed a high J_max/V_cmax for C₄ photosynthesis (19, 40), and measurements show lower Rubisco content and higher chlorophyll and thylakoid content, giving evidence of reallocation in extant C₄ species (21, 22). Empirical estimates of J_max/V_cmax, in C₄ plants, are more variable, ranging from 2 to above 6, with a mean of around 4.5 (41–43), which is higher than the mean J_max/V_cmax estimates for C₃ plants of 2.1 (44). Increasing J_max/V_cmax almost always increases the photosynthesis rate of C₄ grasses (Fig. 4 and SI Appendix, Fig. S10) and therefore could lead to a competitive advantage over C₃ grasses as well as C₄ grasses that do not reallocate. Assuming there is little cost or no genetic constraints for reallocation, the selection pressure to reallocate would have been strongest when CO₂ was high because the CCM alone does not give C₄ a large advantage. When CO₂ was low during the late Miocene C₄ expansion, however, the CCM alone would give C₄ an advantage and reallocation would not change the competitive balance between C₃ and C₄. As CO₂ remained low through to the Pleistocene, selection for nitrogen reallocation to the light reactions would lessen further, especially during the CO₂ minima of the Pleistocene glacial periods (∼180 ppm).

Each evolutionary origin of C₄ photosynthesis represents both different selective pressures and taxonomic (genetic) constraints as climate and CO₂ changed. Taking the Chloridoideae as an example, we can use our model to develop hypotheses along the ecological trajectory of C₄ in this grass subfamily. The ecological advantage of C₄ photosynthesis in the Oligocene, while CO₂ was high, was driven by aridity, acting to decrease stomatal conductance that increased photorespiration in C₄ progenitors initially, and led to higher WUE upon the evolution of the CCM. There would have been enough of a reduction in water use that the turgor-loss point would increase and selection for increased hydraulic conductance would relax, allowing for the development of more resilient—and less conductive—xylem. There would have been strong selection for reallocation of nitrogen from the dark reactions to the light reactions. The large radiation of C₄ within the Chloridoideae occurring in the mid- to late Oligocene was likely driven by low CO₂ and high light, and the previously evolved hydraulic resilience would perhaps relegate this subfamily to being the dry-site specialists observed in current-day distributions (45). There would have been much less selective pressure to reallocate N during the large radiation, but such a reorganization was likely already in place within the clade. In contrast, for the lineages that evolved C₄ in the late Miocene (e.g., Stipagrostis, Eriachne, Neurachne), CO₂ would have been the primary impetus for C₄ evolution, but for these lineages, there would have been little selection to reallocate nitrogen, and we predict that they would have greater hydraulic conductance and lower turgor-loss points than those of the Chloridoideae.

By optimizing carbon gain over water loss, we developed a plausible physiological explanation for the ecological advantage of C₄ through time and further proposed hypotheses about how a variety of traits that accompany the C₄ CCM developed in concert with the climate changes that occurred through this ecological trajectory (46). There are obvious caveats with our interpretations, because we focus solely on physiology and assume that competitive outcomes or selective pressures are decided primarily by photosynthetic rates. We also do not consider how larger ecological processes like disturbance can undermine physiology-based projections of plant distributions (47). However, by examining extant species within select lineages in both controlled and natural environments, these hypotheses can be examined empirically together with our physiological model, ultimately providing an integrative view of the selection pressures that led to the current physiologies and distribution of C₄ plants.

Materials and Methods

Overview of the Plant Model.

We first assume that the CCM is the only difference between C₃ and C₄, corresponding to two closely related species whose other traits have not yet diverged. We then allow for divergence through shifts in nitrogen allocation between the light and dark reactions of C₄. Our model incorporates the soil–plant–air–water continuum into traditional C₃ (48) and C₄ (25) photosynthesis models and assumes that plants optimize stomatal resistance and leaf/fine-root allocation to balance carbon gain and water loss (49). The rate of water loss through transpiration equals the rate of water absorption by the roots, at equilibrium (49). Stomatal resistance (r_s) controls transpiration and photosynthesis. The leaf/fine-root (f) ratio, defined as the ratio of biomass for leaves to the sum of biomasses for leaves and fine roots, controls the biomass allocated to leaf area for transpiration and photosynthesis. The lowering of leaf water potential through transpiration water loss and/or environmental factors (VPD and soil water potential) leads to a lowering of the photosynthetic rate via Weibull-type vulnerability curves (40). A full model description is in SI Appendix, Supporting Information SI1 with SI Appendix, Table S1 for parameter abbreviations and SI Appendix, Table S2 for input parameters. The model derivation and methods for numerical solutions using Mathematica (Wolfram Research, Inc.)/R are in SI Appendix, Mathematica-S1 and R package.

Optimal Stomatal Resistance and Allocation of Energy Between Leaves and Fine Roots.

We assume that the plant adjusts the rs and f to optimize the total carbon gain

$$A_{total}=\frac{fN{A}_n}{\rho },$$

where ρ is the leaf mass density (g⋅m⁻²), and for simplicity, we assume that N and ρ are fixed (49). This amounts to considering the optimization problem faced by the plant in a given instance during growth, where size is a constant. We treat the instantaneous optimization problem as a proxy for the optimal growth path as the growth rate is maximized at any given time. We regard ρ as a species-specific trait that changes at a slower time scale than rs and f.

Allocation of Nitrogen.

The ratio J_max/V_cmax was used as a proxy for nitrogen allocation between RuBP carboxylation and regeneration. The initial condition for J_max/V_cmax was 2.1 (44) for both C₃ and C₄. For the reallocation, the value for C₄ is J_max/V_cmax = 4.5 (19, 40). We used a simple stoichiometry for J_max and V_cmax by considering the sum of J_max and V_cmax as a constant representing total available nitrogen for photosynthesis; such a stoichiometry was drawn from the existing modeling work (19, 40). Two assumptions underlie this stoichiometry: (i) Investing one molecule of N to the dark reactions increases V_cmax to the same degree as investing one molecule of N to the light reactions increases J_max, and (ii) nitrogen allocation to enzymes involved in photorespiration (C₃) and the CCM (C₄) offset each other. These simplified assumptions are meant to represent an initial analysis of the effect of reallocation; they can be further adjusted when more detailed stoichiometry is available.

Modeling Scenarios.

Photosynthesis was modeled over the following ranges of environmental conditions: 10 °C to 40 °C with 0.125 °C intervals; CO₂ 200 ppm to 600 ppm with 50 ppm intervals; water conditions VPD = 0.1, 0.625, 1.25, 1.875, and 2.5 kPa, with corresponding soil water potential (ψ_s) = 0, −0.5, −1, −1.5, and −2 MPa and light intensities 1,400, 1,000, 600, 200, and 100 μmol⋅m⁻²⋅s⁻¹. We consider VPD = 0.1 kPa and ψ_s = 0 MPa as saturated and light intensity of 1,400 μmol⋅m⁻²⋅s⁻¹ as an average light intensity of a day in open habitat. Environmental factors are intended to reflect growing-season averages.

Paleoclimate Modeling of Geographic Centers of Evolution.

Building on existing boundary conditions and simulations using earlier versions of the National Center for Atmospheric Research (NCAR) coupled model (The Community Climate System Model, versions 3 and 4), we implement mid-Miocene simulations in Community Earth System Model (CESM) 1.0.5 (50) incorporating slightly updated boundary conditions (51) within CESM incorporating the Community Atmosphere Model, version 5 atmospheric component (52) and the CLM4 land surface model (53) (SI Appendix, Supporting Information SI2). To drive the vegetation model, growth-season means of atmospheric incident solar radiation, 2 m relative humidity, soil water potential (upper six layers), and daily maximum of average 2 m temperature were generated from 30-y climatological monthly means of CLM output. These fields were masked to include grid cells in the growing season (temperature > 10 °C) and for “open” settings—that is, for grid cells made up of >20% of grassland, shrub-land, woodland, and desert based on the distributions in Herold et al. (51), thus filtering out closed-canopy forests and cold regions. Coding was performed in the NCAR Command Language (NCL); the source code is available from the Purdue University Research Repository https://purr.purdue.edu.