Maximum leaf conductance driven by CO₂ effects on stomatal size and density over geologic time

Abstract

Stomatal pores are microscopic structures on the epidermis of leaves formed by 2 specialized guard cells that control the exchange of water vapor and CO₂ between plants and the atmosphere. Stomatal size (S) and density (D) determine maximum leaf diffusive (stomatal) conductance of CO₂ (g_cmax) to sites of assimilation. Although large variations in D observed in the fossil record have been correlated with atmospheric CO₂, the crucial significance of similarly large variations in S has been overlooked. Here, we use physical diffusion theory to explain why large changes in S necessarily accompanied the changes in D and atmospheric CO₂ over the last 400 million years. In particular, we show that high densities of small stomata are the only way to attain the highest g_cmax values required to counter CO₂“starvation” at low atmospheric CO₂ concentrations. This explains cycles of increasing D and decreasing S evident in the fossil history of stomata under the CO₂ impoverished atmospheres of the Permo-Carboniferous and Cenozoic glaciations. The pattern was reversed under rising atmospheric CO₂ regimes. Selection for small S was crucial for attaining high g_cmax under falling atmospheric CO₂ and, therefore, may represent a mechanism linking CO₂ and the increasing gas-exchange capacity of land plants over geologic time.

Stomata crucially permit plants to regulate transpirational water loss from leaves during the simultaneous uptake of CO₂ for photosynthesis (1, 2). Originating more than 400 Ma, their evolutionary appearance was pivotal to the colonization of the land by plants, permitting the survival and ecological radiation of floras throughout diverse terrestrial habitats experiencing widely fluctuating environmental conditions (2–4). Remarkably, the fundamental design of stomata has remained unchanged over the 400-million year (Myr) history of vascular plants (3, 4) but has been fine-tuned through increases in the operational efficiency of guard cell function (5). Nevertheless, major changes in stomatal size (S) and density (D) are evident in the fossil record (2, 6) (Fig. 1; Table S1), but their significance as land-plant evolution progressed, in parallel with advancements in gas-exchange capacity, is not yet understood. Here, we use diffusion theory and Earth's global atmospheric CO₂ history to provide a unifying functional explanation for these changes in stomatal geometry over evolutionary time scales.

Fig. 1.

The relationship between stomatal size S and density D across the Phanerozoic. Each point is an individual species (see Table S1). The curved line is the estimated upper theoretical limit to stomatal size at a given density, or the upper limit of density at a given size. All combinations of size and density must fall below this line. Diagrams in boxes are comparative representations of possible combinations of stomatal size and density to assist visualization of the scaling of these dimensions in real leaves.

One basic feature of leaves that should be highly conserved is the relationship between maximum pore area and leaf gas-exchange capacity, which is governed by the physics of diffusion through pores. The maximum area of the open stomatal pore (a_max) and its depth (l) are set by stomatal size S (defined here as guard cell length, L, multiplied by total width, W, of the closed guard cell pair). Taken together, a_max, l, and D determine maximum diffusive conductance to water vapor or CO₂ (g_wmax or g_cmax, respectively) according to ref. 7:

where d is the diffusivity of water vapor in air (m²·s⁻¹), v is the molar volume of air (m³·mol⁻¹), and g_cmax = g_wmax/1.6 (1). Critically, it can be shown mathematically that for the same total pore area, a_max, smaller stomata result in higher g_wmax compared with larger stomata (Fig. 2). This is because g_wmax is inversely proportional to the distance that gas molecules have to diffuse through the stomatal pore (l), which increases with S as guard cells inflate to be approximately circular in cross-section (5). It can be further shown, by using Eq. 1, that for a given g_wmax, smaller stomata allow more epidermal space to be allocated to other structures such as subsidiary cells, trichomes, or oil cells (Fig. 3). Stomatal size is important not only to g_wmax and g_cmax but also to the overall structure and broader ecophysiological function of leaf surfaces.

Fig. 2.

Smaller stomata provide higher stomatal conductance for the same total pore area because of the shorter diffusion path length, l (see Eq. 1). For any stomatal size S there is a theoretical maximum stomatal density D_max based on simple geometric packing limitations. Here the total stomatal pore area per unit leaf area remains constant at the theoretical maximum for any given stomatal size S, but because that pore area is made up of ever-smaller and more numerous stomata, the stomatal conductance (g_wmax) increases. See Data and Methods for details.

Fig. 3.

For any given g_wmax, smaller stomata free up more epidermal space for other cell types and functions. Shown are percentages of epidermal surface occupied by stomata as a function of variable stomatal size S for 3 fixed values of g_wmax. CO₂-forcing of changes in g_wmax via changes in S and D have implications for leaf attributes unrelated to g_wmax. See Data and Methods for details.

The 400-Myr fossil history of stomata reveals that although S and D have both varied by several orders of magnitude (Fig. 1), all reported combinations are located within the biophysical envelope defined by maximum packing of stomata on the leaf surface (i.e., the maximum number of stomata of a given size, S, that can fit within a unit area) (Fig. 1; Table S1). Indeed, combinations of S and D must lie somewhat below this upper packing limit to accommodate several developmental, physiological, and mechanical requirements for spacing of stomata (5, 8).

Irrespective of the size, shape, or number of epidermal cells filling the space between individual stomata on a leaf surface, S and D are virtually the only epidermal characteristics determining g_cmax, an important feature constraining maximum leaf gas-exchange capacity. At the time of first appearance of vascular plants in the fossil record, atmospheric CO₂ concentration was several times higher than current ambient CO₂ (9), but subsequent periods of falling atmospheric CO₂ challenged plants with diminished CO₂ availability. Adaptation of g_cmax to these conditions required a change in S and/or D, and we hypothesize from principles of stomatal packing on leaf surfaces (Figs. 2 and 3) and gas-exchange diffusion theory (Eq. 1) that selection for higher g_cmax by falling atmospheric CO₂ is characterized by a trend toward smaller S and higher D.

Results

Consistent with our hypothesis we report that a positive correlation between S and Earth's global atmospheric CO₂ history (Fig. 4A) is mirrored by a negative correlation between D and CO₂ over hundreds of millions of years of plant evolution (Fig. 4B). The magnitude of change in S is far greater than, but consistent with, that observed in short-term CO₂ experiments (Table 1). These short-term changes are presumably reflecting phenotypic plasticity (i.e., the limited range in magnitude of S resulting from the effect of changes in the environment on stomatal development within a single generation). The strong negative correlation of D with CO₂ over 400 Myr (Fig. 4B) is consistent with observations on Quaternary fossil leaves over documented glacial–interglacial CO₂ changes (10, 11), trees experiencing the rapid rise in atmospheric CO₂ over the past century (12), and experiments (13).

Fig. 4.

Relationships between fossil stomatal traits and atmospheric CO₂. Each point is the mean for either a 50- or 100-Myr time slice of the Phanerozoic, beginning at −400 Myr, or the mean for modern times (0 Myr). (A) Stomatal size is positively correlated with atmospheric CO₂ concentration (y = 3.02x − 528; r² = 0.92; P < 0.002). (B) Stomatal density D decreases exponentially with atmospheric CO₂ concentration, hence log₁₀D is linearly correlated with CO₂ (y = −0.000657x + 2.58; r² = 0.98; P < 0.0001). (C) Maximum stomatal conductance to water vapor, g_wmax, is negatively correlated with atmospheric CO₂ concentration (y = −0.000441x + 1.29; r² = 0.84; P < 0.006). (D) g_wmax is negatively correlated with stomatal size S (y = −0.000124x + 1.15; r² = 0.60; P = 0.04).

Table 1.

Increase in stomatal size, S, in response to growth at elevated atmospheric CO₂ (short-term experiments)

Species	S at low CO2, μm2	S at high CO2, μm2	S increase, %	Ref.
Zea mays	918	1,072	16.78	18
Oryza sativa cv. Pusa Basmati-1	209	231	10.53	31
O. sativa cv. P-677	155	281	81.29	31
O. sativa cv. P-834	185	251	35.68	31
O. sativa cv. P-2503-6-693	160	222	38.75	31
Betula pubescens	618	705	14.08	32

Low CO₂ treatment: 350 ppm; high CO₂ treatment: 700 ppm.

The functional consequence of the tradeoff between S and D allows g_wmax and g_cmax to increase as global atmospheric CO₂ declines (Fig. 4C). The requirement for large numbers of small stomata to maximize gaseous CO₂ diffusion into leaves for higher rates of photosynthesis (Fig. 2) is indicated by the negative correlation between g_wmax and S (Fig. 4D). Large numbers of small stomata, linked to a decrease in atmospheric CO₂, could potentially also allow transpiration rates to rise. However, on the multi-million year time scale involved, the climate would also be expected to cool through a weakening of the atmospheric greenhouse effect and thereby diminish the driving force for evaporation from leaves.

The inability of large stomata to sustain high g_wmax is illustrated in Fig. 5. Color contours representing constant g_wmax for various combinations of S and D show that as S decreases, higher values of g_wmax become possible, as delineated by the increasing range of colors falling below the theoretical maximum (black line). Throughout the entire 400-Myr history of land-plant evolution, 2 distinct modes of change in stomatal S and D occur repeatedly in the fossil history of stomata, as revealed by S versus D cross-plots for five 50- or 100-Myr intervals (symbols in Fig. 5). Coordinated changes in S and D occur against a consistent pattern of CO₂ change or regime, as estimated by geochemical carbon cycle modeling (9) that is validated against independent proxy estimates (14).

Fig. 5.

Distinct modes of stomatal trait evolution. Graduations in g_wmax for multiple combinations of S and D are represented by color contours. The curved black line represents the theoretical upper limit of S versus D. Note that g_wmax at this limit increases with D, even though S decreases. Stomatal conductances attainable at small S and high D are theoretically unattainable at much larger S and lower D (red area), even though total pore area per unit leaf area is constant. Overlaid on this surface are data (pink symbols) for S and D from fossil plants, showing the predominance of smaller S and higher D in times of falling atmospheric CO₂ concentration.

The first mode emerges for plants experiencing a relatively stable, high-CO₂ atmosphere with nonglacial climates and is characterized by low densities of stomata (D), but with 10-fold variations in size (S) (Fig. 5 A, C, and D). These combinations of S and D, characterized by predominantly large S and small D, restrict g_wmax to low values. The pattern is consistent across a wide range of evolutionary life histories, from homosporous early vascular plants, such as Cooksonia in the CO₂-rich atmosphere of the Silurian (Fig. 5A), through to advanced gymnosperm and angiosperm trees experiencing “greenhouse” conditions in the Jurassic and Cretaceous (Fig. 5D). Similar responses of S and D are observed in modern plants under drought treatment, whereby S often becomes smaller, with minor increases in D (15–17). Conditions of simulated water stress via treatment with abscisic acid, a plant hormone released under water stress, induce a similar response (7). Ultimately in these circumstances, reductions in S tend to be proportionally greater than any increases in D, reducing g_wmax and improving the water-use economies of leaves (7, 17).

The second distinct mode of change in stomatal traits emerges when atmospheric CO₂ is falling and the Earth system is transitioning from a predominant “greenhouse” to “icehouse” state (Fig. 5 B, E, and F). Falling atmospheric CO₂ levels during glacial inceptions are accompanied by large variations in fossil density (D), but generally small stomates (S), allowing plants to operate with a higher g_wmax. This pattern occurs repeatedly as CO₂ levels drop during the onset of the Permo-Carboniferous glaciation (Fig. 5B), the long-term cooling leading to the Cenozoic glaciation (Fig. 5E), and the current icehouse world characterized by a geological interval of low CO₂ (Fig. 5F). It mirrors the effects of changes in atmospheric CO₂ on the stomata of extant plants (12, 13, 17, 18) and holds even for grasses evolving in the low-CO₂ atmosphere of the Miocene.

High g_wmax values contribute significantly to alleviating the negative impact of diminishing CO₂ availability on photosynthesis at these times by increasing CO₂ diffusion into leaves and can only be attained with considerable reduction in S in combination with high D. Having fewer, larger stomata cannot achieve the same effect because of concomitant increases in the length of the diffusion pathway through the pore (Fig. 2). A possible additional advantage to having flexibility in D relates to energetic cost. The energetic requirements of running stomata are proportionally small in relation to the respiratory costs of the whole leaf (19) but locally, as a fraction of epidermal tissue costs, may be significant. The guard cell respiratory cost in high-conductance cotton varieties, for example, is about twice that of low-conductance varieties (20). The flexibility to reduce D when environmental conditions demand lower g_wmax might, therefore, also constitute a metabolic cost-saving mechanism.

Discussion

Our analyses implicate long-term global atmospheric CO₂ change as a continuous driver of increasing g_wmax and g_cmax throughout the entire evolutionary history of vascular plants (Fig. 4C). The analyses identify a previously unrealized effect of CO₂ on stomatal size that is consistent with the direction of change observed in plant CO₂-enrichment experiments for a grass, C₄ herb, and an angiosperm C₃ tree (Table 1). Our study highlights the functional interdependence of S and D, particularly the inability of large S to support high g_cmax, while reinforcing the more widely recognized effect of CO₂ on D (12, 21, 22). We are not suggesting that atmospheric CO₂ has been the only driver on evolutionary time scales; other features of the climatic and ecological environment are also likely to be involved (2). However, the tight correspondence between changes in S and D with CO₂ is consistent with the biophysical requirements for increasing g_cmax under decreasing atmospheric CO₂ concentration and with physiological (23) and molecular (24) mechanisms linking plasticity of S and D with sensitivity to CO₂. If changing atmospheric CO₂ forced S to change by several orders of magnitude, then this mechanism has profound implications for the evolution of plant function in relation to cell size-dependent plant attributes.

The major physiological significance of the correlation of guard cell size, stomatal density, and g_cmax with atmospheric CO₂ over millions of years suggests a mechanism connecting long-term CO₂ change with the ecological radiation of land plants. Reconstructions of g_wmax from S and D in the fossil record have shown a systematic increase over geologic time (25), a pattern that mirrors the rise in land-plant diversity (26) and the coevolution of vascular water-conducting capacity (27). The mechanistic linkage underpinning the similarity of these records remains to be understood, but with regard to stomatal size, there are additional dynamic properties inherent in small S that, coupled with the higher photosynthetic capacity accompanying high g_wmax, would enhance plant fitness in a broader range of environments. Smaller stomata are capable of faster response times (2, 5), enabling improved water-use efficiency and optimization of long-term carbon gain with respect to water loss (28). Stomata of most plants reduce their apertures to counteract potentially high transpiration rates in dry air or high wind speeds (29). Smaller, faster stomata would, therefore, minimize exposure to excessive water-potential gradients through the plant and help protect plants from xylem embolisms. Taken together, these ecophysiological traits permitted plants to occupy broader ecological and environment niches and allowed diversity to increase.

We conclude that the coevolution of plants' gas-exchange capacity and the geochemical carbon cycle has, therefore, likely been a continuous feature of the Earth system for 400 Myr, entraining a suite of planetary-wide feedbacks (30) arising through the action of CO₂ at the cellular scale of stomata. A better understanding of the processes involved will contribute to elucidating a mechanistic explanation for the rise in land-plant biodiversity over this geologic time period, as documented in the fossil record a quarter of a century ago (26).

Data and Methods

Stomatal Dimensions.

All measures of S and D were obtained from published articles, acknowledging potential sampling bias and incompleteness of the paleobotanical literature. Data and sources are given in Table S1. Values were taken either directly as reported in the text or tables or, in some cases, measured from photomicrographs. Stomatal size S was calculated as guard cell length L multiplied by the width W of the guard cell pair. When W was not available, it was estimated as L/2 for nongrasses or L/8 for grasses. The theoretical maximum stomatal density D_max (in units of mm⁻²) for any given stomatal size, indicated by the hyperbolic black line in Figs. 1, 2, and 5, was calculated as 1/S, with S in units of mm² (i.e., D_max is 1 mm² divided by the area, in mm², of 1 stoma).

Calculating g_wmax.

Maximum stomatal conductance to water vapor, g_wmax, was calculated by using Eq. 1, with a_max approximated as π(p/2)², where p is stomatal pore length (Figs. 2, 4, and 5). When p was not available it was approximated as L/2 on the basis of information provided in ref. 5. Stomatal pore depth l for fully open stomata was taken as equal to guard cell width (i.e., W/2), assuming guard cells inflate to a circular cross-section. Values for standard gas constants d and v were those for 25°C. In Fig. 5, using S and D as inputs and p as L/2 (5), a matrix of g_wmax was generated and plotted as a graduated-color contour map (Fig. 5). Plots of S versus D for individual species in respective geological time periods were overlaid on this surface.

Calculating S for Fixed g_wmax and Variable D.

(Fig. 3.) With respect to Eq. 1, a_max was taken as 0.12S, with 0.12 being midway between the range of pore-area/stoma-area ratios for fully open stomata reported in ref. 5. Rearranging Eq. 1 then gives L ≈ 6(g_wmax·v)/(d·D), from which S was approximated as S = (L²)/2.

Statistical Analysis.

The significance of correlations was tested by using linear regression, with P values of <0.05 considered statistically significant. Means were compared by using one-way analysis of variance and post hoc means comparison (Scheffé Test). All data analysis and plotting were performed with OriginPro 8.0 data analysis software (OriginLab Corporation, Northampton, MA).