exchange of carbon and water, and environmental stress tolerance (Brodribb et al., 2013;Meinzer et al., 2003;Nobel, 2020;Olson et al., 2018;Smith & Sperry, 2014;Sperry et al., 2005;Zhong et al., 2020).

Leaf anatomical allometries have not been tested for grasses, a family (Poaceae) of 12,000 species diverse in morphology (Supporting Information: Table S1), that dominates 43% of the terrestrial surface, and accounts for the majority of crop production (Beer et al., 2010;McSteen & Kellogg, 2022). The optimisation of grass anatomy is part of Grand Challenge efforts to improve the physiology of stress tolerance and productivity, including the engineering of novel C4 crops from C3 precursors (Eckardt et al., 2023;Ermakova et al., 2020;Lowry et al., 2019). Grasses differ from typical eudicotyledons in leaf development and form. Grass leaves arise from an intercalary meristem, in which cells file through distinct zones of division, expansion and differentiation at the leaf base (Table 1; Figure 1; Evert, 2006;Fournier et al., 2005;Skinner & Nelson, 1994) resulting in linearised forms with parallel longitudinal veins T AB LE 1 Glossary of terminology related to allometry, leaf anatomy and grass development.

Study of size related properties, that is dimensions, mass, and/or metabolic processes and consequences for biological function (Huxley, 1932;Niklas, 1994).

C4 photosynthesis Photosynthesis that occurs through compartmentalising and concentrating CO2 at sites of carbon reduction within bundle sheath, leading to elevated rates of carbon accumulation and minimised photorespiratory losses (Christin et al., 2013;Dengler et al., 1985;Sage, 2004).

The height of the central grass shoot, typically quantified after flowering, and preceded by shoot elongation (Clayton et al., 2006;Evert, 2006).

The intercostal zone between vascular bundles that is often much thinner than the leaf section where vascular bundles and mesophyll occur (Ellis, 1976, e.g., Supporting Information: Figure S3d).

The growing region at the base of grass leaves, where cells divide, expand and differentiate; surrounded by the grass sheath (Evert, 2006;Fournier et al., 2005;Skinner & Nelson, 1994).

Mesophyll cell Non-vein cells that contain chloroplasts and generate sugars via photosynthesis (Evert, 2006).

Outer layer of thin-walled parenchymatous cells that surrounds vascular bundles and functions for water and nutrient storage, and regulating water, sugar and hormonal transport; in C4 plants, location of carbon reduction (Dengler et al., 1985;Evert, 2006;Griffiths et al., 2013).

Precursor cell Undifferentiated but often identifiable cells distinct in properties that indicate their mature cell type, for example, procambium (Evert, 2006).

Type I xylem cell Enlarged xylem conduit present in major vein orders; much larger but less numerous than type II xylem. Arises from procambium (Baird et al., 2021;Fournier et al., 2005;Nelson & Dengler, 1997).

Bulliform cell Specialised enlarged upper epidermal cells that regulate leaf rolling and unrolling via changes in cell turgor (Ellis, 1976;Evert, 2006).

Epidermal cell Cells that form the outer layer of the plant, including the upper and lower surface of leaves, regulating gas exchange and providing protection of internal cells (Evert, 2006).

Kranz anatomy Specialised conformation of leaf cells and tissues, with mesophyll cells arranged closely to parenchymatous vein sheath, facilitating CO2 concentration from mesophyll to bundle sheath, and CO2 assimilation in vein sheath (Christin et al., 2013;Dengler et al., 1985;Sage, 2004).

Plasmodesmata Channels connecting plasma membranes of adjacent cells that function for symplastic transport, that is exchange of cytoplasmic materials, including proteins and sugars (Danila et al., 2016;Evert, 2006).

Type II xylem cell Smaller xylem conduit present in all vein orders; much smaller but more numerous than type I. Arises from procambium (Baird et al., 2021;Evert, 2006;Nelson & Dengler, 1997). (1985), Evert (2006), Fournier et al. (2005), Granier and Tardieu (2009), Skinner and Nelson (1994), Volkenburgh (1999).

connected by transverse veins (Ellis, 1976;Evert, 2006). Like eudicots, grasses possess a parenchymatous bundle sheath surrounding all veins, derived from dividing lamina cells. Yet, grass leaves typically also possess a mestome sheath interior to the vein bundle sheath, which is derived from procambium precursors, like the xylem and phloem (Dengler et al., 1985;Evert, 2006). Further, 41% of grasses have C4 photosynthesis, and these possess specialised "Kranz" anatomy, including higher vein length per area, enlarged sheath cells, and much more extensive plasmodesmata connecting mesophyll with sheath cells, relative to C3 grasses (Christin et al., 2013;Danila et al., 2016;Dengler et al., 1985;Sage, 2004), all of which contribute to their C4 syndrome that confers higher rates of CO2 uptake and tolerance to aridity and extreme temperatures (Sage, 2004;Watcharamongkol et al., 2018).

Across species, we hypothesised a framework of inter-related anatomical allometries ("scaling relationships") of the form Cadart & Heald, 2022;Granier & Tardieu, 1998;Volkenburgh, 1999; see Supporting Information: Appendix, "Relationship of leaf developmental and evolutionary allometries, and insights into development and function"). Second, we hypothesised that leaf dimensions would be related to those of their constituent cells (Table 2; John et al., 2013).

Third, we hypothesised that xylem cell areas would increase with leaf size and plant height, such that xylem water transport capacity would at least in part compensate for the longer transport pathlengths in longer leaves of taller grasses (Table 2; Baird et al., 2021;Olson et al., 2018).

Fourth, we hypothesised that grasses would show similar leaf anatomical scaling as eudicots, with exceptions arising from their different leaf morphology (Table 2, Supporting Information: Appendix).

We expected that grasses would differ from eudicots in some leaf allometries, given their fewer cell layers, highly elongated shape and specialised roles of the epidermis and bundle sheath, including high shrinkage and expansion capacity allowing for leaf movements y = ax b or log y = log a + b log x,

(1) (including rolling), and/or water storage enabling buffering of lowwhere y and x are dimensions, and a and b the allometric intercept and slope (Table 2). First, we hypothesised allometries among cell dimensions due to proportional development, and, additionally, due to cell size coordination for integrated function (Table 2; Brodribb et al., 2013; resource availability. We thus expected grasses to differ from eudicots in allometries for cell cross-sectional areas of epidermis and bundle sheath versus overall leaf dimensions. Lastly, we hypothesised that across grass species, light-saturated photosynthetic rate per leaf mass

Framework of hypotheses tested in this study, rationale for hypotheses, traits measured and if the hypothesis was supported (see Table 1 for definitions of terminology). In grasses, the fewer cell layers, highly elongated leaf blade and specialised roles of bundle sheath and bulliform epidermal cells drives different allometries.

Leaf length, leaf area and culm height versus the cross-sectional areas of epidermises; Leaf length, leaf area and culm height versus the cross-sectional area of mesophyll; Leaf length, leaf area and culm height versus the cross-sectional area of parenchymatous bundle sheath.

T AB LE 2 (Continued)

(transport, metabolism and/or photosynthesis).

Amass versus the cross-sectional area of parenchymatous bundle sheath; Amass versus the cross-sectional area of mestome sheath; Amass versus the cross-sectional area of type I xylem; Amass versus the cross-sectional area of type II xylem.

(Amass) would scale positively with cell sizes in multiple tissues due to the integrated impact of cell size on leaf structure and function (Table 2). Amass is equivalent to light-saturated photosynthetic rate per leaf area (Aarea)/leaf mass per area (LMA) (Sack et al., 2013). Given that leaves with large cells would tend to be thicker (John et al., 2017), we hypothesised they would have higher Aarea, as previously found in studies of grasses and eudicotyledonous species (Charles-Edwards et al., 1974;Garnier et al., 1999;Koike, 1988;Wilson & Cooper, 1967), and that they would be wider, with lower major vein length per area (Baird et al., 2021), contributing to a lower LMA (John et al., 2017).

Further, larger xylem conduits drive higher hydraulic supply which would enable higher Aarea and would also be reflected in a high Amass.A parallel coordination of Amass with cell sizes in multiple tissues, including photosynthetic mesophyll and xylem transport tissue, would further support our first hypothesis of functional coordination of cell sizes throughout the leaf for metabolism and transport.

For the majority of relationships among cell and leaf dimensions, we expected that proportional development would result in geometric allometries, which would be reinforced by selection for coordinated and integrated function. Thus, areas (A) would scale together isometrically as A ∝ A 1 and with lengths (L) as L ∝ A 1/2 (Table 1; Supporting Information: Appendix; Baird et al., 2021;John et al., 2013;Niklas, 1994;Sack et al., 2012). We expected divergences from geometric scaling, that is, decoupling of proportional development, for certain functionally specialised tissues (Table 3). Thus, relative to other cell types, we expected disproportional increases in cell size for the upper epidermis, reflecting a greater investment in supporting functions including large specialised bulliform cells that provide water storage and enable leaf rolling (Ellis, 1976;Evert, 2006). Further, we expected divergence from geometric scaling for allometries among xylem cell types that would be coordinated for optimal hydraulic design; for the major and minor vein systems to maintain matched transport efficiency across leaves of different size, the size of type I xylem conduits (which occur only in major veins) would increase disproportionately relative to type II xylem (which occur in both major and minor veins) to compensate for the declining density of major veins that are spaced out further in larger leaves (Baird et al., 2021). We expected leaf dimensions to increase disproportionately with cell cross-sectional areas, as dimensions also depend on the additional role of cell number, which in larger leaves increases disproportionately relative to cell areas (Gázquez & Beemster, 2017;John et al., 2017). We expected leaf length and culm height would increase disproportionately relative to vein xylem cell sizes; increases in xylem cell size that would mitigate of impacts of increasing path length need not be proportionate, because hydraulic conductance through xylem increases as the radius to the fourth power (Sack & Scoffoni, 2013). Finally, we expected that C3 and C4 grasses would differ in allometries, with more generalised relationships across all cell types across C3 species, because specialised C4 cell functions associated with Kranz anatomy and carbon concentrating mechanism, including higher densities of plasmodesmata (Danila et al., 2016), may disrupt cell size-function relationships. We expected that for C4 species, selection for enlarged sheath cells (Christin et al., 2013) would decouple the cell cross-sectional areas of bundle and mestome sheaths, mesophyll and xylem.

To test this framework of hypothesised general relationships, we used a common garden, glasshouse experiment to measure leaf anatomy and photosynthetic rate in a phylogenetically structured sample of 27 grass species.

We selected 27 grass species to represent high functional and phylogenetic diversity, encompassing 11 C4 origins (16 C4 species; 11 C3 species), and including terrestrial and aquatic species and important crops (Figure 2; Supporting Information: Figures S1-S3;

Supporting Information: Table S1). Plants were grown in a common garden to minimise environmentally-driven plasticity. The individuals sampled for anatomical measurements in this study (see "Anatomical sample preparation and measurements") were the same individuals and leaves sampled for leaf size and venation traits in a previous publication (Baird et al., 2021).

Seeds were acquired from seed banks and commercial sources (Supporting Information: Table S1), and before germination were surface-sterilised with 10% NaClO and 0.1% Triton X-100 detergent, rinsed with sterile water, and sown on plates of 0.8% agar sealed with Micropore surgical tape (3M). Seeds were germinated in chambers maintained at 26°C, under moderate intensity cool white fluorescent lighting with a 12-h photoperiod. When roots ranged from 2 to 3 cm long, seedlings were transplanted to 3.6 L pots with potting soil ). We grew all 27 species in potting soil, including the three species classified as aquatic (Oryza sativa, Phragmites australis, Sacciolepis africana), to maximise similarities in growth conditions across species; as in previous studies these aquatic grasses grew to maturity under nonaquatic conditions (Clevering, 1999;Kato & Okami, 2010). All species were grown until flowering to verify species identities.

For three individuals per species that possessed many mature leaves, one leaf was fixed and stored, and 1 µm thick transverse cross sections were prepared, stained, and imaged by light microscopy (Fletcher et al., 2018;John et al., 2013;Nobel, 1976;Nobel et al., 1975) (Leica Leitz DMRB; Leica Microsystems with SPOT Imaging Solution camera; Diagnostic Instruments, Sterling Heights). Leaves were fixed and stored in FAA solution (37% formaldehyde-glacial acidic acid-95% ethanol in deionized water). Central rectangular samples were cut from each leaf halfway along the length of the blade and gradually infiltrated under vacuum with low-viscosity acrylic resin (L. R. White; London Resin Co.). Infiltrated samples were set in resin in gelatin capsules to dry at 55°C overnight. Transverse cross sections of 1 µm thickness and of varying width (species dependent) were prepared using glass knives (LKB 7800 KnifeMaker; LKB Produkter; Bromma, Sweden) in a rotary microtome (Leica Ultracut E, Reichert-Jung California), placed on slides and stained with 0.01% toluidine blue in 1% sodium borate (w/v). Slides were then imaged at 5×, 20×, and 40× objective using a light microscope (Leica Lietz DMRB; Leica Microsystems) and camera with imaging software (SPOT Imaging Solution; Diagnostic Instruments, Sterling Heights).

We quantified leaf thickness and cell cross-sectional areas of the mesophyll, upper and lower epidermis, parenchymatous bundle and mestome sheaths and xylem using the programme ImageJ (Fletcher et al., 2018;John et al., 2013;Nobel, 1976;Nobel et al., 1975) (ImageJ version 1.42q; National Institutes of Health). Cell crosssectional area was used as an index of cell size (Nobel, 2020), which would reflect cell volumes in the case of mesophyll cells, which are symmetrical in shape, but not for epidermal, vascular sheath and xylem cells, which differ in shape between transverse and paradermal planes (Nobel, 1976;Nobel et al., 1975). Measurements of cells of the mesophyll and the lower and upper epidermis were replicated three times for each cross section. In the middle of the left, center and right thirds of the cross section, mesophyll cells were selected for determination of cell area and, given their irregular shapes, were traced. We measured leaf thickness three times at the left, center and right thirds of the cross section that excluded leaf furrows (Table 1; Ellis, 1976). Epidermal cells were similarly selected, but their areas were determined as the area of an ellipse, area = π × a × b, where a and b are the radii of the major and minor axes, that is, the lengths and widths of the cells. Dimensions of parenchymatous bundle and mestome sheath cells and xylem conduits were quantified for each specific vein order, and their areas determined as for epidermal cells.

Cells were measured for vein xylem and parenchymatous bundle and mestome sheaths in the major veins, that is, the 1° "midvein" and 2°

"large" veins, and in the minor veins, that is, the 3° "intermediate" veins, and, for the species that possessed them, the 4° "small" veins; these 4° "small" veins occur in one C4 clade (the NADP-ME of Panicodeae), represented by seven species in this study, for which the mestome sheath functions for carbon reduction and is the only vein sheath, excluding A. semialata which possesses 4° veins, and has both sheaths (Dengler et al., 1985). To reduce biases in calculating average xylem cell sizes, we differentiated two metaxylem conduit types within the major veins, which is consistent with previous studies noting that these conduit types are clearly developmentally and functionally distinct (Dannenhoffer et al., 1990;Russell & Evert, 1985). The major veins contain large "type I xylem" conduits, and both major and minor veins contain the distinctively smaller "type II xylem" conduits (Baird et al., 2021). For each vein order, we selected one small, one medium and one large parenchymatous bundle sheath cell (same for mestome sheath cells), and determined their average area, and we quantified all xylem cell areas within each vein order, and averaged these for type I and for type II xylem. We also calculated average parenchymatous bundle and mestome sheath and type I and II xylem cell areas across all vein orders. We did not quantify second-order vein or sheath traits for the species Lasiacis sorghoidea, as we lacked high magnification images that included their very widely spaced second-order veins. We did not quantify phloem cell dimensions due to the inability to competently distinguish sieve cells from parenchyma in the images.

We also utilised published values for maximum leaf length and width, and leaf area as their product, and published values for culm height data as a measure of plant height, to test relationships with leaf and plant morphology with cross-sectional cell areas (Baird et al., 2021;Clayton et al., 2006). The product of maximum length and width overestimates leaf area for grasses; however no standard correction value exists for grasses (Kemp, 1960;Shi et al., 2019;Stickler et al., 1961). Considering the diverse set of leaf shapes included in our experiment, and noting that a correction factor is unlikely to impact differences on the log scales used for the correlation coefficients, scaling exponents and their statistical significance, we did not apply a correction factor and our estimates of leaf area should be taken as approximate. We utilised published data for major vein length per leaf area (VLAmajor; Baird et al., 2021) to test relationships of cell cross-sectional areas with VLAmajor.

Leaf gas exchange data for the eight C3 terrestrial grasses was previously published (Baird et al., 2021). For all 27 grass species, including the eight C3 terrestrial grasses, we measured light-saturated rates of gas exchange from 17 February to 28 June 2010, between plants per species. We measured steady state gas exchange (<2% change over 6 min) using a LI-6400XT portable photosynthesis system (LI-COR, Lincoln). The leaf chamber was maintained at 25°C, with reference CO2 400 ppm, and PPFD 2000 µmol m -2 s -1 , which was assumed to be saturating irradiance for these species (Taylor et al., 2010). The ranges of relative humidity and vapour pressure deficit (VPD) were respectively 60%-80% and 0.80-1.6 kPa (overall mean 1.1 kPa). Measurements were made for 1-2 leaves from each of six plants (except from 5, 4 and 7 plants for A. purpurea, A. semialata and P. australis respectively, and for 3 leaves from each of two plants for L. sorghoidea); overall, 5-9 leaves (mean of 6) were measured per species. Leaf-area normalised values were determined for net photosynthetic rate per leaf area (Aarea). Leaves were traits with other cell areas (Baird et al., 2021;Niklas, 1994;Poorter & Sack, 2012;Warton et al., 2006).

Typically, allometric relationships arise as two-parameter power laws with zero intercepts when considered with untransformed data (Equation 1). As is typical of allometric studies, we considered a slope to be consistent with geometric scaling when its 95% confidence interval included the test value (Baird et al., 2021;Poorter & Sack, 2012). We tested for differences in trait means between C3 and C4 species using a phylogenetically corrected analysis of variance, both parametric and nonparametric (Garland et al., 1993;Revell, 2012).

For several relationships in our study, data were inconsistent with a power-law, because they had a clear nonzero intercept. In these cases, linear relationships fitted well:

harvested, scanned for leaf area (Canon Scan Lide 90, Canon USA,

(2) Lake Success), dried at 70°C for at least 48 h and weighed to determine the leaf dry mass per unit area (LMA). Net CO2 assimilation rate per unit leaf dry mass (Amass) values were determined as Aarea/LMA.

Before testing cross-species relationships, we evaluated whether species differed meaningfully in mean trait values, using a nonphylogenetic analysis of variance (ANOVA) on all traits, and tested for the influence of species identity, such that residual error was associated with replicate individuals of a species, enabling estimation of the percent of variation in each trait arising across species relative to that arising among individuals of the same species (Supporting Information: Table S2).

Using a published phylogeny, we tested trait-trait relationships across all species and within particular groups: C3 grasses; C4 grasses; C3 terrestrial, that is, removing the C3 aquatic species (which were in several cases outliers); and C4 + C3 terrestrial (Figure 2; Baird et al., 2021). For comprehensiveness, we tested relationships among cell sizes for the seven tissue types (i.e., 21 pairwise combinations). For vein type I and II xylem, and parenchymatous bundle and mestome sheath cells, relationships were tested within each vein order (six pairwise combinations each for 1° and 2° veins; three for 3° veins, lacking type I xylem; and 1 for 4° veins, lacking type I xylem and parenchymatous bundle sheath = 16 combinations). Analyses were performed using the R Language and Environment, modifying published code with phylogenetic functions (Baird et al., 2021). We fitted lines to logtransformed data, the typical approach in allometric analyses (Baird et al., 2021;Niklas, 1994;Poorter & Sack, 2012;Warton et al., 2006). We used the phytools package (Revell, 2012) to fit phylogenetic reduced major axes regressions (PRMA) for the majority of scaling relationships. Because only seven species had fourth order veins, we used non-phylogenetic standard major axis (SMA; a synonym of reduced major axis, i.e., RMA; Warton et al., 2006) regression to evaluate scaling of fourth order vein cell area where y and x are dimensions, and a and b are the intercept and slope. When y and x have the same dimensionality (i.e., two areas, or two lengths), a positive linear relationship would support geometric (proportional) scaling, given the smallness of the a-value. Thus, when hypothesised relationships were not significant as power law relationships, we tested linear regressions, and report these when significant; this was the case for the scaling of the parenchymatous bundle sheath and the lower epidermis, and, for C3 species only, the scaling of the mestome sheath and the upper epidermis (Figure 3).

We utilised a trimmed phylogeny to test relationships with the parenchymatous bundle sheath, which was possessed by only 21 of the grass species (Supporting Information: Figure S1; that is, all C3 and C4 species with three longitudinal vein orders). Finally, analyses including second order vein or sheath traits excluded the species L. sorghoidea, and trimmed phylogenies excluding this species were also implemented.

Grass species varied strongly in the mean cell cross-sectional areas of all tissues, from fourfold for type II xylem conduits to 17-fold for parenchymatous bundle sheath cells, and in leaf dimensions, from threefold for thickness to 24-fold for leaf width (Supporting Information: Table S1). On average, 76% of trait variation was explained by differences among species rather than among individuals in each species (ANOVA; Supporting Information: Table S2, Supporting Information: Figures S2 and S3). C4 species had larger cell areas on average than C3 for the upper epidermis, mestome sheath, and 3° vein xylem (phylogenetic ANOVAs;

Supporting Information: Table S2).

We found allometries among cell sizes across tissues for 15 of the 21 pairwise combinations of tissues, that is, the lower and upper FI GURE 3 Grass cell size allometries and anatomy. (a-u) Allometries across tissues of grass leaves. (v) Schematic of C3 grass cross-sectional anatomy. Green and brown labels in (v) represent cells derived from non-procambium and procambium precursor cells, respectively (unmeasured cells in purple). Each point is one species, n = 11 C3 (eight terrestrial in red, three aquatic in grey) and n = 16 C4 species in blue. Fitted lines are phylogenetic reduced major axis (PRMA) regressions with statistics on the right and in Supporting Information: Table S3. Line colours indicate that the relationship was significant across a specific set of grasses, with black lines across all species, red lines across C3 species, and segmented lines across the terrestrial species either across all grasses or only C3

grasses. b-values are presented for grasses and eudicots; italics indicate departure from geometric scaling. See Table 1 for cell type definitions. *p < 0.05, **p < 0.01, ***p < 0.001. [Color figure can be viewed at wileyonlinelibrary.com] epidermis, mesophyll, parenchymatous bundle and mestome sheaths, and type I and type II xylem (phylogenetic reduced major axis;

Figure 3). The allometries between epidermises, for epidermises versus mesophyll, for parenchymatous bundle sheath versus mesophyll, between xylem types, and for xylem versus mestome sheath were significant across all species. However, several relationships involving xylem, epidermises and vein sheaths, were significant only for the terrestrial grasses or the terrestrial C3 grasses (Figure 3; Supporting Information: Figure S5, Supporting Information: Tables S3 and S4). Xylem cell sizes were statistically independent of those in mesophyll and epidermises. Within vein orders, significant relationships arose for 14 of the 16 allometries, that is, among parenchymatous bundle and mestome sheaths and type I and II xylem (Figure 4 and Supporting Information: Figures S4 and S5; Supporting Information: Table S4).

Cell size allometries were geometric for 10 of the 15 significant across-tissue relationships and for 8 of the 14 significant within-vein relationships (b = 1).

Nongeometric allometries across-tissues were those of mesophyll versus upper epidermis, mesophyll versus parenchymatous bundle sheath, type I versus type II xylem, parenchymatous bundle sheath versus mestome sheath and parenchymatous bundle sheath versus type II xylem. Non-geometric relationships within-veins were those of type I versus type II xylem, mestome sheath versus type I xylem, and parenchymatous bundle sheath versus type II xylem (all within the 1° vein), and mestome sheath versus parenchymatous bundle sheath (within the 1°, 2°, and 3° veins; Supporting Information: Tables S3 and S4). S4). Lines were fitted with phylogenetic reduced major axis regressions (PRMA) and statistics and parameters are found in Supporting Information: Table S4. Italics indicate departure from geometric scaling. See Table 1 for

Across species, leaf dimensions and plant height were positively related to leaf cell sizes in all tissues (Figures 56; Supporting Information: Table S5; Supporting Information: Figure S6). Thus, leaf thickness was allometrically linked with cell areas in the mesophyll and epidermises; leaf width was allometrically linked with cell areas in the mesophyll, parenchymatous bundle sheath and type I xylem (Figure 5); and leaf area was allometrically linked with cell area in the lower epidermis. Further, leaf length, leaf area and plant size (culm height) were allometrically linked with cell areas in the type I and II xylem; leaf length and leaf area with cell areas in the mestome sheath; and culm height with cell areas of the parenchymatous bundle sheath (Figure 6). The majority of allometries held across all species, but several relationships involving the epidermises and vein tissues were significant only for the terrestrial grasses or the terrestrial C3 grasses (Figures 5 and 6). The allometries of leaf thickness versus cell areas were geometric, whereas the majority of the relationships of leaf width, leaf length, leaf area and culm height versus cell areas were greater than geometric (Figures 5 and 6;

Supporting Information: Table S5).

Grasses showed similar allometries between cell sizes for lower epidermis versus upper epidermis and the parenchymatous bundle sheath as previously found for diverse eudicots (Figure 2 Fitted lines are phylogenetic reduced major axis (PRMA) regressions with statistics above each panel and in Supporting Information: Table S5.

Line colours indicate that the relationship was significant across a specific set of grasses, with black lines across all species, red lines across C3 species, and segmented lines across the terrestrial species either across all grasses or only C3 grasses. b-values are presented for grasses and eudicots for comparisons with leaf thickness and bolded when significantly different; italics indicate departure from geometric scaling. See Figure 3 and Table 1 for cell type definitions. *p < 0.05, **p < 0.01. [Color figure can be viewed at wileyonlinelibrary.com] epidermis respectively in grasses; b > 1 for both in eudicots; Figure 3), and for leaf thickness versus cell areas of the upper epidermis (b = 0.5 for grasses; b > 0.5 for eudicots; Figure 5b).

Across species, cell sizes were associated positively with massbased light-saturated photosynthetic rates (Amass) and its determinants, the area-based light-saturated photosynthetic rate (Aarea) and negatively associated with LMA. Cell sizes were also associated negatively with the major vein length per area (VLAmajor) (Figure 7; Supporting Information: Figure S7; Supporting Information: Table S6). Amass was generally positively coordinated with the mean cross-sectional areas of cells in all tissues; however, the association with mesophyll cell size was significant only for C4 species, and marginally nonsignificant for C3 species alone or for all species pooled (Supporting Information: Table S6). Compared with the majority of C3 grasses included in this study C4 grasses achieved higher Amass for a given mesophyll cell size (Figure 7). C4

species had significantly higher Aarea, and the similar investment in LMA between C3 and C4 species resulted in C4 species also having higher Amass (Supporting Information: Table S2). Aarea was correlated with fewer cell cross-sectional areas than Amass, showing significant associations with those of the upper epidermis (terrestrial species only), mestome sheath, and type I and II xylem S5. Line colours indicate that the relationship was significant across a specific set of grasses, with black lines across all species, red lines across C3 species, and segmented lines across the terrestrial species either across all grasses or only C3 grasses. bvalues are presented for grasses and eudicots for comparisons with leaf thickness and bolded when significantly different; italics indicate departure from geometric scaling. See Figure 3 and Table 1 for S6. Line colours indicate that the relationship was significant across a specific set of grasses, with black lines all species and the blue line in (a) across only C4 species. See Figure 3 and Table 1 for

While Kranz anatomy of C4 species meant that C3 and C4 species differed strongly in their anatomy, many allometries were conserved across the two photosynthetic types (Figures 34567; Table 2). Acrossspecies allometries between cell areas within and among tissues would emerge from conserved coordinated cell expansion within organs (Granier & Tardieu, 1998;Volkenburgh, 1999), reinforced by selection for proportional cell sizes (and possibly cell numbers) that would facilitate coordination of metabolic and transport functions within and across tissues (Brodribb et al., 2013;Cadart & Heald, 2022;John et al., 2013). Generally, cell area allometries occurred among cells derived from the same developmental precursors (Table 1). Thus, we found cell size allometries for cells arising from lamina precursor cells, including epidermises, mesophyll and the parenchymatous bundle sheath (Figure 3a-f). Separately, we found independent cell size allometries for cells arising from the procambium, including xylem and mestome sheath (Figure 3o,t-u).

We note that our study did not include a focus on phloem cells, which also arise from procambium precursors. Elucidating potential allometries of phloem with other cell types and whole plant design remains an urgent avenue for future research linking sugar transport with leaf and whole plant function (Hölttä et al., 2013;Ronellenfitsch et al., 2015).

Beyond the allometries that could be explained by shared developmental precursor cells, we found that C3 species showed more generalised scaling of cell areas across tissues than C4 species (Figure 3 and Supporting Information: Figures S4 and S5; Supporting Information: Table 2). For C3 species, we found allometries between cells that arose from different precursors, that is, cells of mestome sheath versus mesophyll, epidermis and parenchymatous bundle sheath, and xylem versus parenchymatous bundle sheath cells (Figure 3g-j,n,s). Allometries among cells arising from different developmental precursors in C3 species suggest selection for coordination of metabolism and transport (Brodribb et al., 2013). In the C4 species, the independence of cell sizes of the parenchymatous bundle sheath from xylem, and mestome sheath from mesophyll, is consistent with the additional constraints imposed by their Kranz anatomy, including the necessity for large sheath cells, irrespective of mesophyll cell sizes (Christin et al., 2013). The large C4 sheath cells, with specialised metabolism and transport, have much more extensive plasmodesmatal connections with the mesophyll than sheath cells of C3 species, which presumably act as an alternative to coordination of cell size and interfacing cell surface areas for transport function (Cadart & Heald, 2022;Christin et al., 2013;Danila et al., 2016).

We found several allometries that occurred only among terrestrial grasses, including the relationships of cell sizes in the parenchymatous bundle sheath versus upper and lower epidermises.

Overall, the aquatic species had consistently smaller epidermal cells than terrestrial grasses, potentially reflecting their generally less pronounced water storage and potentially a lower requirement for large bulliform cells that enables leaves to roll and thereby better avoid overheating and dehydrating under dry conditions (Ellis, 1976;Evert, 2006).

We found strong allometries between leaf dimensions and the sizes of their constituent cells (Figure 5; Table 2). Cell sizes (in addition to cell numbers) may make especially important contributions to leaf dimensions especially given the low airspace porosity of grass leaves (Supporting Information: Figures S2 and S3; Gázquez and Beemster, 2017). Thus, thicker grass leaves are associated with larger cells in the mesophyll and epidermises, and wider leaves with larger and parenchymatous bundle sheath cells (Figure 5 and Supporting Information: Figure S6). Notably, the scaling of leaf width with the cell sizes in the mesophyll and the parenchymatous bundle sheath provides an anatomical mechanism for the global relationship of lower VLAmajor in wider grass leaves (Baird et al., 2021). The major veins are patterned early by the procambium and thus greater mesophyll and parenchymatous bundle sheath cell expansion would space major veins further apart in wider leaves (Baird et al., 2021), a pattern supported by the negative relationship of VLAmajor with cell sizes in those tissues (Supporting Information: Figure S7). Thus, the allometric linkages of cell size and leaf dimensions enables stress tolerance traits to be selected across levels of organisation as smaller cells and narrower leaves, both linked with higher vein densities, would contribute to tolerance of drought (Baird et al., 2021;Cutler et al., 1977).

We found strong allometries of xylem cell sizes with leaf length, leaf area and plant height (Figure 6; Table 2). These relationships are consistent with selection of larger xylem cells for greater biomechanical support, and hydraulic capacity to mitigate both the greater pathlength in longer leaves and the potentially higher evaporative loads in larger plants. Indeed, these trends are consistent with global trends for the scaling of plant height with xylem conduit sizes in the stems of taller plants, including trees (Figure 5h,i,k-l,o,p; Baird et al., 2021;Olson et al., 2018;Sack et al., 2013). Likewise, the larger parenchymatous bundle sheath cells in leaves of taller grasses may provide greater storage and outside-xylem hydraulic conductance that would contribute to mitigating the hydraulic stresses associated with both larger plant size and greater exposure and thus, higher evaporative demand (Figure 5n; Buckley et al., 2015).

Geometric scaling was typical for the allometric relationships of cell sizes across grass species. Geometric scaling is consistent with both proportional cell expansion, and coordination of cell sizes for matched flows of water, nutrients and sugars (Brodribb et al., 2013;Cadart & Heald, 2022;Granier & Tardieu, 1998;John et al., 2013;Volkenburgh, 1999). The cases in which specific allometries departed from geometric scaling could be explained based on specific developmental causes and functional benefits for the disproportionate size of one cell type over another (Table 3). For example, the greater increase in cell sizes in the parenchymatous bundle sheath and upper epidermis relative to the mesophyll (b > 1) is consistent with a disproportionate investment in support functions including water storage in epidermises, and bundle sheath (Griffiths et al., 2013) and for epidermal bulliform cells influencing mechanical protection and leaf rolling during dehydration (Ellis, 1976;Evert, 2006), which would protect leaves with larger mesophyll cells (Figure 3b,f). Further, the less-than-geometric scaling in the cell size of type II relative to type I xylem (b < 1) is consistent with the optimisation of vascular system design, as type I xylem are present only in major vein orders, which decline in vein length per area in wider leaves (Figure 3u; Table 3; Baird et al., 2021). Thus, a disproportionate increase in type I relative to type II xylem cell size would compensate at least in part for the effect of declining vein length per area of major veins on vein transport efficiency and also provide greater mechanical rigidity (Table 3). Several of the allometries of leaf and plant dimensions with cell areas exhibited greater-than-geometric scaling, which would arise for several reasons. First, the greater than geometric scaling of leaf width with the cell areas of mesophyll and the parenchymatous bundle sheath (b > 0.5) is consistent with wider leaves being determined by greater cell numbers even more than by larger cells, with a particular role of the larger diameter veins in wider leaves (Figure 5; Table 3; Gázquez & Beemster, 2017;John et al., 2017;Pantin et al., 2012). This contrasts with the geometric scaling of leaf thickness with the cell areas of mesophyll and the epidermises, which indicates a greater role for cell size than cell number in driving thickness differences.

Further, the greater-than-geometric scaling of leaf length, leaf area and culm height with xylem cell areas (b > 0.5 for leaf length and culm height, b > 1 for leaf area) is consistent with optimisation of the vascular system design, as hydraulic conductance through xylem conduits increases as a function of the radius to the fourth power, so xylem would not need to increase proportionally in size to counteract the impact of increasing path length in longer leaves and taller grass shoots (Nobel, 2020).

Grasses and eudicots were similar in several anatomical allometries, including geometric scaling of cell areas of the epidermises, and of the lower epidermis versus the parenchymatous bundle sheath, consistent with coordinated development and function (Figures 3, 5, and 6; Table 2). However, several trends differed for grasses. The scaling of xylem cell sizes with leaf dimensions in grasses, not observed for eudicots, is consistent with the specific importance of cell sizes for biomechanical support and axial hydraulic transport in longer grass leaves (Figure 6). The less than geometric scaling of cell areas of mesophyll versus upper epidermis in grasses, but geometric scaling in eudicots, is consistent with many grass leaves investing in large bulliform cells for storage and leaf rolling movements, a 3).

The geometric scaling of leaf thickness versus cell area of the upper epidermis in grasses, but greater than geometric scaling in eudicots, indicates coordinated contribution of cell size to leaf thickness in grasses and a greater contribution of cell layers to thickness in eudicots. This is consistent with eudicot leaves having many palisade layers and the lower proportion of airspace in grass leaves relative to eudicots (Figure 5, Supporting Information: Figures S2 and S3). While these differences between grasses and eudicots are consistent with their contrasting structure, sampling additional diversity will improve our ability to generalise; for example, we not know whether the trends we report here for grasses are generalisable more broadly to monocots. Further, it may be possible to resolve similar allometries in some eudicot lineages, depending on taxonomic scale.

Across grass species, light-saturated photosynthetic rate was strongly related to cell sizes. Our data provide a novel resolution of the relationship across grass species of Amass with coordinated changes in cell cross-sectional size across the mesophyll, epidermises, parenchymatous bundle sheath, mestome sheath, and type I and II xylem (Figure 7; Table 2). That photosynthetic rate coordinates with cell size across cell types indicates that the separate allometries between procambium and nonprocambium derived cell types converge to maximise photosynthetic function (Figure 7; Supporting Information: Figure S7).

Notably, light-saturated photosynthetic rate can be limited by many factors (Niinemets et al., 2009;Salvi et al., 2021), and Amass in particular is influenced by structural relative to photosynthetic allocation. Leaves with high Amass allocate more mass to photosynthetic structure relative to structural components that increase leaf longevity (Wright et al., 2004); thus, a higher Amass can arise from a higher Aarea and/or lower LMA (Sack et al., 2013). We expected that larger-celled leaves would have higher Amass, not due to direct causality but from several structural effects. First, larger cells, and particularly larger cells in the mesophyll (Figure 5a), were associated with thicker leaves, as found for eudicots (John et al., 2017) and would correspond to a higher number of chloroplasts (Ellis & Leech, 1985) and a higher concentration of photosynthetic machinery per leaf area (Garnier et al., 1999;Koike, 1988) and thus, a higher Aarea (Niinemets, 1999). Second, we expected that small cells would be related to higher LMA through a higher concentration of cell wall material per leaf area (John et al., 2017), and, as Amass = Aarea/LMA, this higher LMA would correspond to a lower Amass for small-celled species. Indeed, we found that higher LMA was related to smaller cell size in several tissues, including the mesophyll, epidermises and parenchymatous bundle sheath (Supporting Information: Figure S7). Third, VLAmajor may also contribute substantially to higher LMA (John et al., 2017;Sack et al., 2013), and small mesophyll and bundle sheath cells were associated with more closely-spaced veins and thus higher VLAmajor. While a higher VLAmajor is implicated in hydraulic function and contributes to higher Aarea in grasses (Baird et al., 2021), across species, the contribution of high VLAmajor to a higher LMA in smallcelled species would contribute to a low Amass in small-celled species, and higher Amass in large-celled species. Finally, the association of higher Aarea with larger type I and type II xylem conduits (Supporting Information: Figure S7) is consistent with these larger conduits providing greater hydraulic supply that enables greater stomatal opening and higher photosynthetic gas exchange (Sack & Scoffoni, 2013). Thus, the association between Amass and cell sizes in all tissues are consistent with multiple expected impacts of cell size on Aarea and/or LMA (Supporting Information: Figure S7). The possibility that cell size is a relatively simple predictor of mass normalised photosynthetic productivity in grasses is a finding with potential applications both in understanding the ecology of diverse grass species and for improving crop productivity.