Scaling of petiole anatomies, mechanics, and vasculatures with leaf size in the widespread Neotropical pioneer tree species Cecropia obtusa Trécul (Urticaceae)

33 1. Although the leaf economic spectrum has deepened our understanding of leaf trait 34 variability, little is known about how leaf traits scale with leaf area. This uncertainty has 35 resulted in the assumption that leaf traits should vary by keeping the same pace of variation 36 with increases in leaf area across the leaf size range. We evaluated the scaling of 37 morphological, tissue-surface, and vascular traits with overall leaf area, and the functional 38 significance of such scaling. 39 2. We examined 1271 leaves for morphological traits, and 124 leaves for anatomical, and 40 hydraulic traits, from 38 trees of Cecropia obtusa Trécul (Urticaceae) in French Guiana. 41 Cecropia is a Neotropical genus of pioneer trees that can exhibit large laminas (0.4 m² for C. 42 obtusa ), with leaf size ranging by two orders of magnitude. We measured (i) tissue fractions 43 within petioles and their second moment of area, (ii) theoretical xylem hydraulic efficiency of 44 petioles, and (iii) the extent of leaf vessel widening within the hydraulic path. 45 3. We found that different scaling of morphological trait variability allows for optimisation of 46 lamina display among larger leaves, especially the positive allometric relationship between 47 lamina area and petiole cross-sectional area. Increasing the fraction of pith is a key factor that 48 increases the geometrical effect of supportive tissues on mechanical rigidity and thereby 49 increases carbon-use efficiency. We found that increasing xylem hydraulic efficiency with 50 vessel size results in lower leaf lamina area: xylem ratios, which also results in potential 51 carbon savings for large leaves. We found that the vessel widening is consistent with 52 hydraulic optimisation models. 53 4. Leaf size variability modifies scaling of leaf traits in this large-leaved species. 54 56


INTRODUCTION
4 different pace of variation between two traits, and implying changes of organ or organism 92 form and shape. Discerning allometric vs isometric relationships between organ or organism 93 traits is an important priority, since different functional requirements can be reflected between 94 small vs large organs or organisms, and finally different responses to selective pressures 95 (Harvey andPagel 1991, Brouat et al. 1998). The lamina-petiole relationship, or the 96 relationship between a given leaf trait with leaf size, has been little studied in this scaling 97 perspective. This gives scattered ideas if leaf size affects leaf functional requirements, and 98 further if sampling both small and large leaves make a big difference for mechanical, 99 hydraulic, and photosynthetic quantifications. the flexural stiffness between small vs large leaves remains poorly described (Niklas 1999).  In comparison to the leaf dry mass-area scaling or petiole mechanics, little is currently 136 known on the link between leaf size, leaf hydraulic conductivity and vascular architecture.

137
Understanding size-related changes of leaf hydraulics and vasculature is important to address 138 size-independent variation, as pointed out for stems (Olson et al. 2009   We chose to investigate lamina-petiole traits at the intraspecific level as a first step. 178 We focussed this study on the genus Cecropia, which is known for its hyperdominant pioneer   to what is known for the stem, consistent with leaves supporting a large amount of the total 198 hydraulic resistance of plants. We also hypothesise that less construction cost is possible than 199 under the hypothesis of an invariable vessel diameter, thanks to a more efficient xylem due to 200 wider vessels, enabling more lamina area per xylem area.     types that comprise the entire petiole anatomy (Fig. 1d, e). We manually delineated the tissues 269 on the photographs and created layer masks (Fig. 1e). The masks of these layers were used to  (Table 1), 282 slight increases in the ring diameter and/or cross-sectional area has dramatic consequences for 283 I, and thus its contribution to flexural stiffness. We focused on the sclerenchyma, 284 collenchyma and secondary xylem, since these tissues are well-known to be supportive tissues 285 in a section and exhibit lignified thick cell walls (Leroux 2012). We also estimated the 286 behaviour of the petiole flexural stiffness by calculating I for the total petiole section, and by 287 using the known petiole density as a proxy of E (Table 1). We assumed that this 288 approximation was appropriate, since it had been shown that the elastic modulus exhibits a   in a given tissue would have to sustain exactly the same tissue hydraulic conductivity (Tyree 297 and Zimmermann 2002). The number of vessels was counted for primary and secondary 298 xylem. We also calculated the conductive area (mm²) as the sum of the cross-sectional area of 299 all vessels of the surrounding xylem. Knowing the dimensions of each vessel, the number of 300 vessels, and the total petiole xylem area, a theoretical hydraulic conductivity (K th , m kg MPa -1 301 s -1 ) was estimated based on formulas in Table 1. To test the null hypothesis of a decreasing 302 K leaf (kg MPa -1 s -1 m -2 ) across the leaf size range with no vessel widening occurring, we 303 estimated a theoretical leaf conductance (K leaf,null) by firstly dividing the K th by the petiole 304 length. We thus obtained a value for petiole conductance (kg MPa -1 s -1 ) which we divided by     Table 2). PD were negatively, and allometrically 343 correlated to A pet (P < 0.01) but uncorrelated to A lamina (P < 0.05) (Table S1). Petioles showed pronounced radial symmetry (Fig. 1c). The central parenchymatous pith strictly cyclic structure to a wavy one (Fig. 1f), and at the extremity, we observed isolated 351 bundles with complete cambium discontinuities in a more cortical position (Fig. 1g). Primary 352 and secondary xylem and secondary phloem were easy to identify (Fig. 1d). A sub-continuous  Depending on the extent of secondary growth, the primary phloem was crushed between the 357 secondary phloem and cortical parenchyma. In the most external part, there was a ring of 358 collenchyma, between the epidermis and the cortical parenchyma. Laticiferous canals were 359 frequently visible, mainly in the cortex (Fig. 1f) but also in the pith, but were also sometimes 360 completely absent.  ; Table S2), with most of these relationships being allometric. All tissue fractions 365 relative to A pet were correlated to A pet (P < 0.001; Fig. S3b; Table S2). All tissue fractions 366 relative to A pet were correlated to A lamina (P < 0.001; Fig. S3b; Table S2) Table 2), such that large leaves were associated with disproportionately less conductive area.  Table 2), such that large leaves were associated with disproportionately less xylem 375 area.

409
Although the leaf area-leaf mass allometric scaling is significant at the interspecific level, the 410 allometric scaling is not ubiquitous at the intraspecific level, based on this present study for C. 411 obtusa, and Milla and Reich (2007) for 11 species. 412 We found a positive allometric relationship between lamina area and petiole cross-413 sectional area (Fig. 2a), such that large leaves exhibit a larger lamina area for a given petiole 414 cross-sectional area. This change is in agreement with the allometric relationship between 415 lamina mass and petiole cross-sectional area we found (Fig. 2b), such that large leaves exhibit with a ring-geometry, exhibiting the largest change in the second moment of area (Fig. 4a). In 427 the same line, the secondary xylem is also a well-known supporting tissue, exhibiting a ring-428 geometry and which fraction increases with leaf size. Its increasing fraction occurs at the 429 same time as the distance to the cross-sectional centre of inertia increases with pith fraction, 430 and determines an overall increase of the second moment of area of the secondary xylem with 431 Downloaded from https://academic.oup.com/treephys/advance-article-abstract/doi/10.1093/treephys/tpz136/5715054 by Universiteé Fédérale Toulouse Midi-Pyrénées -SICD user on 03 February 2020 leaf size (Fig. 4b). This was also the case for the sclerenchyma (Fig. 4c), although 432 sclerenchyma exhibited relatively low values of I (0.05 to 95 mm 4 ). The allometric exponents 433 of the supportive tissues according to the lamina area (Fig. 4a,b,c) indicate that I increases 434 faster for the sclerenchyma, followed by the secondary xylem, suggesting that the relative 435 geometrical contribution of these tissues to the petiole flexural stiffness increases across the 436 leaf size range.

437
Increasing organ size and mass logically increases the mechanical load (Mahley et al. 438 2018). Moreover, we found an allometric relationship between lamina dry mass and petiole 439 cross-sectional area, with disproportionately higher lamina dry mass for leaves (Fig. 2b). This petiole density with leaf size -and thus petiole elastic modulus-is balanced (Fig. 4d), as also

451
Changing petiole pith fraction and thus collenchyma, secondary xylem, and 452 sclerenchyma I is clearly a cheap mechanism in terms of carbon allocation to balance the self-453 loading mechanical stress arising with leaf size. Moreover, we found a negative relationship 454 between A pet and PD, and no relationship of PD with A lamina . These results suggest that 455 volumetric construction cost can decrease with A pet , or at least does not increase with leaf size.

457
Petiole vascular architecture 458 The estimation of K leaf,null (Fig 5a,b) confirms that K leaf decreases with leaf size in the case of 459 an absence of vessel widening, as the hydraulic resistance is well-known to be dependent on assumes that leaves should be hydraulically more resistant than stems, as "bottlenecks", to 489 always preserve far lower water potentials in leaves, and promote drought-induced embolism 490 containment in easy-to-renew organs. These issues deserve more investigations, to link vessel 491 widening rates in leaves with the relative contribution of leaves in the hydraulic resistance of 492 plants. 493 The allometric relationship between the number of vessels and the supplied lamina 494 area suggests an increase in the number of vessels per leaf area, from the leaf base towards the 495 leaf tip (Fig. 3d). This therefore suggests vessel furcation. This contradicts the WBE model

511
The conductive area-decreasing architecture allows for a reduction of the xylem area 512 supplying the lamina for large leaves, as supported by the allometric relationship between 513 xylem area and lamina area (Fig. 3b). According to the Hagen-Poiseuille"s law, a given 514 conductive area can determine different conductivities, from numerous but small conduits to 515 few but wide conduits. However, according to the packing rule, the building of numerous 516 small conduits would require more xylem area and volume. Therefore, this implies that          Bold values refer to significant correlation (P < 0.05). Table 1 for a list of abbreviations. CI: confidence interval.