DOI: 10.5061/dryad.b8gtht7mc
title: Negative allometry of leaf xylem conduit diameter and double-wall thickness: implications for implosion safety

description: Xylem conduits have lignified walls to resist crushing pressures. The
 thicker the double-wall (T) relative to its diameter (D), the greater the
 implosion safety. Having safer conduits may incur higher costs and reduced
 flow, while having less resistant xylem may lead to catastrophic collapse
 under drought. Although recent studies have shown that conduit implosion
 commonly occurs in leaves, little is known about how leaf xylem scales T
 versus D to trade off safety, flow efficiency, mechanical support, and
 cost. We measured T and D in &gt; 7,000 conduits of 122
 species to investigate how T versus D scaling varies across clades,
 habitats, growth forms, leaf and vein sizes. As conduits become wider,
 their double-cell walls become proportionally thinner, resulting in a
 negative allometry between T and D. That is, narrower conduits,
 which are usually subjected to more negative pressures, are proportionally
 safer than wider ones. Higher implosion safety (i.e higher T/D ratios) was
 found in asterids, arid habitats, shrubs, small leaves, and minor veins.
 Despite the strong allometry, implosion safety does not clearly trade off
 with other measured leaf functions, suggesting that implosion safety at
 whole-leaf level cannot be easily predicted solely by individual conduits’
 anatomy.
description: <strong><em>Study
 species</em></strong> We sampled 122
 species from the University of California Botanical Garden at Berkeley
 (‘UCBG’, 37.87, -122.23; Berkeley, CA, USA). Species selection maximized
 phylogenetic coverage, and included species with different growth forms,
 leaf sizes, and habitats. Because this garden collection often has a
 single or just a few individuals per species, our sampling approach was
 limited to a few branches (&gt; 1 m long) collected from a single
 individual (woody species), or to a few leaves collected from 1-5
 individuals (herbaceous species). Samples were collected in the morning,
 re-cut under water, re-hydrated overnight, and then used for the
 measurement of leaf anatomical and functional traits. As most of those
 traits are destructive, we used different leaves for each
 trait.  <em>  Anatomical
 measurements</em> Fresh and mature leaves (3-4
 per species) were cut into 1 cm<sup>2</sup> sections, fixed in
 FAA (formalin acetic acid), and embedded in paraffin blocks. Sections
 included different leaf portions (base, middle, apex, petiole) and vein
 orders. Transverse cross-sections of 8–10 μm of thickness were cut with a
 microtome (Leica, RM2265), stained using the Johansen’s safranin-O and
 fast green method, and mounted in permanent glass slides using Cytoseal 60
 medium (Richard-Allan Scientific). Sections were observed under a light
 microscope (Leica, DM 2000), and photographed (at 20 –100× objectives)
 with a camera control unit (Nikon, DS-Fi1). We selected 6-8 images per
 species and manually measured the maximum and minimum lumen diameters
 (<em>D<sub>max</sub></em> and
 <em>D<sub>min</sub></em>, μm) and the double-cell
 wall thickness (<em>T</em>, μm) on all or, at most, 10
 adjacent conduits per image using ImageJ (https://imagej.nih.gov/). In vascular bundles with more than 10 conduits we systematically selected conduits to cover the range of conduit sizes observed in each picture. <strong><em>Functional traits</em></strong> Implosion safety ratio (<em>T/D</em>) was calculated as the ratio between <em>T</em> and <em>D<sub>max</sub></em>  for each conduit. Higher <em>T/D</em> values are assumed to be associated with greater implosion safety. Per this assumption, we estimated a theoretical critical implosion pressure (<em>P<sub>cri</sub></em>, MPa), i.e. the critical pressure above which a cell wall collapses. <em>P<sub>cri</sub></em> should be a function of <em>T/D</em>, but the specific equation depends on what type of stress (radial or hoop) induces the implosion. Because the prevalent type of stress causing leaf conduits to collapse is not known precisely, we used two different mechanical models of <em>P<sub>cri</sub></em>. The first model (Blackman et al., 2010), is based on Timoshenko's equation for an isolated and perfectly rounded pipe under negative pressure ( and considers that hoop forces are the main underlying stress inducing collapse. In the absence of per-species data, <em>P<sub>cri1</sub></em> was calculated assuming that the radial elastic modulus of xylem conduits ranges from 100 (<em>P<sub>cri1</sub></em> low) to 300 MPa (<em>P<sub>cri1</sub></em> high) (Blackman et al., 2010). To estimate how much the leaf conduits cross-sectional shape deviates from a rounded shape, we calculate the conduit ovality as <em>O</em> = (<em>D<sub>max</sub></em> - <em>D<sub>min</sub></em>)/(<em>D<sub>max</sub></em> + <em>D<sub>min</sub></em>), where <em>D<sub>min</sub></em> is the minimum conduit lumen diameter in μm (Ikeda et al., 2013). An ovality value of 0 indicates a perfectly rounded conduit. Conduits with <em>O</em> &lt; 0.005 still behave as a cylindrical pipe under compressive forces, but above this value conduit shape starts interfering in <em>P<sub>cri1 </sub></em>(Ikeda et al., 2013). Note that <em>O </em>was not directly used to adjust <em>P<sub>cri1</sub></em><sub>.</sub> The second model ( Hacke et al., 2001), considers the double-wall between neighboring conduits as a flat solid plate of finite <em>D<sub>max</sub></em> and effectively infinite length. It also assumes that radial stresses occurring in the common wall between an embolized and a water-filled conduit are the main cause of implosion, while hoop stresses are negligible (Sperry and Hacke, 2004). Cell wall strength is unknown for the species evaluated. In wood xylem, cell wall strength ~ 40-80 MPa, but it could be lower for leaf xylem. Therefore, we calculated <em>P<sub>cri2</sub></em> assuming that <em>W </em>ranges from 10 (<em>P<sub>cri2</sub></em> low) to 80 MPa (<em>P<sub>cri2</sub></em> high). Although both mechanical models described above are approximations and may not give accurate pressures for collapse, they likely account for enough variation across species to provide useful insights. Flow efficiency was quantified as the maximum leaf hydraulic conductance (<em>Kleaf<sub>max</sub></em>, mmol m<sup>-2</sup> s<sup>-1</sup> MPa<sup>-1</sup>), measured on 4-10 leaves per species using the evaporative flux method (Sack and Scoffoni, 2012) with a pressure-drop flow meter (Melcher et al., 2012). In this method, a transpiring leaf was firmly connected to a tube running to a water source, which was then placed in series with a resistance tube (PEEK tubing, VWR, Radnor, PA, USA) of known hydraulic conductance. To accelerate the evaporation process, leaf samples were placed over a box fan and below a light source. Once a steady-state flow rate was achieved, pressures across the resistance tube were recorded, for at least 10 minutes, using two pressure transducers (model PX26-001GV, Omega Engineering, Norwalk, CT, USA) interfaced to a data logging system (U6 USB, Labjack, Lakewood, CO, USA). Next, the leaf was disconnected from the tubing system, and placed in a sealable plastic bag for about 20 minutes for water potential equilibration. Final leaf water potential was measured using a pressure chamber (model 1505D, PMS, Albany, OR, USA); and leaf area (<em>LA</em>, cm<sup>2</sup>) was obtained using a flatbed scanner and the leafarea macro (https://github.com/bblonder/leafarea) in ImageJ software version 1.53t (https://imagej.nih.gov/). Finally, <em>Kleaf<sub>max </sub></em> normalized by leaf area and corrected for leaf temperature was calculated following Sack and Scoffoni (2012). <em>Kleaf<sub>max</sub></em> describes how much water flows across the leaf in response to a water potential gradient between the leaf and the surrounding atmosphere, hence higher values indicate higher flow efficiency. <em>LA</em> obtained as above, was used to classify species as microphyllous (<em>LA</em> ≤ 20.25 cm<sup>2</sup>), mesophyllous (20.25 &lt; <em>LA</em> &lt; 45 cm<sup>2</sup>), and macrophyllous (<em>LA</em> ≥ 45 cm<sup>2</sup>). Mechanical support was quantified as the leaf flexural modulus of elasticity (<em>ε</em>, MN m<sup>-2</sup>). To obtain <em>ε</em>, we performed 3-point bending tests using a Universal Testing Machine (Test stand ES30, Mark-10, Copiague, NY, USA) on 3-4 leaves per species. Leaves were placed in the UTM machine with their longitudinal axis parallel to the bending fixture. During the bending test, the force (force gauges M5-5 and M5-20, Mark-10, Copiague, NY, USA) and the displacement (travel display ESM0001, Mitutoyo, Aurora, IL, USA) were recorded, and then used to produce force-displacement plots. After each test, leaf width and thickness at the bending point and the span length between the two bending fixtures were measured with a digital caliper, and then used for the calculation of <em>ε </em>following Read et al. (2005). Higher values of <em>ε</em> (i.e. stiffer leaves), indicate higher mechanical support. In 14 species, leaves were too small to be properly attached to the bending fixture and/or too flexible to produce detectable bending forces, so <em>ε</em> was not measured. Construction cost was estimated using two different proxies: leaf mass per area (<em>LMA</em>, g m<sup>−2</sup>) and total volume of veins per area (<em>VTotV</em>, mm<sup>3</sup> mm<sup>−2</sup>). <em>LMA</em> describes the total amount of resources invested in constructing each unit of leaf area. To obtain <em>LMA</em>, 3-5 leaves per species were scanned to obtain the leaf area and oven-dried at 50 °C for 48 hours to determine their dry mass. <em>LMA</em> was then calculated as leaf dry mass divided by leaf area (Pérez-Harguindeguy et al., 2016). <em>VTotV</em> describes the total volume of veins per unit of leaf area and it is a reasonable proxy of the construction cost of conduits <em>per se</em>. To calculate <em>VTotV</em>, we first obtained leaf cleared images of all species, except for <em>Nymphaea </em>spp. and <em>Aucuba japonica</em> Thunb., because it was impossible to obtain a clear image of their venation networks. Next, we used the LeafVeinCNN app in Matlab to calculate the total volume of veins (Xu et al., 2021) assuming that veins have a cylindrical shape. Finally, we divided the total volume of veins by leaf area to obtain <em>VTotV</em>. Higher <em>LMA</em> and <em>VTotV</em> values reflect higher construction cost. <em>  Species habitat</em> We inferred habitat for each species based on its current geographic range. To retrieve the geographic range, we used occurrence data from BIEN (Botanical Information and Ecology Network) and GBIF (Global Biodiversity Information Facility, https://www.gbif.org/) databases. Occurrence records were manually cleaned by removing duplicated, outdated (pre-1950), or suspect geographical coordinates (outside the species natural habitat). Next, the mean annual precipitation (MAP) for each coordinate was extracted from the Worldclim database (https://www.worldclim.org/data/bioclim.html) at 2.5’ resolution (~ 5 km). For each species, we averaged the MAP for all occurrence points and then classified the species habitat as hydric (MAP &gt; 2000 mm), mesic (500 mm &lt; MAP ≤ 2000 mm) or arid (MAP ≤ 500 mm). <strong><em>Statistical analysis</em></strong> To investigate how leaf conduits’ <em>T</em> and <em>D<sub>max</sub></em> scale to each other, we log<sub>10</sub>-transformed both variables and then used the ‘smatr’ R-package version 3 (Warton et al., 2012) to fit standardized major axis (SMA) regression models. We used the functions sma(log(<em>T</em>) ~ log(<em>D</em>), slope.test = 1) to test if the coefficient<em> b</em> for all species together was significantly different from one. To investigate whether the coefficients <em>b </em>(log(<em>T</em>) ~ log(<em>D</em>) * group)<em> </em>and <em>a</em> (log(<em>T</em>) ~ log(<em>D</em>) + group) differed across groups (species, clades, habitats, growth forms, leaf sizes, and vein orders), we used Likelihood ratio (𝜆) and Wald (<em>W</em>) statistics, respectively (Warton et al., 2012). We also performed Kruskal Wallis tests followed by pairwise Wilcox tests with Benjamini and Hochberg p-value adjustment method to test for differences in anatomical traits across those groups.  Currently, the ‘smatr’ package does not support multiple regressions (Warton et al., 2012). Thus, to investigate any potential influence of both leaf sizes and species in the <em>T</em> ~ <em>D</em> scaling relationship across vein orders we fitted a standard mixed model regression using the function “lme” from the ‘nlme’ R-package. Leaf area was model as fixed effect, while vein orders nested within species, and species nested within genus as random effects, i.e. lme(log(<em>T</em>) ~ log(<em>D</em>) * log(<em>LA</em>), random= ~1|genus/species/vein orders). We used the ‘nlme’ function ‘anova()’ to assess the significance of each predictor variable effect and the function ‘residplot()’ from the ‘predictmeans’ R-package to perform residual analysis. To further examine phylogenetically driven variation in implosion safety, we built a phylogenetic tree for all species using ‘V.PhyloMaker2’ R-package (Jin and Qian, 2022) and the ‘GBOTB.extended.WP.tre’ mega-tree. Next, we used the function ‘fastAnc’from the ‘phytools’ R-package to perform a fast estimation of the ancestral states for <em>a</em>, <em>b</em>, and <em>T/D</em>. We also conducted Blomberg’s <em>K</em> tests (Blomberg et al., 2003) using the ‘phytools’ function ‘phylosig’ to test for phylogenetic signals in those same traits (i.e. the tendency for related species to resemble each other, more than they resemble species drawn at random from a tree). <em>K</em> &lt; 1 indicates faster trait evolution than expected under a Brownian model (weaker phylogenetic signal), while <em>K</em> &gt; 1 indicates slower trait evolution (stronger phylogenetic signal). To investigate possible trade-offs among leaf functions, we used two complementary approaches. First, we carried out a principal component analysis (PCA) using the ‘prcomp’ function in R. Prior to the PCA, we centered and z-transformed all traits to improve comparability among them and reduce bias towards traits with higher variance. We used the broken stick method for estimating the number of principal components to be retained. Our PCA analysis was carried out with 106 out of the 122 studied species, as we removed 16 species with missing data for <em>VTotV</em> and <em>ε</em>. Second, we ran ordinary least-squares regression models to test for pairwise trade-offs between implosion safety (response variable) and the other leaf traits (predictor variables). We also regressed <em>P<sub>cri1</sub></em> and<em> P<sub>cri2</sub></em> values to assess the relationship between our two different models of conduit collapse. All analyses were carried out using the R version 4.3.1. Code to reproduce analyses is available at https://github.com/ilamatos/xylem_implosion_safety. Regressions or differences were considered significant if <em>P</em> &lt;0.05.
description: # Negative allometry of leaf xylem conduit diameter and double-wall
 thickness: implications for implosion safety
 [https://doi.org/10.5061/dryad.b8gtht7mc](https://doi.org/10.5061/dryad.b8gtht7mc) This dataset is part of the manuscript Matos et al., 2024 New Phytol. In this study, we measured leaf xylem conduit double-wall thickness (T) and lumen maximum diameter (D) in &gt; 7,000 conduits of 122 plant species to investigate (1) how *T* versus *D* scaling varies across clades, habitats, growth forms, leaf and vein sizes; and (2) how the *T* versus *D* influences xylem safety against implosion. ## Description of the data and file structure This dataset comprises the following files: **(1) species_list.csv =** a comma separated file containing taxonomic information for the 122 plant species investigated in this study: spp_code = species code comprising the three first letters of the genus and the three first letters of the species name; Species_UCBG = species binomial nomenclature as presented in the University of California Botanical Garden at Berkeley archives; Species_WP = species binomial nomenclature standardized following the world plant database ([https://wfoplantlist.org/);](https://wfoplantlist.org/\);) Genus_WP = genus following the world plant database; Family_WP = family following the world plant database; order_apg4 = order following the APGIV classification (see [https://www.mobot.org/](https://www.mobot.org/)); clade = taxon clade following the APGIV classification: ferns, basal angiosperms, monocots, basal eudicots, rosids, asterids; **(2) species_occurrences.csv** = spatial coordinates (latidute, longitude in decimals) for species occurrences as retrieved from BIEN ([https://bien.nceas.ucsb.edu/bien/](https://bien.nceas.ucsb.edu/bien/) and GBIF ([https://www.gbif.org/](https://www.gbif.org/)) databases. species = species binomial nomenclature following the world plant database; latitude = latitude of species occurrence in decimals; longitude = longitude of species occurrence in decimals; source = source of information about species occurrence. **(3) species_tree.tre** = phylogenetic tree for the 122 plant species investigated in this study saved in .tre format. **(4) implosion_data.csv** = comma separated file containing the data analyzed in this study: Species_name = species binomial nomenclature following the world plant database; order_apg4 = order following the APGIV classification (see [https://www.mobot.org/](https://www.mobot.org/)); clade = taxon clade following the APGIV classification: ferns, basal angiosperms, monocots, basal eudicots, rosids, asterids; growth_form = species growth form: tree, shrub, herb, aquatic, climbing; habitat = species habitat: hydric (Mean Annual Precipitation - MAP &gt; 2000 mm), mesic (500 mm &lt; MAP ≤ 2000 mm) or arid (MAP ≤ 500 mm); leaf size = species leaf size: microphyllous (leaf area - LA ≤ 20.25 cm2), mesophyllous (20.25 &lt; LA &lt; 45 cm2), and macrophyllous (LA ≥ 45 cm2); max_Diameter = leaf xylem conduit lumen maximum diameter in microns; min_Diameter = leaf xylem conduit lumen minimum diameter in μm; Thickness = leaf xylem conduit double cell-wall thickness in μm; TD = ratio between xylem conduit double cell-wall thickness and lumen maximum diameter, dimensionless; O = leaf xylem conduit ovality, calculate as *O* = (*Dmax* - *Dmin*)/(*Dmax* + *Dmin*), where *Dmin* is the minimum conduit lumen diameter in μm and *Dmax* is the maximum conduit lumen diameter. An ovality value of 0 indicates a perfectly rounded conduit Pcri1_low = critical pressure for xylem conduit implosion, calculated following [Blackman et al., 2010](https://doi.org/10.1111/j.1469-8137.2010.03439.x), and using a radial elastic modulus of xylem conduits of 100 MPa. Pcri1_up = critical pressure for xylem conduit implosion, calculated following [Blackman et al., 2010](https://doi.org/10.1111/j.1469-8137.2010.03439.x), and using a radial elastic modulus of xylem conduits of 300 MPa. Pcri2_low = critical pressure for xylem conduit implosion, calculated following [Sperry and Hacke, 2004](https://doi.org/10.3732/ajb.91.3.369), and using a xylem conduit cell wall strength at saturation of 10 MPa. Pcri2_up = critical pressure for xylem conduit implosion, calculated following [Sperry and Hacke, 2004](https://doi.org/10.3732/ajb.91.3.369), and using a xylem conduit cell wall strength at saturation of 80 MPa. vein_order = vein order at which the measured conduit was located: major, medium, minor; LA = one-side leaf area in cm2; Kmax = maximum leaf hydraulic conductance in mmol m-2 s-1 MPa-1; LMA = leaf mass per area in g m-2; TotA = leaf total area included in the analysis of total volume of veins per leaf area, in mm2; TotV = total volume of veins in mm3; VTotV = total volume of veins per unit of leaf area in mm3 mm-2; e = leaf flexural modulus of elasticity in MN m-2; MAP = averaged mean annual precipitation for the species occurrence sites in mm. **(5) anatomy_photos** = a ZIP file that when decompressed contains 122 subfolders named after the Spp_code of each plant species. Inside each species subfolder there are 6-8 leaf cross-sectional microscopic photos saved in Tag Image File Format (TIFF). **(6)** **anatomy_photos_metadata.csv** = comma separated file containing information about the leaf cross-sectional images analyzed in this study: photo_file_name = file names of the leaf cross-sections microscopical photos. spp_code = species code, comprising the first three letters of the genus and the first three letters of the species name. objective = objective (20x, 40x, 100x) at which photo was taken; levels: 20, 40, 100. scale_value = value of scale printed in the photo; levels:1, 10, 100. scale_unit = unit of the scale printed in the photo; levels: micrometer, millimeter. OBS = observations about the photo. ## Code/Software * R-code to reproduce all analysis and figures of the Matos et al., 2024 New Phytologist paper is available at **[https://github.com/ilamatos/xylem_implosion_safety](https://github.com/ilamatos/xylem_implosion_safety).** ## Funding This study was supported by the US National Science Foundation (grant DEB-2025282).