Hydraulic and structural constraints jointly shape root-to-leaf scaling of xylem conduit traits

Hydraulic and structural constraints jointly shape root-to-leaf scaling of xylem conduit traits | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL Plant, Cell & Environment This is a preprint and has not been peer reviewed. Data may be preliminary. 31 January 2025 V1 Latest version Share on Hydraulic and structural constraints jointly shape root-to-leaf scaling of xylem conduit traits Authors : Milos Simovic 0000-0001-8325-3406 [email protected] and Sean Michaletz 0000-0003-2158-6525 Authors Info & Affiliations https://doi.org/10.22541/au.173833017.79033598/v1 598 views 316 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Xylem conduit morphology is shaped by the dual challenges of minimizing hydraulic resistance and preventing conduit wall collapse during vertical sap transport. While hydraulic theories predict that conduits widen from tip to base to minimize resistance, theory has not addressed how collapse prevention influences vertical variation in conduit morphology. Additionally, scaling relationships in roots remain largely unexplored. Here, we evaluate existing theories for conduit diameter scaling and derive new theory for vertical variation in thickness-to-span ratios. We test these theories using a novel bootstrapping approach to minimize sampling biases and analyze a dataset of nearly seven million observations spanning above- and belowground organs from five conifer species. As predicted, conduits widened with distance from the stem tip, with scaling exponents closely aligning with theoretical predictions. Conduits also widened from fine roots to coarse roots, mirroring aboveground patterns. Thickness-to-span ratios increased from base to tip and consistently exceeded the predicted critical collapse limit. These findings reveal how the physics of sap transport shape xylem morphology to balance hydraulic efficiency and structural stability. By combining novel theory, robust statistical methods, and comprehensive data, this study refines scaling predictions and advances understanding of mechanisms shaping xylem anatomy across plant organs. Introduction Water transport through plants is tightly linked to the carbon assimilation rates and microclimates of leaves and canopies, influencing plant-atmosphere feedbacks and driving vegetation responses to climate change (Blonder et al ., 2023, Garen et al ., 2023, Michaletz & Garen 2024). Understanding how xylem morphology balances the competing demands of water transport and structural integrity is essential for predicting plant functioning and adaptation in a changing climate. Vertical sap transport imposes two fundamental constraints on xylem morphology: hydraulic resistance and the risk of conduit wall collapse (Tyree & Zimmermann, 2002, Hacke et al . 2001). To function effectively, vascular plants must balance these constraints to ensure efficient sap transport while maintaining structural stability during periods of water stress (Niklas, 1992, 1997). The first constraint arises from hydraulic resistance increasing with the length of the xylem network, limiting the efficiency of sap transport over long distances. The hydraulic resistance, r (MPa s m -3 ), for a single cylindrical conduit is described by the Hagen–Poiseuille equation where ∆P (MPa) is the pressure difference between the ends of the conduit, Q (m 3 s -1 ) is the volumetric flow rate, η (MPa s) is the viscosity of the sap, l (m) is the conduit length, and d is the conduit diameter (m; Tyree & Zimmermann, 2002). Eqn. (1) shows that resistance increases linearly with conduit length. For a series of conduits, the total resistance, R (MPa s m -3 ), is the sum of the resistances of individual conduits where r i (MPa s m -3 ) is the resistance of an individual conduit i (Eqn. 1), from the terminal tip ( i = 1) to the base ( i = n ). Eqn. (1) also shows that resistance varies inversely with the fourth power of conduit diameter. Consequently, the total resistance R is highly sensitive to the scaling profile of conduit diameters along the network, which is characterized by where d is lumen (conduit) diameter (µm), d 0 ( µm m - b ) is a normalization constant, L (m) is the distance from the tip of the plant, and α (dimensionless) is the path length-scaling exponent. If conduit diameters remained constant along the hydraulic path, R would increase linearly with L (Eqn. 1 & 2; Olson et al ., 2021). In tall plants, such an increase in resistance would necessitate high sap tensions capable of causing air seed embolisms and reducing the hydraulic conductivity of the stem or branch (Sperry et al. , 1988; Tyree & Sperry, 1989; Tyree & Zimmermann, 2002). Instead, conduit diameters increase from tip to base, which is hypothesized to be an adaptive response that minimizes resistance to vertical sap transport (Olson et al ., 2021; Koçillari et al ., 2021). Several hydraulic models make quantitative predictions for α (Table 1). The pipe model assumes that conduit diameter remains constant across the path ( α = 0; Shinozaki et al., 1964a,b). In contrast, the West-Brown-Enquist (WBE) model predicts α = ¼ based on a hierarchical, volume-filling branching network of tapering conduits optimized to minimize hydraulic resistance while maintaining constant resistance across L (West et al. , 1999). The height-corrected WBE model revises this prediction to α ≈ ⅕ by accounting for conduit widening as a function of L to reflect tree height (Anfodillo et al ., 2006; Olson et al ., 2018, 2021). The packed conduit model predicts α = ½ by incorporating conduit branching and packing constraints (Savage et al. , 2010), while the carbon cost-gain model predicts α = ⅙ by optimizing for net carbon gain rather than hydraulic resistance (Hölttä et al. , 2011). Finally, the widened pipe model predicts α = ¼ near the plant tip, with deviations near the base driven by trade-offs between hydraulic resistance and construction costs (Koçillari et al ., 2021). Empirical data for aboveground organs yielded α ≈ 0.24 (Koçillari et al ., 2021), consistent with the WBE and widened pipe models. Although conduits are known to widen beyond the stem base into structural and coarse roots (Petit et al ., 2009; Prendin et al ., 2018; Lintunen & Kalliokoski, 2010), conduit–path length scaling across the entire root network (including fine roots) remains unexplored. This represents a critical knowledge gap, as fine roots are essential for water uptake and transport (McCormack et al ., 2015) and play a central role in whole-plant hydraulic function. Scaling of conduit diameters can also be expressed in terms of the external diameter of plant organs such as stems and roots. Since L ∝ D 2/3 (Appendix S1; Greenhill 1881), Eqn. 3 can be rewritten as where d 0 is the normalization constant (µm m - b ), D (m) is the external organ diameter, and β (dimensionless) is the diameter-scaling exponent. Several hydraulic models also make quantitative predictions for β (Table 1). For example, the WBE model predicts that β = ⅙ (West et al. , 1999), the height-corrected WBE model predicts that β ≈ 0.11, and the packed conduit model predicts that β = ⅓ (Savage et al. , 2010). For tree stems, an empirical estimate of β ≈ 0.36 (95% CI: 0.32-0.39; Olson & Rosell, 2013) is consistent with predictions of the packed conduit model (Savage et al. , 2010) but not with other models (Table 1). In roots, scaling between conduit diameter and external diameter has been seldom explored (but see Biondini, 2008), and there is no evidence that β agrees with predictions from any of the models listed in Table 1. The second fundamental constraint on xylem morphology is the risk of conduit collapse in response to stresses caused by tensile sap. The cohesion-tension theory posits that transpiration creates surface tension forces in the leaf’s evaporative surfaces that are transmitted through a continuous water column by cohesion, adhesion, and tension forces, effectively pulling water from the soil into the roots and through the xylem to the leaves (Dixon & Joly, 1894, 1895; Tyree & Zimmermann, 2002; Angeles et al. , 2004). Sap tension transmitted via adhesion to conduit walls induces bending stresses that can cause wall collapse (Hacke et al. , 2001), reducing the hydraulic conductivity of the organ (Michaletz et al., 2012) and limiting stomatal conductance and photosynthesis rates. In severe cases, this hydraulic bottleneck can lead to desiccation and death of distal organs (Tyree et al. , 1994; Rood et al. , 2000; Sperry et al. , 2002 Michaletz et al. , 2012). Conduit wall collapse can be characterized as bending of a rectangular plate (Young et al., 2012, Hacke et al., 2001), such that where P crit (MPa) is the critical collapse pressure, σ (MPa) is the modulus of rupture, β (dimensionless) is a coefficient that varies with the span-to-length ratio, t (µm) is the thickness of the double conduit wall, and b (µm) is the length of the conduit wall. The thickness-to-span ratio ( t / b ) 2 (dimensionless) quantifies the ability of the conduit wall to resist collapse. The vulnerability of conduit walls to collapse under extreme conditions can be assessed using the safety factor, which is the ratio of the observed thickness-to-span ratio to the critical value (Hacke et al . 2001). While the mechanics of conduit wall collapse have been well-described (Hacke et al ., 2001), their potential role in driving vertical variation in thickness-to-span ratios remains unexplored. Variation in thickness-to-span ratios has been reported for three tree species in two studies (Domec et al ., 2009; Prendin et al ., 2018), but no mechanistic hypotheses have been proposed to explain this pattern. Here, we propose for the first time that vertical variation in sap tension, combined with conduit diameter variation, co-drives the critical thickness-to-span ratio required to prevent collapse. As water potential decreases from roots to leaves, reaching its lowest value in leaf airspaces proximal to the stomata (Buckley & Sack, 2019), conduit walls must be sufficiently reinforced to withstand the extreme sap tensions experienced, particularly at higher positions. This hypothesis predicts a negative relationship between thickness-to-span ratio and path length L , with greater reinforcement near the tip where sap tensions are highest. In this study, we examine how xylem conduit morphology is constrained by the physics of sap transport. We derive and test mechanistic theory that predicts vertical variation in thickness-to-span ratios from first principles, predicting that ( t / b ) 2 decreases with L while remaining sufficiently high at all points along the hydraulic path to prevent conduit wall collapse. Additionally, we evaluate competing theories that predict scaling exponents α and β (Table 1) by analyzing empirical scaling relationships between conduit diameter d, path length L , and organ diameter D . To achieve these goals, we use a semi-automated approach to measure conduit dimensions in 188 tissue samples across hydraulic paths up to 28 m in length. Our dataset comprises nearly 7 million trait measurements from ~600,000 individual conduits spanning above- and belowground organs - approximately 100 times larger than those used in most previous studies. We analyze this unprecedented dataset using a novel bootstrapping approach, which ensures robust parameter estimation and addresses biases inherent in xylem morphology datasets. Together, these approaches provide exceptional resolution for testing mechanistic theories and advancing our understanding of xylem structure-function relationships across plant organs. Materials and Methods Plant material In May and June of 2021, we sampled 5-6 individuals from each of five conifer species: Callitropsis nootkatensis (D.Don) Oerst ., Picea sitchensis (Bong.) Carr., Thuja plicata Donn ex D.Don , Tsuga heterophylla (Raf.) Sarg., and Tsuga mertensia (Bong.) Carr. We selected the most common conifers inhabiting the temperate rainforests of British Columbia, which are nevertheless absent from or underrepresented in global datasets (Koçillari et al ., 2021). The individuals were located at The University of British Columbia Botanical Garden (49.25383, -123.24731) and the Capilano Watershed (49.46189, -123.04511), both near Vancouver, British Columbia, Canada. From each individual, we sampled one terminal branch (~ 1 m in length), one coarse root with intact fine roots (~ 0.5 m in length), and one stem increment core (~ 5 cm in length; Fig. S1). Unlike with stems, we did not sample along the longest existing root due to the difficulty and destructiveness associated with such excavation procedure. Increment cores were sampled just above the root collar using a 5.15 mm I.D. increment borer (Haglöf). Cores were immediately placed in centrifuge tubes containing 40% ethanol to inhibit microbial growth (Gärtner & Schweingruber, 2013). All samples were then transported to the laboratory, where the branches and roots were sectioned into 10 cm segments, placed in 50 ml centrifuge tubes containing 40% ethanol, and stored at 4 °C. The path length L from leaf tip to each sampling point was measured using a meter tape or laser hypsometer (Forestry Pro II, Nikon). We employed the 2-point tangential method for measuring branch height, which accurately estimates vertical distances in non-leaning trees growing on flat terrain (Larjavaara & Muller-Landau, 2013; Simovic et al. , 2024). Samples were sectioned to enable measurement of xylem morphological traits. We obtained 20 µm cross sections from leaves, twigs, branches, stem cores, coarse roots (outside diameter ≥ 3 mm), fine roots (5th – 3rd order roots; McCormack et al ., 2015), and very fine roots (1st order roots). Fully intact, healthy leaves from terminal buds were selected for sectioning, and the sections were taken from the middle of the leaf. Twig sections were taken a few millimeters below the terminal bud. Branch sections were taken 1-2 cm from the proximal end. Tree cores were mounted onto wooden dowels using clear waterproof gel glue (Clear Grip, The Gorilla Glue Company) prior to sectioning (Wegner et al. , 2013) and sectioned in the radial direction. Coarse roots were sectioned near the proximal end. Fine roots were sectioned halfway between their junction with coarse roots and 2 nd and 1 st order fine roots, whereas very fine roots were sectioned near the root cap. Branches, stem cores, and coarse roots were sectioned using a sliding microtome (AO 860, American Optical). Leaves, fine roots, and very fine roots were first mounted in a 4% agarose solution (low melting-point agarose, BioBasic) and then sectioned using a vibrating blade microtome (VT1000 S, Leica Biosystems). Fresh sections were immediately stained with 0.8% safranin and mounted onto microscope slides. Sections were observed under a light microscope (Olympus BX51WI) at various magnifications depending on the size of the xylem conduits (100× for branches, coarse roots, and cores, 200 – 400× for leaves, fine and very fine roots, and twigs). For shoots containing only primary xylem (leaves, twigs) we photographed a minimum of five vascular bundles per sample, and for fine roots we photographed the entire vascular cylinder in each sample. For organs containing mostly secondary xylem (branches, stem cores, and coarse roots) we scanned across the growth rings and took a minimum of ten photographs per sample. Image analysis of xylem morphological traits We measured xylem conduit diameters, cell wall thicknesses, and thickness-to-span ratios using ROXAS version 3.0.1 (von Arx & Carrer, 2014) in the ImagePro Plus software (version 6.3; Media Cybernetics, Rockville, MD, USA). Cell wall thickness was measured for the two radial and two tangential cell walls bordering the conduit, and the smaller measurement (i.e., the wall most susceptible to collapse; Eqn. 5) was used to calculate the thickness-to-span ratio. Each image was carefully inspected for undetected conduits and “pseudo-conduits” (e.g., resin duct epithelial cells) that the software had erroneously identified as conduits. Additionally, as our focal species are tracheid-bearing conifers, the data obtained with the software are not subject to errors that affect vessel measurements, such as the accidental inclusion of imperforate tracheary elements in some angiosperms (Olson, 2023). Missing conduits were manually traced following the automated analysis and their dimensions were added to the dataset, while pseudo-conduits were manually deleted from the dataset. In total, we analyzed 1,036 images containing 580,049 xylem conduits from 188 tissue samples. To characterize the mean conduit diameter of each tissue sample, we calculated the hydraulic diameter ( d h ; µm) as where d i (µm) is the diameter of the n th conduit in each sample (Sperry et al. , 1994). Unlike the arithmetic mean, d h gives more weight to larger, earlywood xylem conduits, which contribute disproportionately more to the overall hydraulic conductivity despite being far less numerous than latewood vessels (Sperry et al. , 1994). Modeling the critical collapse limit of xylem conduits We simulated the critical collapse limit of xylem conduits along the hydraulic path using models for water potential gradients in the soil-plant-atmosphere continuum (Lechthaler et al. , 2020) and for bending of a rectangular plate supported on four edges (Young et al. , 2012, p. 532). First, we used Model II standardized major axis (SMA) regression to fit a linearized form of Eqn. (3) to our data using the sma function in the smatr package (Warton et al. , 2012). The linearized form is obtained by log-transforming Eqn. (3) to give SMA regression is appropriate for quantifying power law relationships (Warton et al. , 2006) as it minimizes residual variation in both the x and y dimensions rather than in y only as in Model I ordinary least squares (OLS) regression. The resulting regression equation was used to predict variation in d in 100 µm increments along L from leaves to the base of the tree. As a first approximation, the hydraulic path of each tree was modeled as a series of vertically stacked pipes that gradually widen from the tips of the leaves to the base of the tree (Lechthaler et al ., 2020; Olson et al ., 2021). The pressure head due to gravity (approximately 0.01 MPa per meter height) is relatively small for the tree heights in this study (e.g., 0.3 MPa at the tip of the tallest tree) and was therefore excluded from the model; however, it should be considered for taller trees. The resistance r of each segment was calculated using Eqn. (1). Volumetric sap flow rate Q (m 3 s -1 ) through the hydraulic path was calculated using Darcy’s law (Reid et al. , 2005) where ∆Ψ s,l (MPa) is the difference in water potential between the soil ( ψ soil ; MPa) and leaf ( ψ leaf ; MPa), and R (MPa s m -3 ) is the sum of the individual resistances of all segments (given by Eqn. (2)). From here, the difference in water potential between ψ of segment n and ψ leaf ( ∆ψ n,l = ψ n - ψ l , MPa) was calculated as where r i is the resistance of segment i . ψ leaf was taken -4.7 MPa, which is the minimum ψ measured from July 2022 – July 2023 in these species (Simovic & Michaletz, unpublished manuscript). ψ soil was taken as -1.5 MPa, which is a typical wilting point (Tolk, 2003). The water potential for any given segment, i (dimensionless), along the hydraulic path ( ψ i ; MPa) was then calculated as Water potential influences sap tension, P i (MPa), where, which determines the mechanical stresses conduits must withstand. The critical thickness-to-span ratio, ( t/b ) 2 crit (dimensionless), at which wall collapse occurs for a given sap tension was calculated by rearranging Eqn. 5 (Hacke et al. , 2004; Young et al. , 2012, p. 532), such that where σ (MPa) is the modulus of rupture for green cell wall material. β (dimensionless) is a bending stress constant that depends upon the ratio of conduit width ( b ) to conduit length ( L ); it approximates 0.25 when b / L ≤ 0.5, which is always the case in xylem conduits (Sperry et al. , 2006). We obtained species-specific values of σ (Forest Products Laboratory, 2021) and used the mean value (41.6 MPa) in our simulations. Earlywood and latewood conduits often exhibit substantially different critical thickness-to-span ratios due to their differing lumen diameters. To distinguish between them, we used Mork’s index, M (dimensionless), defined as where x tan (µm) is the mean tangential single-cell wall thickness (averaged across inner and outer tangential walls), and d rad (µm) is the radial lumen diameter (Mork, 1928; Denne, 1988). The factor of 4 accounts for the duality and double thickness of adjacent cell walls. ROXAS calculates M using tangential wall thickness instead of radial wall thickness due to the latter’s sensitivity to artifacts such as pit-pore widening (von Arx & Carrer, 2014). Cells with M > 1 are classified as latewood, while M ≤ 1 corresponds to earlywood. This approach aligns well with other methods for identifying earlywood and latewood transitions, such as threshold density and inflection point methods (Antony et al ., 2012). Statistical analyses All scaling relationships were estimated using SMA fits of Eqn. 8 to data using the sma function in the smatr package (Warton et al. , 2012). Differences in slope estimates between organs were tested using the slope.test function in the smatr package. The organ where the values of d and ( t / b )² peaked and subsequently declined was identified using the segmented function from the segmented package. To fit SMA regressions to ( t / b ) 2 data, we used relative path length ( L / H ) instead of absolute path length ( L ), as sap tension depends on both tree height and position along the path length (Lechthaler et al ., 2020). Using L / H standardizes path length across trees of different heights, facilitating meaningful comparisons of ( t / b ) 2 scaling relationships among individuals. Because models could not be fitted between d and L or d and D in the full dataset due to the unequal number of conduits sampled across L and D (Fig. S2 and S3) , we used subsampling and bootstrapping to resample the dataset prior to model fitting (Simovic & Michaletz in review; Maitner et al ., 2023). First, we divided the raw dataset into equally spaced logarithmic bins, using both L and D as the binning variables. We ensured that each bin had at least n = 100 observations, setting the number of bins so that the bin with the fewest observations met this minimum. For the subsampling approach, we determined which L and D bin has the lowest number of raw conduit diameter observations ( n d,min ). We then sampled, without replacement, n d,min observations from each of the bins. For the bootstrapping approach, we first split the data into equally spaced logarithmic bins and determined which L and D bin has the highest number of raw conduit diameter observations ( n d,max ). We then randomly sampled, with replacement, n d,max - n d,bin observations from each bin, where n d,bin is the number of raw conduit diameter observations in each bin. The bootstrapped data were then combined with the raw data, yielding a sample size of n d,max in each bin. Given that SMA slope and confidence interval estimates will vary stochastically between resampled datasets, both the subsampling and bootstrapping procedures were repeated for a set number of iterations (1 – 50,000 for subsampling and 1 – 1000 for bootstrapping). The maximum number of iterations was set by re-running the resampling and fitting procedures until the slopes and confidence intervals remained stable with additional iterations (Fig. S4 – S9). Unless otherwise stated, all reported model fits used bootstrapped data. All statistical analyses were performed in R (R Core Team, 2024), and the code for replicating all the analyses and figures is available at https://github.com/MichaletzLab/Xylem-scaling. Results Frequency distributions of xylem conduit diameters and thickness-to-span ratios for different organs along the hydraulic path, from fine roots to leaves, are shown in Fig. 1. Across all species and individuals, xylem conduit diameters ranged from 1.62 µm to 70.79 µm (Fig. 1A) while thickness-to-span ratios varied from 0.0024 to 90.65 (Fig. 1B). Mean conduit diameter increased from the tips of leaves (4.76 µm) to the base of the trunks (13.19 µm) and decreased from trunk bases to the tips of fine roots (7.82 µm; p < 2.0 × 10 -16 ; Fig. 1A). Mean thickness-to-span ratio increased from leaves to branches ( p < 2.0 × 10 -16 ) where it reached its apex (mean ( t / b ) 2 = 0.78), and progressively decreased from branches to the trunks (mean ( t / b ) 2 = 0.33) and roots ( p < 2.0 × 10 -16 ; mean ( t / b ) 2 = 0.15 – 0.25; Fig. 1B). The relationship between xylem conduit diameter and distance from the stem tip is shown in Fig. 2A. Conduit diameters increased with distance from the stem tip following α = 0.15 ( p = 2.22 × 10 -16 , r 2 = 0.21), with extremely tight 95% confidence intervals (CIs; 0.15 to 0.15) that statistically excluded all values predicted by hydraulic models (Table 1). Our empirical estimates of α did not differ significantly ( p = 0.89) between the subsampled and bootstrapped datasets (i.e., non-averaged diameter data, d ), but were significantly different ( p = 0.01 and 0.008, respectively) from α obtained when averaged data was fitted (i.e., hydraulic diameter, d h ; Fig. S10). The relationship between xylem conduit diameter and external stem diameter is shown in Fig. 2B. Conduit diameters scaled with external stem diameter following β = 0.33 ( p = 2.22 × 10 -16 , r 2 = 0.43; Fig. 2B), again with extremely tight 95% CI (0.33 – 0.33) that exactly matched the value of β = 0.33 predicted by the packed conduit model and excluded all other model predictions (Table 1). In roots, conduit diameters scaled with external root diameter following β = 0.41 ( p = 2.22 × 10 -16 , r 2 = 0.18; Fig. 2C), with extremely tight 95% CI (0.41 – 0.41) that excluded all values predicted by theory (Table 1). The organ diameter-scaling exponent β was significantly greater in roots than in stems ( p < 1.11 × 10 -16 ). Furthermore, the normalization constant d 0 was significantly higher for roots ( d 0 = 2.17) than for stems ( d 0 = 1.47; p < 1.11 × 10 -16 ). Finally, our empirical estimates of β for both stems and roots did not differ ( p = 0.71 and 0.44, respectively) between the subsampled and bootstrapped datasets (i.e., non-averaged diameter data, d ). However, stem and root β for subsampled data were significantly different ( p = 0.003 and p = 0.013, respectively; Fig. S11 & S12) from β for hydraulic diameter data. Stem and root β estimated for bootstrapped data were also significantly different ( p = 0.001 and p = 0.004, respectively) from β for hydraulic diameter data. Model simulations (Eqns. 7-11) predicted a 3-fold decrease in the critical collapse limit ( t / b ) 2 crit from the tip ( L / H ≈ 0%) to the base ( L / H ≈ 100%), ranging from 0.028 to 0.009 (Fig. 3). Consistent with this prediction, observed thickness-to-span ratios ( t / b ) 2 exhibited a significant exponential decrease across relative position from stem tip to base, L / H ( p < 2.22 × 10 -16 ; Fig. 3). Nearly all conduits (99.96%) had thickness-to-span ratios that exceeded the critical collapse limit required to prevent failure under extreme water stress. Of the tiny fraction of conduits predicted to collapse (0.04%), most were located in the earlywood ( n =183), with only a few in the latewood ( n = 3) and primary xylem of leaves and twigs ( n = 2). Across all conduits, the median safety factor was 43.60 (IQR: 18.53 – 124.04), with 90% of values falling between 6.35 and 542.32. As with ( t / b ) 2 (Table S1), safety factors differed substantially between different types of xylem (Table S2). Discussion This study examines how xylem conduit morphology is shaped by the physics of sap transport, striking a balance between hydraulic efficiency and mechanical stability. We assessed predictions from competing theories for scaling of conduit diameters with hydraulic path length (Table 1) and evaluated our novel theory (Eqns. 7-11) for thickness-to-span ratios ( t / b ) 2 . Although the observed diameter-length scaling exponents were statistically different than the values predicted by the theories, they were numerically close to several predictions, supporting the hypothesis that xylem morphology evolves to minimize hydraulic resistance along increasing path lengths (Fig. 2A). Additionally, we observed that ( t / b ) 2 decreased with relative distance from the tip but consistently exceeded the critical collapse limit in essentially all conduits (Fig. 3), emphasizing the importance of structural reinforcement in maintaining xylem integrity. Scaling relationships between conduit diameter d and path length L have been modelled for decades, with predictions for α varying widely (Table 1). Several models predict scaling exponents with magnitudes that are quantitatively similar (West et al ., 1999; Anfodillo et al ., 2006; Hölttä et al ., 2011; Olson et al ., 2018, 2021; Koçillari et al ., 2021) or identical (West et al ., 1999; Koçillari et al ., 2021), despite the substantial differences in assumptions, optimization criteria, and level of mechanism between the models (Appendix S1). Our results for five conifer species show that d scales as the 0.15-power of L (Fig. 2A). While this is substantially lower than the value of α = 0.24 observed for data comprising many more species and plant functional types (Koçillari et al ., 2021), it broadly agrees with predictions of α = ⅙ – ⅕ from some models (Anfodillo et al., 2006; Hölttä et al ., 2011; Olson et al., 2021). While these models differ in some respects (see Appendix S1), they share a common goal of minimizing the cumulative hydraulic resistance with any increase in total path length (Appendix S1). The fact that so many studies report empirical α varying from ca. 0.1 – 0.3 is strong evidence for the primacy of resistance minimization in shaping of tip-to-base conduit morphology (Olson et al., 2021). The scaling of conduit diameter d with distance from the stem tip L can also be expressed in terms of stem diameter D stem , assuming a consistent scaling relationship between L and D stem from tip to base (e.g., L ∝ D stem ⅔ ; Greenhill, 1881; Rosell et al ., 2017). We found that d scaled with outside stem diameter D stem as β ≈ 0.33, which is identical to the β = ⅓ predicted by the packed conduit model (Savage et al. , 2010). The packed conduit model predicts β = ⅓ and α = ½, the latter prediction being simply an expression of the former under the assumption that L and D stem scale to the 2/3 rd power (see Appendix S1; Savage et al., 2010). Why did our data and analyses strongly support the β = ⅓ prediction while rejecting the α = ½ prediction, given that both arise from the packed conduit model (Savage et al., 2010)? The most likely explanation is that L does not consistently scale as the ⅔ power of D stem . This scaling relationship is typically observed only in large datasets spanning diverse of species and height ranges. Within individual trees, however, the stem diameter-length exponent can vary substantially (e.g., exceeding ⅔ in twigs and small branches; McMahon & Kronauer, 1976; Bertram, 1989). In this study, L ∝ D stem ⅔ was observed only in trunks, not branches or twigs (Fig. S13). The ⅔-power assumption reflects the central tendency of tree form but may not hold in smaller datasets with limited numbers of species, such as ours. Applying WBE-based models (West et al., 1999; Savage et al., 2010) in similar cases may require adjusting the stem diameter-length exponents using species-specific values. For example, using the species-specific value from our study (1.58) revises the packed conduit model prediction to α = 0.21, which is much closer to our observed α = 0.15 (Fig. 2A). This violation of the ⅔-power scaling assumption could also explain why Olson & Rosell (2013) found strong support for β = 1/3 as predicted by the packed conduit model (Savage et al. , 2010), even though the same model performed poorly when D stem was expressed as L (Koçillari et al ., 2021). While the scaling of aboveground xylem conduit traits with distance along the hydraulic path has been studied for over a century (Sanio, 1872; West et al. , 1999; Savage et al. , 2010; Olson & Rosell, 2013), comparatively little attention has been given to belowground organs such as coarse and fine roots (Petit et al ., 2009; Prendin et al ., 2018; Lintunen & Kalliokoski, 2010). Larger and more rapidly widening conduits in roots suggest a prioritization of water and nutrient transport efficiency, potentially at the cost of increased vulnerability to air-seed and freeze-thaw embolism (Pittermann & Sperry, 2003, 2006). However, unlike leaves and stems, roots are largely protected from air-seed embolism due to lower sap tensions and buffered against freeze-thaw embolism by insulating soil and snow cover (Simovic & Michaletz, unpublished manuscript). Furthermore, since belowground organs generally constitute a smaller proportion of a tree’s total biomass compared to aboveground organs (Niklas, 2005; Qi et al. , 2019), the construction of larger conduits may help maximize hydraulic conductance per unit biomass and help maintain constant conductance across the root-shoot xylem network. Extensive evidence shows that while tip-to-base conduit widening is a universal feature among terrestrial plants, gymnosperms and angiosperms exhibit distinct patterns of widening (Anfodillo et al ., 2006; Prendin et al ., 2018; Lechthaler et al ., 2020; Koçillari et al ., 2021). Gymnosperms generally have lower xylem conduit-path length scaling exponents ( α ) and normalization constants ( d 0 ) than angiosperms. Consequently, gymnosperm conduits (tracheids) widen more gradually with increasing distance from the stem tip and are narrower at any given point along the hydraulic path compared to angiosperm conduits (vessels; Anfodillo et al ., 2006; Prendin et al ., 2018; Lechthaler et al ., 2020). In gymnosperms, dense networks of tracheids provide both sap transport and mechanical support, whereas in angiosperms, these functions are divided between vessels (transport) and fibers (support). Despite their narrower and more gradually widening conduits, gymnosperms likely achieve hydraulic conductivity values that are comparable to angiosperms because a greater proportion of their cross-sectional area is dedicated to conductive tracheids. In contrast, angiosperms compensate for their smaller conductive area by producing larger, more rapidly widening conduits (Koçillari et al ., 2021). We observed that essentially all conduits had thickness-to-span ratios sufficiently large to prevent wall collapse under the mechanical stresses imposed by extreme sap tensions, as simulated using Eqns. 1-2, 5, and 7-11. This finding suggests that the risk of collapse is a key driver shaping conduit morphology, selectively eliminating conduits lacking sufficient reinforcement to withstand extreme drought conditions. Across our dataset, conduits had a median safety factor of 43.60, with even the lowest values exceeding the critical collapse limit in 99.96% of cases. This median safety factor is substantially higher than the values of 3.5 to 9.5 previously reported for conifers (Hacke et al ., 2001; Hacke et al . 2004; Domec et al ., 2009), likely reflecting the high proportion (81%) of latewood conduits in our dataset, which had a median safety factor of 62.24 (Table S2). In contrast, earlywood conduits in our dataset had a median safety factor of 10.02, which closely aligns with values reported in previous studies. Such concordance is expected, as the range of earlywood ( t / b ) 2 in our study (0.03 to 0.25) largely overlap with the range of mean values (0.04 to 0.19) previously reported for gymnosperm tracheids (Hacke et al ., 2001; Hacke et al ., 2004; Domec et al ., 2009). In our dataset (Fig. S14), conduits narrower than approximately 10 µm spanned nearly the full range of cell wall thickness, but those exceeding 10 µm with thin cell walls (~1 – 1.5 µm) were exceptionally rare. This rarity became even more pronounced among conduits exceeding 30 µm in diameter (Fig. S14), consistent with the findings of Echeverría et al., ( 2022), who reported that thin-walled vessels larger than 90 µm were conspicuously absent across 858 woody angiosperm species. These results suggest that selective pressures against collapse have shaped conduit morphology, eliminating at-risk morphologies while conferring additional reinforcement to wider conduits to maintain functionality under extreme sap tensions. Furthermore, the high safety factors observed here align with broader trends of xylem adaptation to mechanical stresses, as previously reported (Hacke et al ., 2004). These findings underscore that xylem reinforcement is not only sufficient to prevent collapse, but also provides additional structural safety, particularly for wider conduits. This extra reinforcement likely reflects the critical role of wider conduits in maintaining hydraulic efficiency while withstanding the mechanical challenges imposed by extreme environmental conditions. Conclusion Our study provides strong evidence that xylem conduit anatomy is fundamentally constrained by the physics of sap transport. Conduits widen predictably from the stem tip to base, minimizing hydraulic resistance across the path length. However, previous studies examining this scaling relationship often relied on regression models fitted to averaged data, which can bias scaling exponents and reduce statistical power (Simovic & Michaletz, in review). Recent advances in automated image analysis, including artificial intelligence-based techniques (Katzenmaier et al ., 2023), offer promising opportunities to substantially increase the sample size of conduits measured per image, though with important caveats (Olson, 2023). These advances could enhance statistical power, leading to more accurate and precise estimates of empirical scaling exponents and enabling detailed exploration of developmental zones within individual plants (Olson et al., 2021). While the former is critical for comparative studies of tip-to-base conduit widening, the latter is an empirical priority that could reveal the limits of plant hydraulic development (Olson et al., 2021). We also observed that thickness-to-span ratios decrease slightly from the stem tip to the base along with sap tension but consistently remain above the critical collapse limit. Notably, wide conduits with thin cell walls were nearly absent from our dataset, underscoring strong selective pressure against collapse-prone structures. These findings suggest that the risk of conduit wall collapse has exerted a substantial influence on xylem evolution, as collapse is an extremely costly and generally irreversible form of hydraulic failure. Despite this, tension-induced conduit collapse has received less attention than other forms of hydraulic dysfunction, such as air seed and freeze-thaw embolism (but see Michaletz et al ., 2012). Our hydraulic model represents an initial attempt to simulate critical collapse limits, but future iterations could incorporate varying water potential scenarios, such as those occurring during extreme droughts and heatwaves (Couvreur et al. , 2018). These scenarios are becoming increasingly relevant as climate change intensifies the frequency and severity of extreme weather conditions (White et al. , 2023; Calvin et al. , 2023; Baum et al ., in review). Moreover, empirical research on conduit collapse remains limited, particularly outside of leaves, leaving critical gaps in understanding the specific conditions that induce collapse. Comparative studies integrating experimental data with collapse model predictions are urgently needed to validate and refine existing models, advancing our understanding of this underexplored aspect of xylem physiology. Acknowledgements This research was supported by NSERC Discovery. M.S. received support from the UBC Four Year Doctoral Fellowship and Wall Research Award. Daniel Mosquin approved the field work at the UBC Botanical Garden, and Ben Stormes assisted with tree location, identification, and tissue sampling. Brendan Hansen helped M.S. with sampling, sectioning, imaging, and image processing. Justin Chan sectioned and imaged preserved twigs and assisted with image processing. Josef Garen contributed to the coding of the hydraulic model. Competing Interests The authors declare no competing financial or non-financial interests. Author Contributions M.S. and S.T.M. designed the study. M.S. collected and analyzed the data with the guidance of STM. MS wrote the first draft of the manuscript and both authors contributed to manuscript revisions. ORCIDs Milos Simovic: https://orcid.org/0000-0001-8325-3406 Sean T. 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Collection Plant, Cell & Environment Keywords bootstrapping plant allometry scaling thickness-to-span ratio water relations xylem transport Authors Affiliations Milos Simovic 0000-0001-8325-3406 [email protected] The University of British Columbia Department of Botany View all articles by this author Sean Michaletz 0000-0003-2158-6525 The University of British Columbia Department of Botany View all articles by this author Metrics & Citations Metrics Article Usage 598 views 316 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Milos Simovic, Sean Michaletz. Hydraulic and structural constraints jointly shape root-to-leaf scaling of xylem conduit traits. Authorea . 31 January 2025. DOI: https://doi.org/10.22541/au.173833017.79033598/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. 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