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Keywords:

  • allometry;
  • biomechanics;
  • streamlining;
  • wind;
  • wood density

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information
  • Wind is a key mechanical stress for woody plants, so how do shoot traits affect performance in wind?
  • We used a vehicle mounted apparatus to measure drag, streamlining and mechanical safety in 127 vertical lead-shoots, 1.2 m long, across 39 species in tropical Australia.
  • Shoot dimensions and stem tissue properties were closely coupled so that shoots with low stem specific gravity or larger projected area had thicker stems. Thicker stems provide larger second moment of area (I), which increased shoot safety and bending stiffness but impeded shoot reconfiguration in strong winds, including frontal area reduction. Nonetheless, increasing I also improved streamlining. Streamlining was unrelated to traits except I. Stem tissue material properties only had small effects. Higher modulus of rupture increased shoot safety and higher Young’s modulus impeded shoot reconfiguration.
  • We found no conflict between bending stiffness and streamlining for woody shoots. Stiffness might help streamlining by increasing damping and stability, thereby reducing flagging in wind. Tissue-level traits did influence shoot-level mechanical safety and behaviour, but shoot geometry was much more important. Variable shoot and stem traits, which all influenced shoot biomechanics, were integrated in shoots to yield a relatively narrow range of outcomes in wind.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Woody stems are specialized organs enabling vegetative persistence at substantial heights above the ground (Harper, 1977). They must withstand diverse stresses encountered by literally sticking up into air, and wind is certainly among the most ubiquitous and potentially damaging of those stresses (Niklas & Speck, 2001). Wind drags on leaves, branches and stems, repeatedly testing and sometimes exceeding their strength. Questions of strength and safety in woody stems inevitably involve the material properties of their tissues, which in turn depend upon stem tissue specific gravity (SG, dry mass per fresh volume relative to density of water) (Anten & Schieving, 2010). At a given cross-sectional area, stems with high SG are generally stiffer and more resistant to breakage (Chave et al., 2009). These differences in material properties are sometimes extrapolated to suggest that stems of lower SG are generally weaker and more susceptible to damage. However, material properties of stem tissues are only part of the equation for shoot resistance to breakage and bending (Niklas, 1992, 2000; de Langre, 2008; Sellier & Fourcaud, 2009).

Species’ relative risks of breakage from wind have mainly been studied opportunistically following intense storms. The majority of evidence points vaguely toward a benefit from building stems with higher SG (Putz et al., 1983; Zimmerman et al., 1994; Francis, 2000; Duryea et al., 2007a; Curran et al., 2008; largest plants only in Yoshida & Noguchi, 2008). However, many of these studies reported weak correlations and several studies have found no correlation between tissue properties and storm damage (Duryea et al., 2007b; Gleason et al., 2008; most size classes in Yoshida & Noguchi, 2008). Only one study (Asner & Goldstein, 1997), has found a negative relationship between Young’s modulus and damage. They examined hurricane damage to five Hawai’ian tree species.

More broadly, species with lower stem tissue SG have been shown to suffer higher mortality from a wide range of causes (King et al., 2006; Osunkoya et al., 2007; Chao et al., 2008). There is, however, an important caveat to these observations and those from storm studies. Most come from studies in forests, and especially tropical rain forests, where wood SG is strongly correlated with a growth/mortality trade-off (Wright et al., 2010). This trade-off arises because the fast-growing light-demanding species that tend to produce low SG wood do not compensate for the relative weakness of their tissues by growing thicker stems (King et al., 2006; van Gelder et al., 2006; Kooyman & Westoby, 2009). Thus observations of higher vulnerability among species with low stem tissue SG in these systems might also be understood as a consequence of a high-risk life-history strategy rather than as a consequence of low stem tissue SG per se. For example, Zimmerman et al. (1994) noted the strong influence of a small suite of ‘pioneer’ species on the correlation they found between stem SG and hurricane survival. It remains to be seen whether stem SG or tissue mechanical properties are correlated with mechanical safety or mortality outside forest biomes.

Very few studies have directly measured and compared shoot performance in wind across species or linked species attributes such as stem SG to shoot safety or streamlining (Vogel, 1996). Studies of drag (force from wind) in terrestrial plants have mainly focused on species of forestry significance (Mayhead, 1973; Rudnicki et al., 2004; Vollsinger et al., 2005; Kane & Smiley, 2006; Kane et al., 2008). These studies provide data on drag and its variation with wind speeds that can be combined with tree pulling studies and analysis of wind profiles to model windthrow and inform silviculture (Gardiner et al., 2008).

Basic theory for fluids predicts drag (D), the force from fluid movement on an immersed object, as:

  • image(Eqn 1)

Where cd is a ‘drag coefficient’ quantifying drag per shoot area, ρf is the fluid’s density, U is the speed of flow and A is the object’s projected area (for plants A is conventionally assessed ‘at rest’; Mayhead, 1973; Vogel, 1989; Kane et al., 2008).

Plants can minimize drag in strong winds by being flexible and assuming streamlined forms (Wainwright et al., 1976; Vogel, 1989). Shoots can bend and realign, reducing their area perpendicular to airflow, and changing the dynamics of that flow and therefore their drag coefficient. One way to empirically describe the effectiveness of complex adjustments involved in streamlining by biological structures is to assess the form of the relationship between drag and wind speed (Vogel, 1984). A coefficient (v) describing scaling of drag with wind speed (drag ∼ wind speedv) can be used to quantify streamlining efficacy (Vogel, 1984; though note that Vogel reported a coefficient E equal to v – 2). Larger v means poorer streamlining, with = 2 for an unstreamlined ‘bluff-body’ with unchanging area and drag coefficient, as in eqn 1. For large conifer specimens, c. 3.5–7 m tall, v is c. 1.3 (range c. 1.2–1.4, data from Mayhead, 1973; reanalysed by Vogel, 1984, 1989; Kane et al., 2008). Studies of smaller shoot sections and individual leaves by Vogel (1984, 1989) suggest that streamlining efficacy at the whole-tree level is broadly comparable to that of branches and even leaves. This is probably because tree-level streamlining largely reflects reconfiguration of these smaller organs (Vogel, 1984). It is well established that drag on trees scales with less than the square of wind speed, but we know little about the extent of variation across species, or whether streamlining efficacy and breakage risk are related to one another or to other plant traits.

Stem tissue SG influences both resistance to breakage and bending stiffness, but how are these traits correlated with streamlining efficacy? There may even be a trade-off between strength and flexibility, mediated by stem SG. For example, a stem with low SG tissues can have the same breaking strength as a stem with higher SG by having a larger diameter, but, as explained below, the stem with higher SG could show lower bending stiffness and could therefore also exhibit more effective streamlining. If the relationship between modulus of rupture (MR) and Young’s modulus (E) (material stiffness) is of the general form MR ∼ Ea, then for stems with the same resistance to breakage those with lower SG will be less stiff if a < 0.75 (for derivation see the Supporting Information, Notes S1). However, MR and E are directly proportional to wood SG (Chave et al., 2009), so = 1 and higher SG will result in lower bending stiffness for any given breaking strength. It is clear that optimal balance between shoot costs and shoot safety and the relative contributions of tissue material properties and shoot geometry to performance in wind are complex problems: What solutions to these problems have evolved in plants?

This study assesses interaction between stem tissue material properties and other traits of woody shoots, and quantifies their effects on biomechanical outcomes, including streamlining efficacy and risk of breakage in wind. Although we focus on loads imposed by drag in wind, our findings are applicable to the broader understanding of plant function and biomechanics, including the implications of variation observed across species in stem SG. Specifically we asked: Is breakage risk in wind correlated with stem SG? Do species building stems of low SG sacrifice streamlining efficacy? Are other shoot traits associated with safety in wind, or with streamlining efficacy? We measured traits and shoot performance in wind at several sites arrayed along a moisture gradient to assess whether the answer to these questions depends strongly on where we look, and whether known association between wood density and aridity might influence outcomes.

Materials and Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

We used a vehicle-mounted apparatus to measure drag on ascending ‘lead’ shoots 1.2 m long, at wind speeds up to 30 m s−1. We studied the most prominent woody species at each of three sites, arrayed along a rainfall gradient. Shoots sampled were healthy and vigorous and were collected immediately before testing. Stem diameters, shoot geometry and tissue material properties were measured and used to calculate bending moment, bending stress and safety factors for the main stem at the shoot base. Data on a range of other plant traits were collected to assess association between performance and safety in wind and other shoot attributes. We tested 127 shoots from 39 species. Most species had three replicate samples.

Site framework

Sampling occurred at three sites chosen to sample a rainfall gradient in tropical Australia (Table 1). The sites are referred to as WET, DRY and ARID, and all occurred on relatively nutrient-poor soils. The ratio of average annual precipitation and potential evapotranspiration was used to guide site selection (Willmott & Feddema, 1992). Average annual rainfall decreased by c. 40% each step from WET to DRY to ARID, but potential evapotranspiration was approx. constant.

Table 1.   Site locations and climate summaries
Site nameLocationSampling timeMean annual temperature (°C)Mean annual precipitation (mm)Mean annual potential evapotranspiration (mm)Vegetation structure
  1. Climate data from spatially interpolated datasets compiled by the Australian Bureau of Meteorology for the standard 30-yr period 1961–1990.

Wet18.45°S 146.13°EOct 200924.119231887Forest 25 m tall, c. 50% canopy cover plus mid-dense lower tree stratum 5–12 m tall
Dry18.30°S 145.49°ENov 200921.311391837Forest 25 m tall, c. 50% canopy cover, sparse lower trees
Arid18.70°S 141.79°EMay 201026.96341764Open woodland 12 m tall, c. 30% canopy cover

All sites were open canopied, with eucalypts (sensu lato) among their canopy dominants. Canopy tree height and crown cover were c. 25 m and 50% at both at the WET and DRY sites, but the lower tree and shrub layers were much denser at WET than DRY. The WET site supported a well-developed lower tree layer, mainly 5–12 m tall, which included a few species that also grow in closed canopy rainforests nearby. Grasses and other herbs were patchy and sparse at WET. Lower trees and shrubs (1–10 m tall) were sparse at DRY and the ground stratum was dense with tall tussock grasses. Both WET and DRY occupied granitic landscapes, with WET occupying a low slope of north-easterly aspect, and DRY occupying a broad flat plateau. The ARID site was also flat, occupying a sheet of unconsolidated Tertiary sediments with deep and rather sandy soils. Here canopy height and cover were much lower than in the other two sites, c. 12 m and 30% respectively.

Data for daily maximum wind gust speed were obtained from the Australian Bureau of Meteorology for five climate stations surrounding the sample locations. The stations had mean maximum daily gust speeds that ranged from 9.7 to 12.1 m s−1. The frequency of days with wind gusts above 25 m s−1 ranged from once in 4 yr to once per year (see the Supporting Information, Fig. S1). However, the region is subject to severe tropical storms so all sites are likely to infrequently experience extremely strong wind, particularly the two sites closest to the coast (WET and DRY). The strongest gust in the data was 51 m s−1 (185 kph) from a station close to the WET site.

Species attributes

Lists of species sampled are provided in the Supporting Information (Table S1). Some species were sampled at two sites. For each species at each site we also measured the traits listed and described in Table 2. Only ascending ‘lead’ shoots from the upper, outer crown of vigorous individuals were collected. Each shoot was from a separate plant. Species level traits were assessed on four or five replicate shoots per species. Drag measurement was carried out on three replicate shoots for each species, except at the arid site where equipment failure reduced replication for eight species to two samples.

Table 2.   Traits for species and shoots, with notes on measurement methods
TraitSymbolUnitNotes on procedure
Species traits
 Shoot dry mass to 1.2 mDMgAverage dry mass of ascending shoots 1.2 m long. Four representatives per species
 Young’s modulusEPaThree-point bending test on fully hydrated stems with bark, c. 8 mm diameter & 200 mm span (few shorter). Five representatives per species
 Leaf mass per unit areaLMAg cm−2Dry mass of leaf per unit leaf area (one-sided) for c. 5–20 expanded leaves from five shoots per species.
 Leaf sizeLScm2Mean, one-sided, projected area of c. 5–20 expanded leaves from five shoots per species. Log10 transformed for analyses.
 Modulus of ruptureMRPaAs for Young’s modulus.
 Stem tissue basic specific gravitySG Ratio of oven dry mass (70°C, < 1% moisture content) to fresh volume for whole stem sections (bark, sapwood & pith), c. 8 mm diameter, relative to density of water. Volume measured by Archimedes method. Five representatives per species
Shoot specific traits – directly measured
 Shoot frontal projected areaAS A11 A22m2Measured on calibrated images for each shoot drag measurement. AS is for still air, A11 and A22 were at 11 m s−1 and 22 m s−1.
 Resistance to bendingE.I.N m2Product of Young’s modulus and stem second moment of area.
 Stem second moment of areaIm4Calculated from measurements of stem dimensions at top of apparatus mount (1.2 m from shoot tip). inline image Where, rd & rc are stem radii in direction of travel and perpendicular to it.
 Bending moment arm lengthLMmVertical distance from top of mount to centre of shoot area, measured on calibrated images for each shoot. LM is for still air, LM11 and LM22 are at 11 and 22 m s−1.
Shoot specific traits – derived or interpolated
 Drag coefficientcd Calculated from drag at 20 m s−1 (D20) as inline image where ρf is 1.2 kg m−3, = 20 m s−1 and AS is shoot area at 0 m s−1.
 Drag at 11 & 22 m s−1D11 D22NInterpolation via quadratic fit (through origin) of drag vs speed data.
 Bending momentMNProduct of drag and bending moment arm length (LM) at a given speed.
 Safety factor (bending) at 22 m s−1SF22 Ratio of species MR to bending stress from drag at 22 m s−1. A SF was also calculated for 11 m s−1.
 Bending stressσmaxPaBending stress at stem surface at top of specimen mount: inline image. Where M is the bending moment, I the second moment of area, and r is stem radius in the direction of travel.
 Streamlining efficacyvSlope of standardized major axis regression fit to log–log plot of drag vs wind speed, where wind speed is > 10m s−1.

All dry masses, including those used to calculate stem SG are for material dried to constant mass at 70°C. Drying to 70°C left < 1% of mass as bound water in woody tissues (D. W. Butler unpublished ). A laboratory precision balance was used for all mass determinations, and a material testing machine (Model 5542; Instron Corporation, Canton, MA, USA) was used to measure Young’s modulus and modulus of rupture on fully hydrated stem samples with their bark intact and c. 8 mm in diameter. Maximum height was estimated for each species based on field observations, published descriptions, and herbarium specimen labels.

Drag measurement

We measured drag on 1.2 m long shoots, including all side-branches and leaves. Shoots were vertically oriented in situ and were harvested immediately before measurement. Drag measurements used an apparatus attached to the top of a motor vehicle with the shoot sitting above and slightly forward of the windscreen (Fig. 1). Shoots were mounted to a horizontal low-friction stage which was free to move small distances to and fro in the direction of travel. Drag force on the mount and shoot was measured directly by a load cell behind the mount. Wind speed was measured using a directional vane anemometer (Tenma 72–6638, accuracy c. 3%), mounted at the same position as the middle of the specimen but on the other side of the vehicle. A web-cam mounted on a shaft above the vehicles’ front bumper, in front of the centre of the specimen, captured frontal images during measurement.

image

Figure 1. Diagram of vehicle mounted drag apparatus (not to scale).

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To avoid systematic influence from vehicle acceleration we measured drag while maintaining vehicle speed as close to constant as possible. Vehicle speed was increased in 10 km h–1 steps from 10 to 100 km h–1 (2.8–27.8 m s−1), with measurements made during periods of steady speed.

A typical measurement run proceeded as follows (the start and end times for each speed step were noted): (1) collect shoot and photograph it against a neutral background; (2) mount shoot in apparatus and measure stem diameters immediately above the mount parallel to direction of travel and at right-angles to it; (3) capture frontal web cam image of shoot in still air with scale bar beside it; (4) record load while stationary, each second for c. 10 s; (5) step through speeds 10, 20, 30, 40, 50 and 60 km h–1 maintaining each speed for c. 10–20 s, logging wind speed and load each second, and automatically capturing images from front webcam every 5 s ; (6) turn vehicle around, repeat steps 4 and 5 but travelling in opposite direction; (7) repeat steps 4 and 5 but step speeds 70, 80, 90 and 100 km h–1; (8) turn vehicle around, repeat step 7; (9) repeat step 4; (10) remove shoot from mount, record notes on extent of damage to leaves and stem, and photograph shoot against neutral background.

Completing two low-speed runs (steps 5 and 6) before applying higher speeds (steps 7 and 8) meant that any damage or reconfiguration that occurred at high speeds did not affect replication of low-speed measurements. If the sample broke at the base we stopped measurement. Roads used during drag measurement were fairly flat and were as smooth as could be found in the vicinity of the sites. Only the high-speed measurements (≥70 km h–1) at the WET site were conducted on paved road. Tests were not conducted under windy conditions, but there were breezes up to c. 5 m s−1 during some measurements. The directional anemometer, and the up-and-back measurement protocol we used, left us confident that background air movement did not substantially compromise the data. Measurement order was staggered across species so that replicates of a single species were not all tested under the same conditions. Drag on the empty apparatus was measured during c. 10 runs at each site.

Drag data processing

Data from periods of changing vehicle speed or compromised by anemometer problems were deleted. The anemometer suffered some interference from the direct sunshine and various other malfunctions, but comparison with vehicle speeds allowed identification of unreliable data. The remaining wind speed and load measurements from each speed step were averaged. Final drag was the raw measurement from the load cell minus drag on the empty mount for the same wind speed. Drag on the empty apparatus was described by quadratic regression models fitted without intercepts fitted to data from measurement runs with the apparatus empty with the ‘lm’ function in R (R Development Core Team, 2010).

Final drag data were fitted to their accompanying wind speed data using quadratic models, without intercepts, using the lm function in R. These fits were used to estimate drag at specific speeds, e.g. 22 m s−1 , to calculate parameters such as drag coefficients, bending moments and safety factors. Standardized major axis (SMA) regression of log-transformed drag and wind speed data was used to estimate v with the ‘smatr’ package in R (Warton et al., 2006). The SMA regressions only included data for wind speeds above 10 m s−1 because of poor signal to noise ratio in drag measured at low speeds. Three species from the DRY site were excluded from all streamlining analyses because they were too small to work well with the apparatus (Gastrolobium grandiflorum, Acacia leptostachya and Allocasuarina torulosa).

The clearest available image from the frontal webcam for 0, 11 and 22 m s−1 was used to digitize the shoot’s position. Shoot frontal area was measured from resulting binary images with imagej software (Rasband, 2009) calibrated with the scale photographed at the start of each specimen run. The length of the bending moment arm was calculated as the vertical distance from the centroid of the shoots area to the top of the mount. Bending moment at the top of the apparatus mount was calculated as the product of the drag and the length of the bending moment arm. Bending stress (maximum) was calculated from bending moment and stem dimensions using the formula provided in Table 2. Safety factors were calculated for 22 m s−1 (SF22) as the species’ modulus of rupture divided by the shoot’s bending stress at 22 m s−1.

Drag coefficients were calculated relative to shoot area at rest for drag at 20 m s−1:

  • image(Eqn 2)

(D20, drag predicted by the quadratic fit for each branch at speed = 20 m s−1; ρf, density of air (1.2 kg m−3); AS, shoot projected area at rest).

Statistical analysis

Histograms and normal q–q plots were used to assess variable distributions and prompted log transformation of leaf size, height, safety factors, stem second moment of area and drag coefficients for use in all analyses.

Statistical analyses addressed four questions: (1)Was breakage risk correlated with shoot safety factors? (2) How were traits associated with one another within sites and across the moisture gradient the sites sampled? (3)Which shoot attributes predict performance in wind? (4) How does modulus of rupture scale with Young’s modulus?

To check whether shoot safety factors for 22 m s−1 could predict breakage risk (question 1), a hierarchical linear model with binomial errors was fitted to a binary variable distinguishing stems that snapped during measurement, with safety factor as the lone fixed predictor and species as random effects to accommodate repeated measures (lmer function in R).

Correlation between traits across species (question 2) was examined with a combination of principal components analysis (PCA, prcomp function in R) and bivariate Pearson’s correlation tests (cor.test function in R). Site moisture availability was indexed by a continuous variable ‘Moisture’, which had values of 1, 2 and 3 for measurements in the WET, DRY and ARID sites, respectively. Observations of species that occurred in two sites were averaged for this analysis, leaving 39 species records. Exploratory PCA and bivariate correlations were used to select seven variables for the final PCA. This selection decreased colinearity and increased the number of data per variable observed. Variables were standardized and centred by subtracting their mean and dividing by one standard deviation before PCA analysis.

More detailed regression modelling was applied to the question of correlation between shoot attributes and performance in wind (question 3). We assessed five indicators of shoot performance in wind: (1) change in shoot projected area; (2) change in centre of drag (length of bending moment arm); (3) bending safety factor; (4) drag coefficients; (5) streamlining efficacy (v).

For each of these outcomes we fitted linear mixed effects models to shoot-level data, with species as a random grouping effect, using the ‘lmer’ function in R. Site-level variation was included by using ‘Moisture’ as a fixed effect in all initial models. Four other parameters were included in initial models based upon our expectation of what would influence the response. All initial models included variables related to shoot geometry as well as the most relevant tissue mechanical property (Young’s modulus for bending or modulus of rupture for breaking). The number of variables was restricted so as to maintain a reasonable number of observations per variable. Initial models also included two-way interactions between predictors.

Initial models were simplified by sequentially deleting terms with coefficients with the lowest t-value, starting with interactions, and refitting the reduced model using the ‘update’ function in R. After each step in this process the reduced model was compared with its predecessor using a χ2 to compare model fits with the ANOVA function in R. The ‘minimal’ model included interactions that could not be deleted without significantly changing model fit (i.e. ANOVA returned P < 0.05) as well as terms for each parameter included in those interactions, and terms for all other parameters that also significantly affected model fit when deleted. A null model with only intercept and nested error structure (y∼1 + (1|species)) was used to help evaluate the fit of the minimal model and to partition variance among and within species. Other exploratory models were fitted but their results are not presented in detail. For example, species maximum height was not included in the primary initial model for SF22 but we assessed association between height and shoot safety with mixed effect models as well as bivariate linear models within each site. To aid interpretability of model coefficients and intercepts all variables were standardized and centred by subtracting their mean and dividing by one standard deviation.

We assessed scaling of stem tissue material properties (modulus of rupture and Young’s modulus – question 4) using standardized major axis regression on log10 transformed species average values using the ‘line.cis’ function in R-package ‘smatr’.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Fig. 2 presents some key indicators of the effects of wind on shoots. Drag on shoots increased at a gently accelerating rate with increasing wind speed (Fig. 2a), and there was 20-fold variation in drag at 22 m s−1 across the shoots sampled. Drag at any given wind speed was correlated with shoot frontal projected area, which varied about 10-fold. Drag coefficients, which are proportional to drag per unit area at a given wind speed, varied three- to four-fold across species (Fig. 2b). Bending moment, which integrates drag and the location of the shoot’s centre of drag, increased more gradually with increasing wind speed than drag alone did (Figs 2c, 3). This difference was caused by the reduction in the length of the bending moment arm as shoots bent and reconfigured in wind. Stem second moment of area was closely coordinated with bending moment (Fig. 2d) so that bending stress at the base of the shoots was uncorrelated with bending moments (Fig. 2e). Bending stress was correlated with stem tissue modulus of rupture so that bending safety factors at 22 m s−1 ranged from less than two up to seven (c. sixfold) across the range of tissue modulus of rupture (Fig. 2f).

image

Figure 2. Scatterplots showing fundamental aspects of performance in wind for woody shoots 1.2 m long. (a) Drag vs wind speed. (b) Drag at 20 m s−1 against shoot projected frontal area at rest; dashed lines are isoclines of drag coefficients. (c) Bending moment (drag × distance from shoot base to centre of drag) against wind speed. (d) Bending moment against stem second moment of area (c. diameter4, for shoot base 1.2 m from tip). (e) Bending stress (which integrates bending moment and stem diameter) against bending moment (both 1.2 m from shoot tip). (f) Bending stress against stem modulus of rupture (breaking stress); dashed lines are isoclines of shoot safety factor. Points and lines are averages for species/site combinations with patterns distinguishing sites: WET, square symbols or solid lines; DRY, circles or short dashed lines; ARID, triangles or long dashed lines. Whiskers are 1 SE for species means of three shoots.

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image

Figure 3. Diagram summarizing relative change in key variables for an average shoot in increasing wind speeds. Curves are splines fit to average values at 0, 11 and 22 m s−1 for 127 shoots from 39 species.

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Was breakage risk correlated with safety factors calculated from drag and shoot dimensions?

Six of the 127 shoots tested broke during testing and all but one of these broke at above 25 m s−1, the other broke at c. 20 m s−1. All broke at the top of the mount on the upwind side. Safety factors calculated for shoots at 22 m s−1 did prove useful in predicting likelihood of stem breakage (hierarchical logistic regression of breaking or not on SF22 with species as random effects, regression coefficient = − 16.9, SE = 5.9, P = 0.004, for 127 stems and 39 species). Almost no other damage was done to stems but many shoots lost some leaf area during testing (median = 10% of area lost). A quarter of shoots lost more than a quarter of their leaf area. Leaf area loss was mainly from torn leaf tips, and tearing along the mid-rib or other longitudinal veins was also common. Shoots from species with higher leaf mass per area (LMA) tended to lose a smaller percentage of their leaf area and to suffer damage to a smaller percentage of remaining leaves (Spearman’s rank correlation species median per cent loss and per cent damage vs LMA, ρ = − 0.34 and − 0.43, respectively, = 45 species, = 0.02 and 0.003).

How were species traits associated with one another within sites and across the moisture gradient the sites sampled?

Species with larger shoot area tended to be taller plants and to have larger leaves (Table 3, Fig. S2 and Table S2). They also showed a weak tendency to have stems with low specific gravity. Species with larger shoot area and those with lower Young’s modulus also had thicker stems. This increase in stem thickness was sufficient to produce a counter-intuitive negative correlation of Young’s modulus with stem bending stiffness (E.I). However, most species fell within a similar range of bending stiffness across the range of Young’s modulus. The negative correlation observed between Young’s modulus and stem stiffness can be attributed to a few species with extreme Young’s modulus and small shoot projected area (Fig. 4). This pattern is similar to the coordination shown between surface stress caused by bending at 22 m s−1 and tissue modulus of rupture, such that shoot safety factors fell within a relatively narrow range and were largely unrelated to the modulus of rupture of their stem tissues (Fig. 2f).

Table 3.   Matrix of Pearson’s correlation coefficients for pairs of species’ traits
 ASDMD22IE.IMRESGLMALSHTLMvSFcd
  1. Italic font indicates < 0.05 but > 0.01; bold font < 0.01. As, shoot frontal area; DM, shoot dry mass; D22, Drag at 22 m s−1; I, shoot second moment of area; E.I., resistance to bending; MR, modulus of rupture; E, Young's modulus; SG, stem tissue specific gravity; LMA, leaf mass per area; LS, leaf size; HT, species maximum height; LM, bending moment arm length; v, streamlining efficacy; SF, bending safety factor (22 m s−1); cd, shoot drag coefficient.

DM0.5              
D220.660.66             
I0.480.680.74            
E.I0.670.670.760.92           
MR−0.230.430.430.830.6          
E−0.160.480.460.840.60.95         
SG0.350−0.060.390.380.470.32        
LMA−0.20.280.040.10.05−0.01−0.110.54       
LS0.540.240.10.160.35−0.050.090.48−0.31      
HT0.550.390.20.320.4−0.25−0.230.36−0.140.42     
LM0.290.230.130.180.18−0.030.030.390.450.540.16    
v−0.18−0.28−0.280.39−0.39−0.250.26−0.06−0.26−0.08−0.020.04   
SF220.370.13−0.220.240.24−0.19−0.210.010.49−0.14−0.050.3−0.17  
cd0.160.280.590.620.350.390.520.170.220.39−0.27−0.14−0.130.05 
Moisture0.360.150.220.220.03−0.220.370.430.510.590.420.35−0.250.170.69
image

Figure 4. Scatterplots relating stem Young’s modulus (tissue level resistance to bending) to (a) stem second moment of area at the base of the shoot (mechanical expression of stem diameter) and (b) shoot frontal projected area at rest. Dashed lines in panel (a) show isoclines of shoot bending stiffness (Young’s modulus × stem second moment of area). Points are averages for species/site combinations with whiskers showing 1 SE either side of the mean. Sites are differentiated by the following symbols: WET, squares; DRY, circles; ARID, triangles.

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Stem second moment of area was by far the most variable trait across species within sites but only showed a weak (nonsignificant) tendency to increase with aridity across sites. Averages and ranges of species traits for sites are in Table 4, and values for species are provided as Supporting Information (Table S3). The sites differed mainly in terms of two stem-tissue material properties (SG and Young’s modulus) as well as LMA, leaf size and drag coefficients. SG showed a twofold range within each site and was lower in the WET site. Stem tissue modulus of rupture and Young’s modulus varied eight- to ten-fold within sites and were lowest in the ARID site. Drag coefficients varied two to three-fold within sites and increased with aridity. Shoot projected area and dry mass varied five to ten-fold within sites, but stem second moment of area had > 50-fold range within each site.

Table 4.   Means and ranges of species traits in sites
 Site mean (standard error)Range
WETDRYARIDWETDRYARID
  1. *Indicates variables that differ between sites (one-way ANOVA, < 0.05). As, shoot frontal area; cd, shoot drag coefficient; D22, drag at 22 m s−1; DM, shoot dry mass; E, Young's modulus; E.I., resistance to bending; I, shoot second moment of area; LM, bending moment arm length; LMA, leaf mass per area; LS, leaf size; MR, modulus of rupture; SF22, bending safety factor (22 m s−1); SG, stem tissue specific gravity; v, streamlining efficacy.

AS0.37 (0.03)0.28 (0.04)0.28 (0.03)0.13–0.550.04–0.50.15–0.55
*cd0.26 (0.01)0.31 (0.02)0.45 (0.03)0.19–0.370.21–0.460.27–0.71
D22 (N)26 (2.5)24 (3.6)35 (4)7–453–5515–66
DM (g)303 (33)283 (43)373 (58)134–61446–631126–899
*E (MPa)4514 (1577)5199 (706)2857 (458)1520–6982844–109511270–7008
E.I. × 1052.5 (0.3)2.9 (0.6)3.5 (0.9)0.3–4.40.1–8.10.9–14.3
I × 109 (m4)7.1 (1.6)9.3 (3.2)18.3 (5.5)0.4–260.1–521.3–71
*LM0.68 (0.027)0.59 (0.02)0.63 (0.021)0.47–0.850.41–0.720.50–0.75
*LMA (g m−2)96 (8)163 (11)172 (18)62–18897–264100–387
*LS (cm2)78 (15)19 (2.9)35 (25)1–2560.7–461.2–380
MR (MPa)48 (3)54 (5.3)42 (3.5)24–6414–10025–72
SF222.6 (0.3)3.4 (0.3)2.9 (0.4)1.3–6.51.2–6.11.6–7.0
*SG0.45 (0.02)0.54 (0.08)0.54 (0.08)0.35–0.630.34–0.660.43–0.67
v1.43 (0.04)1.56 (0.09)1.34 (0.07)1.13–1.711.18–2.340.92–2.23

Which shoot attributes predict performance in wind?

Stem second moment of area was consistently more influential than stem tissue properties on all indicators of shoot performance in wind, including drag coefficients, shoot safety factors, changes in the length of the bending moment arm and shoot projected area, and streamlining efficacy (Table 5). Drag coefficients tended to be higher among shoots with greater second moment of area and shoots in drier sites, but shoots with larger frontal projected area had lower drag coefficients.

Table 5.   Mixed regression models predicting five different indicators of woody shoot performance in wind from shoot traits with species intercepts modelled as random effects
ResponseInitial predictorsMinimal modelError SD for minimal model and null model (in parenthesis)
Predictors (ordered∼p)Standardized partial regression coefficient (SE)Species interceptsResidual
  1. ns, not significant.*P < 0.05, **P < 0.01. As, shoot frontal area; cd, drag coefficient; E, Young's modulus; I, shoot second moment of area; LM, bending moment arm length; LS, leaf size; `Moisture', site aridity; MR, modulus of rupture; SF22, bending safety factor (22 m s−1); SG, stem tissue specific gravity; v, streamlining efficacy.

Change in shoot area log10 (Projected area at 22 m s−1: area at rest)ASlog10I0.98 (0.11)**0.44 (0.8)0.47 (0.6)
log10LSAS−0.69 (0.09)**  
Elog10LS−0.24 (0.09)*  
log10IE0.23 (0.10)*126 observations 
MoistureAS: log10I0.21 (0.05)**39 species 
 AS: log10LS0.16 (0.08)*  
Change in centre of drag log10 (length of bending moment arm at 22 m s−1: length at rest)LMlog10I0.73 (0.11)**0.37 (0)0.72 (1)
ASLM−0.47 (0.08)**  
EE0.27 (0.12)*  
log10I  126 observations 
Moisture  39 spp. 
Safety factors log10 SF22log10Ilog10I1.2 (0.12)**0.31 (0.56)0.63 (0.84)
LMAS−0.83 (0.10)**  
ASMR0.56 (0.11)**  
MRLM−0.26 (0.07)**127 observations 
MoistureMoisture−0.22 (0.08)**39 spp. 
log10I: AS0.29 (0.08)**  
MR: AS0.18 (0.09)*  
Drag coefficients log10 (cd)log10Ilog10I0.64 (0.09)**0.3 (0.67)0.66 (0.77)
ASMoisture0.32 (0.09)**  
EAS−0.30 (0.09)**  
log10LS  127 observations 
Moisture  39 spp. 
Streamlining efficacy vlog10Ilog10I−0.51 (0.20)**0.57 (0.57)0.79 (0.84)
ASAS0.11 (0.13)ns  
log10 (A22/AS)Moisture0.05 (0.12)ns  
Elog10 (A22/AS)0.01 (0.14)ns117 observations 
Moisturelog10 (A22/AS): Moisture−0.33 (0.11)*37 spp. 
log10I: log10 (A22/AS)0.33 (0.13)*  
AS: Moisture−0.21 (0.10)*  

Increasing wind speed induced substantial reductions in shoot frontal projected area. On average, a shoot’s projected area at 11 m s−1 and 22 m s−1 were 35% and 19%, respectively, of their projected area at rest (Fig. S3). Greater relative reduction in area was associated with lower stem second moment of area (Fig. 5a), greater initial shoot projected area, lower Young’s modulus and bigger leaves (Table 5). The length of the bending moment arm (LM) changed far less with increasing speed than projected area did (Fig. 3). On average, the length of the moment arm at 11 m s−1 was 84% of its length at rest and this declined to 68% at 22 m s−1 (Fig. S4). As with projected area change, higher Young’s modulus limited reconfiguration and moment arm shortening, but Young’s modulus was the weakest predictor retained in the minimal model (Table 5).

image

Figure 5. Scatterplots of key interactions between shoot traits. (a) Shoot area change against stem second moment of area (c. diameter4). (b) Bending safety factor against stem second moment of area. (c) Bending safety factor (modulus of rupture/bending stress) against streamlining efficacy (drag ∼ wind speed scaling coefficient). (d) Streamlining efficacy against change in drag from 11 to 22 m s−1. (e) Streamlining efficacy against change in shoot area. (f) Streamlining efficacy against stem second moment of area. One point per species/site with sites differentiated by symbols: WET, squares; DRY, circles; ARID, triangles. Whiskers are 1 SE for species means of three shoots.

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Shoots that showed greater shortening of the moment arm had higher safety factors. Greater safety was also conferred by thicker stems (Fig. 5b), higher modulus of rupture, and smaller projected area at rest. Graphic illustration of the strong (cubic) effect of stem diameter in reducing bending stress in a stem is provided as Supporting Information (Fig. S5a). Species from drier sites tended to be somewhat less safe. However, the minimal model was complex, with interactions involving shoot area with both stem second moment of area and modulus of rupture. Streamlining (v) was included in exploratory modelling of safety factors but did not prove to be a useful predictor (Fig 5c). Similarly, there was no evidence that safety factors varied predictably with species maximum height either within sites or across the study.

There was substantial variation in streamlining efficacy (v) across shoots but we found little evidence for consistent variation related to traits of either shoots or species. Streamlining efficacy was well correlated with relative change in drag with increasing wind speed (Fig. 5d) but was surprisingly poorly correlated with shoot area change (Fig. 5e). Regression modelling revealed some effect of shoot reconfiguration via interactions with site moisture and with stem second moment of area. The modelling of streamlining efficacy resulted in the least impressive reduction in residual variation and produced the most complex minimal model (Table 5). The extent of leaf area lost during testing was unrelated to streamlining efficacy, as was leaf size.

Shoot geometry, particularly stem second moment of area, was more useful than Young’s modulus in predicting streamlining efficacy, but the relative importance of predictors varied between sites and was subject to complex interactions. Most surprisingly, shoots with larger stem second moment of area tended to show more effective streamlining (Fig. 5f), especially if shoot area change was relatively large.

How does modulus of rupture scale with Young’s modulus?

The scaling coefficient for Young’s modulus against modulus of rupture was 0.61 (95% confidence interval 0.55–0.67) (Fig. 6a). This was significantly below the theoretically critical value of 0.75, below which lower SG stems are expected to be less stiff at any given resistance to breakage (Notes S1). Average shoot resistance to bending and breakage showed a very consistent ratio across species (Fig. 6b).

image

Figure 6. Scaling of tissue mechanical moduli and repercussions for bending stiffness and resistance to breakage. (a) Modulus of elasticity (maximum stress) against Young’s modulus (tissue level resistance to bending), line shows standardized major axis (SMA) regression fit (log–log). (b). Bending stiffness (Young’s modulus × stem second moment of area) against resistance to breakage (bending moment at breaking stress), larger symbols ∼ higher Young’s modulus. One point per species/site with sites differentiated by symbols. WET, squares; DRY, circles; ARID, triangles.

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

This study confirms the fundamental observation that most woody shoots are effective streamlined objects in wind. Drag increased with wind speed to the power of c. 1.4 rather than the power of 2.0 that would be expected from an object that did not change conformation. This average value compares well with values reported from the few other published studies of streamlining in woody plants (Vogel, 1984, 1989; Kane et al., 2008). It is also markedly influential on the likely drag incurred by woody plants in strong winds. For example, if wind speed increased from 11 m s−1 to 22 m s−1 the extra drag on a streamlined shoot (drag ∼ wind speed1.4) would be about half of the extra drag on a rigid body (drag ∼ wind speed2, Fig. S5b).

Streamlining efficacy showed considerable variation across species but was poorly correlated with species traits. Although species maximum height might be expected to correlate with risk from strong winds (Niklas, 2000), we found no evidence that height was associated with shoot safety factors or streamlining efficacy. The risk of shoot breakage in wind at 22 m s−1 was similar for shrubs and taller canopy trees, and they were also as effectively streamlined, despite a tendency for taller species to produce more massive shoots. The relatively limited range of functional outcomes, such as safety factors, streamlining efficacy and bending stiffness (E.I.), that emerge from the integration of some much more variable underlying traits (particularly I) is prima facie evidence for functional convergence across woody plant shoots.

Stem second moment of area (proportional to stem diameter to the power of 4) was the best predictor of streamlining efficacy and all other indicators of shoot performance in wind. Surprisingly, increasing stem diameter predicted more effective streamlining even though it means increased bending stiffness. Less surprisingly, increasing stem diameter also predicted less shoot reconfiguration with increasing wind speed, either for relative change in shoot projected area or for relative change in the length of the bending moment arm. Why should greater resistance to bending impede shoot reconfiguration but also result in more effective streamlining?

It is possible, but we think unlikely, that the drag ∼ wind speed scaling coefficient (v) used to quantify streamlining efficacy is not a sound descriptor. Perhaps stiffer shoots incur relatively high drag at low wind speeds, making modest reconfiguration at higher wind speeds appear effective in terms of streamlining. At low speeds, reconfiguration can bring more leaves and stems ‘broadside’ to airflow, producing an initial decline in streamlining (Vogel, 1984). For example, Rudnicki et al. (2004) found frontal projected area was greater at 4 m s−1 than at rest for three conifer species. However, changes in shoot area between 0 and 11 m s−1 and between 11 m s−1 and 22 m s−1 were strongly correlated in our study. Also, v was estimated over wind speeds from 10 m s−1 to nearly 30 m s−1, so small differences in drag and reconfiguration at low wind speeds were unlikely to be influential. Overall, the range of shoot area change was rather small compared with variation in bending stiffness, so that all shoots showed substantial shoot area change despite clear evidence for some constraint associated with bending stiffness because of thicker stems or higher Young’s modulus.

A more likely explanation for greater streamlining efficacy in stiffer shoots is that such shoots might exhibit less ‘flagging’ at higher speeds because their bending stiffness reduces wobble and enables them to assume stable streamlined forms. For example, Milne (1991) found that increasing stem diameter was associated with a linear increase in damping of oscillations in swaying trees. Vogel (1989) found individual leaves of white oak performed very poorly in wind. Their drag increased with the cube of wind speed. They were also the least stable of the leaves tested, flagging and continuously moving in the flow. Such flagging creates vortices, ‘splits’ air flow and undermines streamlining (Vogel, 1984). It will be interesting to see whether future studies also find positive association between shoot resistance to bending, drag at low wind speeds, and streamlining efficacy implied by low v. Whatever the cause, the negative association between stem second moment of area and v suggests there is no trade-off between shoot safety and streamlining. Increasing stem second moment of area also predicted greater shoot safety and there did not appear to be a streamlining cost associated with greater shoot safety.

Although shoot dimensions were much more influential, stem tissue material properties did influence shoot performance in wind. Young’s modulus was a significant predictor of the extent of shoot reconfiguration and the modulus of rupture had some effect on safety factors. Considering the more general issue of the relationship between breaking resistance and flexibility in woody stems, the scaling coefficient estimated for modulus of rupture with Young’s modulus in this study was slightly less than three-quarters. This implies that for stems with a given resistance to breakage those with lower stem SG were marginally more flexible. Most importantly, stems with lower tissue SG did not sacrifice flexibility for their strength, as they would have if the stem tissue material properties had scaled to the power of 1 with each other.

Few studies have reported allometric (power-scaling) relationships between stem SG and tissue mechanical properties. The direct proportionality of isometric scaling is well supported for wood in tree trunks (McMahon, 1973; Chave et al., 2009; Anten & Schieving, 2010). However, Onoda et al. (2010) reported that moduli of elasticity and rupture of stems 4–6 mm sapwood diameter increased more than proportionately with increasing SG across a suite of species in southern Australia. Niklas & Spatz (2010) found disproportionate scaling of Young’s modulus and modulus of rupture with the density of green wood (coefficients of 1.16 and 1.32, respectively), which implies that modulus of rupture scaled with Young’s modulus to a power slightly > 1. This suggests a substantial flexibility/strength trade-off from low tissue SG in tree trunks and is very different from the coefficient of 0.61 we found for more distal stems. However, flexibility is not a prominent feature of large woody stems and tree trunks. Perhaps stem tissue material properties relate differently to one another in more distal stems, such as those studied here. The scaling we observed implies a near-consistent relationship between resistance to breakage and bending stiffness across a wide range of stem SG.

In conclusion, tissue-level mechanical properties did discernibly influence shoot level mechanical attributes, but their influence was much weaker than that of shoot dimensions. Stem modulus of rupture was correlated with breakage risk, and Young’s modulus was correlated with the relative amount of shoot reconfiguration with increasing wind speed. Aridity affected some traits, decreasing Young’s modulus and leaf size, and increasing LMA and stem SG, but it had little effect on shoot performance or safety in wind other than higher drag coefficients. Stem second moment of area, proportional to the fourth power of stem diameter, was the single strongest determinant of shoot behaviour and safety in wind. Stem second moment of area was closely coordinated with tissue material properties as well as shoot size, both within and across sites. Increasing stem second moment of area increased shoot safety and drag coefficients, and impeded reduction in frontal projected area with increasing wind speed, but it also improved streamlining efficacy. Streamlining efficacy was essentially unrelated to shoot traits other than their stem’s second moment of area. Greater stability in wind, increasing damping and reducing flagging, is one possible explanation for the positive effect of bending stiffness on streamlining efficacy.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

This work was supported by Australian Research Council funding to MW. Thanks to editor David Ackerly, Frank Sterck and three anonymous referees for helpful advice and constructive criticism of the manuscript. Special thanks to Macquarie University’s METS team for making the apparatus. Collections of plant material in this research were permitted by the Queensland Government. Thanks also to Claraville Station and to staff in Girringun National Park for their hospitality.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Supporting Information

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Fig. S1 Site locations and wind-speed histograms for weather stations across the study region.

Fig. S2 Biplot of principal components analysis.

Fig. S3 Projected frontal area for shoots at rest vs 11 m s−1 and 22 m s−1.

Fig. S4 Length of bending moment arms for shoots at rest vs 11 m s−1 and 22 m s−1.

Fig. S5 Diagrams showing (a) scaling of stress against stem diameter for average bending moment, and (b) affect of streamlining efficacy (v) on changes in drag with increasing wind speed.

Table S1 Species sampled in each site, grouped by mature canopy position and ordered by estimated abundance

Table S2 Variance and loadings of variables on first four principal components

Table S3 Species traits

Notes S1 Background theory for tissue material properties and relative resistance to bending and breaking in woody shoots.

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