The relationship between stem biomechanics and wood density is modified by rainfall in 32 Australian woody plant species

Authors


Author for correspondence:
Yusuke Onoda
Tel: +61 2 98506270
Email: yusuke.onoda@gmail.com

Summary

  • Stem mechanical properties are critically linked to foliage deployment and growth strategy, yet variation in stem mechanics across species and habitats is poorly understood.
  • Here, we compared 32 plant species growing across four sites of contrasting rainfall and soil nutrient availability in Australia.
  • The modulus of elasticity (MOE) and modulus of rupture (MOR) were tightly correlated with dry sapwood density within sites, but species from low-rainfall environments had higher wood density for a given MOE and MOR compared with species growing in high-rainfall environments. The ratio of MOE to MOR was slightly lower for species at low-rainfall sites, suggesting that wood was stronger for a given elasticity. Most species had thick bark, but the mechanical contribution of bark to stem MOE was small.
  • Our results suggest that arid-adapted species would need to deploy more dry mass to support stems. Our results also highlight the importance of understanding how the biomechanics–wood density relationship evolves under different environmental conditions to better understand plant growth across diverse habitats.

Introduction

Plant stems mechanically maintain plant structure, and transport water and nutrients between different organs (Niklas, 1992; Tyree & Zimmermann, 2002). While mechanical properties of timber derived from the main tree trunk are well known from forestry studies (Bootle, 1983; Green et al., 1999), we know relatively less about mechanics of distal stems (hereafter called ‘stem’), which may be more directly related to leaf traits and deployment (Pickup et al., 2005). Stem elongation enables plants to capture more light and maintain a competitive advantage over neighbours (Givnish, 1988; Niklas, 1992). High stem strength reduces the risks of buckling, wind snap and damage by herbivores, and consequently contributes to plant survival (Niklas, 1992; Asner & Goldstein, 1997; Alvarez-Clare & Kitajima, 2007). However, greater mechanical stability may come at the expense of growth rate because strong and stiff wood has high construction costs, owing to higher wood density (van Gelder et al., 2006), and stiff, dense wood can limit hydraulic conductivity and efficiency of water transport (Hacke et al., 2001; Sperry et al., 2008). A trade-off between mechanical and hydraulic efficiency could allow different trait combinations to achieve similar net fitness. Correspondingly, stem biomechanical properties do vary considerably among species coexisting in a common environment.

Bending stiffness (EI) is important for potential plant height and stem length. It is a product of the modulus of elasticity (MOE) and the second moment of area (I) of the stem (EI = MOE × I). The MOE is a material property independent of stem geometry, and I is a geometrical factor that scales to the fourth power of stem diameter when stem has a circular cross-section (Gere & Timoshenko, 1999). Another important mechanical property describing stem flexure is modulus of rupture (MOR; also termed bending strength), which is the maximum surface stress (force per unit area) in a bent stem at the point of failure. A high MOR indicates high breaking resistance and is critical for mechanical safety of stems under their various loads (Gere & Timoshenko, 1999; van Gelder et al., 2006).

While MOE and MOR are different mechanical properties, they are both generally well correlated with wood density across different plant species (Bootle, 1983; Niklas, 1992; Pratt et al., 2007; Chave et al., 2009). For this reason, wood density has been used as an indicator of MOE or MOR (McMahon, 1973; King et al., 2006). Dry wood density ranges from 0.1 to 1.4 g cm−3 across plant species (Chave et al., 2009) and tends to be higher in dry environments than in wet environments (Wiemann & Williamson, 1989; Hacke et al., 2001; Chave et al., 2006; Preston et al., 2006; Swenson & Enquist, 2007), and higher in sites with low soil nutrient availability than in sites with high soil nutrient availability (ter Steege et al., 2006; Chave et al., 2009). Despite a number of studies on wood density, changes in mechanical properties across contrasting environments have rarely been investigated. While the mechanical properties of wood are expected to be correlated with wood density, the relationship between wood density and mechanical properties could be affected by different environmental conditions. For example, environmental conditions may change the mechanical properties of wood through alteration in solid fraction, cellulose microfibril angle and the relative abundance and distribution of different tissue types (Mencuccini et al., 1997; Chave et al., 2009).

The aim of this study was to determine how stem wood density, MOE and MOR were coordinated across sites with contrasting annual rainfall and soil nutrient availability. Thirty-two tree and shrub species were sampled from four sites with high and low rainfall, and high and low soil nutrient content, in a 2 × 2 factorial design. Both MOE and MOR were measured on stems at a standard diameter in order to remove any potential size-dependent effects on tissue mechanical properties.

As bark (including phloem and cambium) accounts for a significant fraction of intact stem, the mechanical properties of bark may also be important for intact stem biomechanics. Bark is softer and weaker than sapwood but has been shown to contribute substantially to bending stiffness in a few species from moist temperate climates (Xu et al., 1997; Niklas, 1999). Therefore, we compared the mechanical properties of both intact stems and de-barked stems (hereafter called ‘sapwood’). We address the following questions: Do inland species from low-rainfall environments have higher wood density and, consequently, higher MOE and MOR? Do plants growing on soils that differ in nutrient content have different wood density, MOR and MOE? Do changes in rainfall or soil nutrient content change the relationship between wood density, MOE and MOR? How much do the MOE and MOR of bark and sapwood differ, and what influence does bark have on the stem mechanical properties?

Materials and Methods

Site and species selection

Field sites were located in a relatively high-rainfall climate at Ku-ring-gai Chase National Park near Sydney on Australia’s east coast, and in a low-rainfall zone c. 500 km west of Sydney at Round Hill Nature Reserve (Table 1). Two sites differing in soil nutrient availability were chosen within each rainfall zone (Wright et al., 2002). All sites fell along a common latitudinal band (mean annual temperature 17.5°C), and experienced aseasonal patterns of rainfall. Eight evergreen tree and shrub species were sampled at each site giving a total of 32 species from 12 plant families (Table 2). Species were chosen from comprehensive species lists for each site to ensure a diverse representation of plant families and growth forms. Although species selection was not strictly random, the selection procedure did ensure that the dominant species of each community were represented.

Table 1.   Description of the four study sites
 High rain, high PHigh rain, low PLow rain, high PLow rain, low P
  1. High-rainfall sites were located in Ku-ring-gai Chase National Park, Sydney; low-rainfall sites in Round Hill Nature Reserve, western New South Wales. Data are taken from Wright et al. (2002).

Latitude (S), Longitude (E)33°34, 151°1733°41, 151°0832°58, 146°0832°58, 146°08
Vegetation typeClosed forestLow open woodlandOpen woodlandOpen shrub mallee
Annual rainfall (mm)12201220387387
Annual mean temperature (max., min.)22.0, 13.022.0, 13.024.1, 11.124.1, 11.1
Soil typeRed-brown clayYellow-grey sandLight red clayLoamy red sand
Total P (ppm)442.393.6250.4132.4
Total N (%)0.2560.0300.0710.031
Total C (%)5.910.951.200.67
Cation exchange capacity (mEq kg−1)55.69.065.838.7
Table 2.   Stem traits of 32 species from four different sites
HabitatSpecies nameFamilySapwoodSapwood + barkBark
ρfreshρdryMOEMORρfreshρdryMOEMORMOE
  1. Fresh wood density (ρfresh, g cm−3), dry wood density (ρdry, g cm−3), modulus of elasticity (MOE, MPa) and modulus of rupture (MOR, MPa).

High rainfall, high nutrientAcacia floribundaFabaceae1.0280.62711 0761031.0660.5675915724034
Astrotricha floccosaAraliaceae0.8880.4579014770.9150.401436345−215
Lasiopetalum ferrugineumMalvaceae1.1370.73817 6121681.1580.66012 2221249344
Lomatia silaifoliaProteaceae1.1130.55711 444961.1350.5526960652836
Persoonia linearisProteaceae1.0970.5469106881.0980.5024854553255
Pultenaea flexilisFabaceae1.0370.58111 132871.0800.5419528867979
Synoum glandulosumMeliaceae0.9190.4077262720.9720.3634094502609
Syncarpia glomuliferaMyrtaceae1.1080.62011 0321091.1000.5665524754182
High rainfall, low nutrientAcacia suaveolensFabaceae0.9430.5868654761.0040.595401448854
Boronia ledifoliaRutaceae1.0340.66616 6541311.1230.663768980−1384
Eriostemon australasiusRutaceae1.0500.66515 6391221.0010.5595871692816
Hakea dactyloidesProteaceae1.1310.6569470961.1590.6647032876455
Lambertia formosaProteaceae1.1180.58110 191791.1310.5915104544366
Leptospermum trinerviumMyrtaceae1.1010.64894151030.9770.5353895573335
Persoonia levisProteaceae1.0750.5466937661.0860.5292072321777
Phyllota phylicoidesFabaceae1.0990.67812 9961041.0960.565494052−404
Low rainfall, high nutrientAcacia doratoxylonFabaceae1.1210.76812 5281241.1430.7086848835457
Brachychiton populneusMalvaceae1.0370.5143078491.0520.45587018258
Dodonaea viscosa ssp. angustissimaSapindaceae1.2570.89713 3311311.0770.690525876−3439
Eremophila longifoliaMyoporaceae0.9750.6216436800.9920.583225942767
Geijera parvifloraRutaceae1.1210.7446512821.1180.6292015401126
Hakea tephrospermaProteaceae1.1530.6958890881.1740.679355248−1910
Philotheca difformisRutaceae1.1580.76511 4441221.0880.611390660−2511
Senna artemisioidesFabaceae1.1670.73612 0261091.1520.6386329723099
Low rainfall, low nutrientAcacia havilandiorumFabaceae1.1530.86117 6581741.1710.8026558901614
Bertya cunninghamiiEuphorbiaceae0.9720.6407330821.0220.6244042563333
Beyeria opacaEuphorbiaceae1.0070.6937249801.0250.6442964431265
Cassinia laevisAsteraceae1.0330.6417439911.0360.5993733572568
Eremophila glabraMyoporaceae1.0450.6879173961.0340.5934013641554
Eucalyptus socialisMyrtaceae1.0840.6856551751.1180.6482519491930
Melaleuca uncinataMyrtaceae1.1030.72712 3751281.1010.6895590803030
Olearia pimeleoidesAsteraceae1.1700.75981881011.0930.667320055−419

Samples of stem (from the terminal axis of the main branch) at 4–6 mm sapwood diameter from the outer canopy were removed from five individuals of each species at each site. This diameter was chosen for consistency with other studies of the same species that used 10 mm2 sapwood cross-sectional area as a standard measurement point (Pickup et al., 2005). Samples were stored in sealed plastic bags with a piece of moist paper towel in cool conditions and analysed within 2 wk of collection. All samples were collected between February and April 2008.

Measurement of wood density and mechanical properties

The stem samples taken from the field were divided into two subsamples for measurement of wood density and mechanical properties. One subsample was measured intact, while the other subsample was measured after removal of the outer bark, phloem and cambium layers (hereafter collectively called ‘bark’) by hand. The cross-sectional area of the resulting ‘sapwood’ subsample included the pith. However, visual inspection suggested there was very little pith in our samples except for stem samples of Astrotricha floccosa.

For each stem section we measured diameters at the mid-point and at each end, length, fresh weight, fresh volume and dry weight (after oven-drying at 60°C for at least 5 d). The volume of each stem section was measured as the volume of water (cm3) displaced in a graduated measuring cylinder after complete submersion of the stem. Stem sections were saturated before measuring the volume to prevent uptake of water into the stem during measurement. Fresh wood density (ρfresh, g cm−3) and dry wood density (ρdry, g cm−3) were calculated by dividing the dry and fresh weight of stem sections by their fresh (green) volume. Bark thickness was calculated from the difference in diameter between whole stems and those with bark removed (sapwood only) divided by two.

Young’s MOE and MOR were measured on both intact stems and sapwood with three-point bending tests using a general materials testing machine (Model 5542; Instron Corporation, Canton, MA, USA). Stem specimens were placed on two supports, generally 120 mm apart, with a vertical force applied to the middle of the stem at a speed of 25 mm min−1. The span was > 20 times longer than the stem diameter for all cases. The MOE was calculated from the linear, elastic region of the relationship between load (F, N) and deflection (δ, mm) (Gere & Timoshenko, 1999):

image( Eqn 1)

(I, second moment of area (m4); L, span length (m) of the supports). The second moment of area of stem with a circular cross-section is:

image( Eqn 2)

(R, radius (m) of the stem section measured at the middle point of the specimen). Bending stiffness for each stem section was calculated as MOE × I.

The MOR was determined at the point of maximum load (Fmax) when the stem sample broke (Gere & Timoshenko, 1999):

image( Eqn 3)

The MOE of composite materials is a weighted sum across the components, with the MOE of each component multiplied by its second moment of area (rule of mixtures, Niklas, 1992). Therefore, by recording the mechanical properties of intact stems and sapwood, we could determine the contribution of the bark layer to intact stem bending stiffness. The bending stiffness of the bark can be calculated from the following relationship:

image( Eqn 4)

where ‘intact’ and ‘sap’ refer to measurements made on intact stems and sapwood, respectively. From the radius of the intact stem (R, m) and the bark thickness (d, m), the second moment of area of the bark was calculated as:

image( Eqn 5)

The MOEbark was then calculated by combining Eqns 3–5:

image( Eqn 6)

Data analysis

For the traits measured, 57–82% of variation was found between species rather than within species (variance components analysed using a linear mixed model with species as random factors, five individuals per species, 32 species), in the R statistical package (version 2.7.2, package lme4, function lmer; R Foundation for Statistical Computing, Vienna, Austria). This confirmed that species differences were substantial despite within-species variation. For the analyses reported here, which are concerned with comparing across species, each species was represented by a single mean trait value. Effects of rainfall and soil nutrients were tested with two-way anova. The MOE and MOR were log-transformed to meet assumptions of normality (Shapiro–Wilk test) and homogeneous variances (Bartlett’s test) before the analysis. Relationships between traits (MOE, MOR, fresh or dry wood density) were explored across species within sites using the standardized major axis (SMA) test (Warton et al., 2006). Changes in these relationships between sites, indicated by differences in slope or shifts in elevation along a common slope, were tested by likelihood methods (Warton et al., 2006).

In our study, many families occur repeatedly across sites, so, in general, the site differences are not driven by deep divergences between clades, but rather arise repeatedly within clades. Phylogenetic independent contrast (PIC) values, obtained using the phylocom software (Webb et al., 2008), were calculated from phylogenies constructed in phylomatic (Webb & Donoghue, 2007). Phylogenies were obtained from a conservative seed plant tree and branch lengths (in phylogenetic sense) were calculated using the ‘phylocom bladj’ program.

Results

Across 32 species, sapwood fresh wood density (ρfresh) varied from 0.89 to 1.26 g cm−3 (1.42-fold range) and sapwood dry wood density (ρdry) varied from 0.41 to 0.90 g cm−3 (2.21-fold range). Intact stems (including bark) had similar ranges to those of sapwood (0.92–1.17 and 0.36–0.80 g cm−3 for ρfresh and ρdry, respectively). Wider ranges of variation were found in MOE and MOR values: 5.7-fold for sapwood MOE (3.1–17.7 GPa), 3.6-fold for sapwood MOR (49–174 MPa), 14-fold for intact stem MOE (0.9–12.2 GPa) and 6.9-fold for intact stem MOR (18–124 GPa) (Table 2).

Across habitats, sapwood ρdry was significantly higher in low-rainfall sites than high-rainfall sites, while ρfresh, MOE and MOR were not significantly different across sites (Table 3). Similar trends were observed for intact stems (see the Supporting Information, Table S1). Species from high-rainfall sites had a higher stem water fraction than species from low-rainfall sites (data not shown).

Table 3.   Nested anova of stem traits and environmental conditions
 dfρdryρfreshMOE1MOR1
MSFMSFMSFMSF
  1. 1Data were log-transformed before analysis.

  2. Species are nested within rainfall and soil combinations. Traits are fresh wood density (ρfresh, g cm−3), dry wood density (ρdry, g cm−3), modulus of elasticity (MOE, MPa) and modulus of rupture (MOR, MPa) of sapwood. Rainfall and soil and their interaction are tested using the species-within-site MS as denominator in the F-ratio; these tests have df = 1,28. The species effect is tested using the within-species MS as denominator in the F-ratio; these tests have df = 28,128. See the Supporting Information Table S1 for the same analysis for intact stem. Significance levels; ns, > 0.05; ***, < 0.001.

Rainfall10.54814.123***0.0722.345ns0.3512.711ns0.0000.000ns
Soil10.0310.796ns0.0060.204ns0.0090.073ns0.0030.040ns
Rainfall × soil10.0451.164ns0.0652.13ns0.0070.053ns0.0160.195ns
Species within site280.03918.19***0.03113.03***0.12912.48***0.08010.46***
Error (species)1280.002 0.002 0.010 0.008 

For both sapwood and intact stems, MOE and MOR were strongly correlated with ρdry within each site (Fig. 1, Table 4). The standardized major axis (SMA) slopes of the relationships were similar in low-rainfall sites compared with high-rainfall sites, but the low-rainfall sites had significantly lower elevation (Table 4), in other words, lower MOE or MOR at a given ρdry. Soil nutrient content did not significantly change the relationship between MOE and ρdry. The SMA slopes for MOE or MOR and ρdry had negative y-intercepts, indicating that MOE and MOR increased more than proportionately with increases in ρdry across species.

Figure 1.

 Relationship between modulus of elasticity (MOE) or modulus of rupture (MOR) and dry wood density for sapwood (a,b) and intact stem (sapwood, vascular cambium and bark) (c, d) across 32 species from sites with different rainfall and soil nutrient availability. HR-HN, high-rainfall and high soil nutrient site; HR-LN, high-rainfall and low soil nutrient site; LR-HN, low-rainfall and high soil nutrient site; LR-LN, low-rainfall and low soil nutrient site. Each point denotes a species mean value (= 5) with error bar (± 1 SD). Standardized major axis (SMA) slopes were fitted to individual sites (eight species per site). See Table 4 for regression results.

Table 4.   Standardized major axis (SMA) slope fitted to individual sites, corresponding to Figs 1,3
XYGroupnR2PSlopePost hocInterceptPost hoc
  1. Data given are sample number (n), R2, P-value of Pearson’s correlation, SMA slope with 95% confidential intervals and SMA intercepts with 95% confidence intervals. When SMA slopes are nonheterogeneous (> 0.05), shift in elevation over a common slope was tested between sites. Different letters within each trait combination denote significant differences (< 0.05) between sites. Fresh wood density (ρfresh, g cm−3), dry wood density (ρdry, g cm−3), modulus of elasticity (MOE, MPa) and modulus of rupture (MOR, MPa). ‘sap’ and ‘int’ attached to x- or y-variables denote sapwood and intact stems, respectively.

  2. HR-HN, high-rainfall and high soil nutrient site; HR-LN, high-rainfall and low soil nutrient site; LR-HN, low-rainfall and high soil nutrient site; LR-LN, low-rainfall and low soil nutrient site.

ρdry,sapMOEsapHR-HN80.8170.00229 697 (19 612, 44 968)a−5871 (−13 148, 1407)a
HR-LN80.5320.0470 187 (37 054, 132 950)a−32 843 (−63 042, −2644)a
LR-HN80.7580.00532 327 (20 128, 51 919)a−13 912 (−25 429, −2394)b
LR-LN80.730.00752 119 (31 679, 85 748)a−27 594 (−46 912, −8275)b
ρdry,sapMORsapHR-HN80.8050.003292.6 (190.8, 448.9)a−65.91 (−140.01, 8.19)a
HR-LN80.7790.004455.6 (289.4, 717.4)a−189.02 (−323.78, −54.27)b
LR-HN80.8130.002248.2 (163.1, 377.6)a−80.02 (−157.73, −2.31)c
LR-LN80.7680.004457.8 (287.6, 728.6)a−222.57 (−380.12, −65.03)c
ρdry,intMOEintHR-HN80.5950.02529 518 (16 211, 53 750)a−8640 (−18 522, 1243)a
HR-LN80.710.00934 479 (20 611, 57 678)a−15 184 (−26 110, −4258)b
LR-HN80.5890.02626 725 (14 624, 48 837)a−12 800 (−23 551, −2049)c
LR-LN80.5130.04620 514 (10 705, 39 312)a−9427 (−18 885, 31)c
ρdry,intMORintHR-HN80.7250.007263.2 (159.3, 434.9)a−65.23 (−137.75, 7.28)a
HR-LN80.6290.019341.6 (192, 607.6)a−140.72 (−263.25, −18.2)b
LR-HN80.6950.01276.2 (163.1, 467.8)a−117.49 (−213.23, −21.76)c
LR-LN80.5170.044239.3 (125.2, 457.4)a−95.8 (−205.61, 14.01)c
MOEsapMORsapHR-HN80.92500.00986 (0.00752, 0.01292)a−8.061 (−38.523, 22.401)a
HR-LN80.8380.0010.00649 (0.00439, 0.00960)a24.165 (−6.223, 54.554)a
LR-HN80.95600.00768 (0.00624, 0.00945)a26.788 (11.05, 42.527)b
LR-LN80.97800.00878 (0.00759, 0.0102)a19.798 (6.82, 32.776)b
Figure 3.

 Relationship between sapwood modulus of elasticity (MOE) and sapwood modulus of rupture (MOR) across 32 species from sites with different rainfall and soil nutrient availability. HR-HN, high-rainfall and high soil nutrient site; HR-LN, high-rainfall and low soil nutrient site; LR-HN, low-rainfall and high soil nutrient site; LR-LN, low-rainfall and low soil nutrient site. Each point denotes species mean value (= 5) with error bar (± 1 SD). Standardized major axis (SMA) slopes were fitted to individual sites (eight species per site). See Table 4 for regression results.

Sapwood and intact stem biomechanics were tightly correlated (Fig. 2). However, MOE and MOR were lower in intact stems than in sapwood by 53% and 38% because of the presence of soft and relatively thick bark (i.e. a dilution effect). The MOE of bark calculated by Eqn 6 was highly scattered (Table 2) partly owing to noise in measurements, heterogeneity of mechanical properties within individuals and a technical problem associated with bark measurements (see the Discussion). In general, bark MOE values were much lower than sapwood MOE and no correlation was observed between the two MOE measurements (Fig. S1).

Figure 2.

 Comparison of bending properties between sapwood and intact stem (sapwood, vascular cambium and bark) across 32 species from sites with different rainfall and soil nutrient availability. (a) Modulus of elasticity (MOE), (b) modulus of rupture (MOR). HR-HN, high-rainfall and high soil nutrient site; HR-LN, high-rainfall and low soil nutrient site; LR-HN, low-rainfall and high soil nutrient site; LR-LN, low-rainfall and low soil nutrient site. Each point denotes species mean value (= 5) with error bars (± 1 SD). Standardized major axis (SMA) slopes were fitted to individual sites (eight species per site). Tests for common slopes and elevation differences (where slopes are nonheterogeneous, > 0.05): (a) slopes heterogeneous, = 0.01; (b) slopes nonheterogeneous, = 0.116, Elevation: intact stem MOR was higher for a given sapwood MOR in HR-HN compared with LR-HN and LR-LN (< 0.005).

MOE and MOR were strongly correlated (0.84 < R2 < 0.98), which means that stiff material also had high breaking resistance. However, different rainfall sites showed a slight but significant difference in elevation of SMA slopes relating MOE to MOR (Table 4). For a given MOR, species in low-rainfall sites had lower MOE.

The cross-species correlations described were also found as correlations of evolutionary divergences in trait values (phylogenetically independent contrast or PIC analyses, Table S2). This means that the traits have evolved in coordination with each other in multiple independent clades. The cross-species correlations did not arise only from differences between major clades.

Discussion

Both sapwood and intact stems had higher ρdry in the low-rainfall sites than in the high-rainfall sites (Table 3), which is consistent with previous studies (Pickup et al., 2005; Chave et al., 2006; Swenson & Enquist, 2007). It has also been suggested that ρdry is higher at low soil nutrient availability (ter Steege et al., 2006; Chave et al., 2009). At a continental scale, ρdry tends to be higher in species from Australia than many other regions (Chave et al., 2009) which may be associated with the fact that Australia is a continent with ancient, weathered, nutrient-poor soils (Beadle, 1966; Orians & Milewski, 2007). At a local scale, however, we did not find significant differences in ρdry between high and low nutrient soils, and our results suggest that rainfall gradients affect ρdry more strongly than soil nutrient.

Although ρdry was higher in low-rainfall sites, there was not a concurrent increase in MOE and MOR, resulting in lower material strength and stiffness for a given wood density at low-rainfall sites compared with high-rainfall sites. However, despite this, there was a good correlation between MOE or MOR and ρdry within each site. To our knowledge, this is the first observation that relationships between stem mechanical properties and ρdry are shifted by environmental gradients.

Our sapwood MOE and ρdry data fit well within the range of reported values for various timbers (Fig. S2; Bootle, 1983; Green et al., 1999). In the larger dataset assembled in Fig. S2 there is a reasonably strong correlation between MOE and ρdry, with considerable scatter (three to four times difference in MOE for a given ρdry). Part of the variation in the broader MOE–ρdry relationship could be explained by differences in habitat conditions where trees grow. Our results suggest that species growing at low-rainfall sites deploy high wood density for functions other than mechanical stiffness and strength. Sapwood in angiosperm species from dry habitats commonly has a lower lumen fraction and reduced vessel lumen diameters (Preston et al., 2006; Mitchell et al., 2008). Thicker vessel walls relative to lumen diameters are important for preventing vessel implosion at very low water potential (Hacke et al., 2001; Pratt et al., 2007). Increased amounts of wood tissues associated with hydraulic safety may increase ρdry but may not directly contribute to MOE and MOR.

In lower rainfall zones there is less total leaf area which is deployed at lower heights, and species occurring in these regions have lower total foliage mass per unit sapwood cross-sectional area (Pickup et al., 2005). Species in sparse vegetation at low rainfall may be under less selective pressure to grow tall to compete for light. They may have less to gain from stem stiffness supporting tall canopies and may therefore be free to develop more flexible stems, which can decrease wind drag (Vogel, 1989). These factors may account for the lower ratio of MOE to MOR observed in low-rainfall sites, which indicates that stems were more elastic for a given stem strength compared with high-rainfall species. In other words, mechanical constraint for stems might shift from self-support to adaptation to wind exposure in arid habitats. Physiologically, the observed variation in MOE or MOE for a given ρdry could be associated with cellulose microfibril angle, the amount of non-structural compounds (e.g. starch and resin), and with the fraction of different types of tissues (e.g. fiber, parenchyma, vessel and ray) (Mencuccini et al., 1997; Salmen & Burgert, 2009).

Within a site, there was still substantial variation in MOE and MOR which co-varied with ρdry (Fig. 1; van Gelder et al., 2006). Stems with higher MOE and MOR are expensive to construct in the sense that more biomass needs to be invested to achieve a given volumetric growth. Bending stiffness (EI), which may be related to the amount of biomass a stem can support, is a product of MOE and the second moment of area (I) (see Eqn 4). In stems with a circular cross-section, I scales to the fourth power of diameter (see Eqn 2), thus EI is equal to ¼π R4MOE. Dry mass of a nontapered stem with length L is equal to π R2 L ρdry. From these relationships, stem length for a given dry mass (L/M) can be expressed as:

image( Eqn 7)

For stems with a given bending stiffness (EI), L/M scales to the –1 power with ρdry and to the 0.5 power with MOE. This equation suggests that if scaling between MOE and ρdry is greater than the second power, then higher MOE with a thinner diameter is the more efficient strategy to achieve a certain bending stiffness for a given mass. If MOE scales to less than the second power with ρdry, then the opposite is true. In the forestry literature, MOE of timber was almost linearly related to ρdry (Green et al., 1999; Chave et al., 2009; Fig. S1), which suggests that stem with lower ρdry and a larger diameter may be more efficient at achieving a certain bending stiffness for a given mass and length. However, in our study, common SMA slopes in log-transformed relationships of MOE–ρdry for sapwood across four sites were not significantly different from 2 (mean 2.63, 95% CI 1.98–3.36) (note Fig. 1 shows linear-scale relationships of MOE–ρdry for practical reasons, but the negative y-intercept in this relationship suggests that slopes in log-transformed relationships are greater than 1). This suggests that, in theory, the diverse combinations of MOE and ρdry observed within a site can still achieve a certain bending stiffness with a similar biomass investment for stem length growth. The different scaling slopes between distal stem data and the forestry timber data could result from different mechanical requirements between distal and basal stems, but too few data for distal stems have been published to test this idea at present. Furthermore, dry mass cost and mechanical safety of stems is complex and depends on several other traits (stem length, side branches, leaf distribution, leaf weight, tapering, angle, water content and other mechanical properties), and these factors need to be considered when developing a comprehensive understanding of dry mass cost and mechanical design of stems.

The MOE of bark was surprisingly low in our study (Table 1, Fig. S1). This result somewhat contradicts Niklas’s (1999) finding that bark MOE was c. 40–50% of wood MOE. Compared with Niklas’s species, which grew in a humid temperate climate, our species had much thicker bark, averaging 30% of stem diameter for 5 mm diameter intact stems (range 16–52%). This may result from adaptation to drought and frequent fires experienced by Australian sclerophyll vegetation (Orians & Milewski, 2007). In the bending test, cross-sectional shape of the stem is generally assumed to be unchanged during measurement. However, when bark is thick and soft, it may compress during measurement, which would underestimate the MOE of intact stems and bark (see Eqn 5). Whether intact stems or sapwood are used in biomechanics measurements depends on the purpose of the study. However, our results clearly show that the presence of bark may significantly affect the estimation of MOE and MOR in intact stems.

Conclusion

Both MOE and MOR were well correlated with ρdry within a site but the relationship clearly shifted between low- and high-rainfall sites. Previously, growth models based on mechanics have assumed a single relationship between MOE and wood density (McMahon, 1973; Niklas et al., 2004; King et al., 2006), but this assumption might not be relevant for understanding plant growth across a range of environments. Our findings highlight the need for further studies to examine stem architecture and mechanics in relation to diverse habitat conditions.

Acknowledgements

We thank Barbara Rice for her kind help with field work, Ian Wright for the bark thickness data and Don Butler, Amy Zanne, Niels Anten, Hanns-Christof Spatz and David Ackerly for helpful discussion on the early draft. The study was made possible by funding to M. W. and Ian Wright from the Australian Research Council and from Macquarie University. The NSW Department of Environment and Climate Change kindly gave permission to work at field sites.

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