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Wood biomechanics and anatomy of PACHYCEREUS PRINGLEI¹

² Department of Plant Biology, Cornell University, Ithaca, New York 14853-5908 USA; and ³ Instituto de Ecologia UNAM, Apartado Postal 1354, Hermosillo, Sonora CP83000, Mexico

Received for publication April 20, 1999. Accepted for publication July 27, 1999.

ABSTRACT

We report the longitudinal, biomechanical, and anatomical trends observed for tissue samples drawn from the parallel aligned, prismatic woody vascular bundles running the length of a Pachycereus pringlei plant measuring 5.22 m in height. The main vertical stem of this plant was cut into five segments (labeled A through E in the acropetal direction) measuring ~1.02 m in length. Four of the 14 vascular bundles in each segment were surgically removed to obtain 20 vascular bundle segments that were tested in bending to determine their stiffness measured in the radial E_R and tangential E_T direction. We also determined the lignin content of representative samples of wood.

A nonlinear trend in stiffness was observed: E_R and E_T were highest in segments B or C (1.67 GN/m and 1.09 GN/m, respectively), lower in segment A (E_R = 1.18 GN/m and E_T = 0.35 GN/m), and lowest in segment E (E_R = 0.03 GN/m and E_T = 0.20 GN/m). Similar longitudinal trends were seen for axial tissue volume fraction and fiber wall thickness, which achieved their highest values in segment B (69.8% and 6.59 µm, respectively). Wood stiffness also correlated significantly with cell wall lignin content: with respect to segment B (which had the highest lignin content, and was thus used as the standard reference for percent lignin content), lignin content, was 15, 60, 85, and 43% in segments E, D, C, and A, respectively. Fiber cell length, which increased toward the base of the stem and toward the vascular cambium in the most proximal vascular bundle segment, did not correlate with E_R or E_T.

Basic engineering principles were used to calculate stem stresses resulting from self-loading and any wind-induced bending moment (produced by drag forces). Calculations indicated that the less stiff wood produced in segment A eliminates a rapid and potentially dangerous increase in stresses that would otherwise occur in segments B or C. The less stiff wood in segment A also reduces the probability of shear failure at the cellular interface between the wood and surrounding tissues in this portion of the stem.

We conclude that P. pringlei wood stiffness is dependent on the volume fraction and lignification of axial tissues, less so on fiber wall thickness, and that wood development in this species is adaptively responsive to self-loading and differentially applied external mechanical forces

Key Words: biomechanics • Cactaceae • lignin • plant stems • Young's modulus • vascular tissues • wind drag • wood

Based on an examination of two plants, the stiffness of wood samples drawn from the vascular bundles running the length of Pachycereus pringlei (Cactaceae) stems is reported to vary nonlinearly, such that wood achieves its maximum stiffness near but not at the stem base of this species (Niklas, Molina-Freaner, and Tinoco-Ojanguren, 1999 ). Although this trend is somewhat counterintuitive, because bending stresses achieve their maximum intensities at the base of any vertical structure (Wainwright et al., 1976 ; Niklas, 1992 ), the amount of wood produced in P. pringlei stems increases basipetally such that the flexural rigidity (i.e., the ability to resist bending forces) increases exponentially toward the base of stems due to an increase in the axial second moment of area, which increases as the third or fourth power of transection size. Nonetheless, no mechanical explanation was offered for the adaptive (if any) role of less stiff wood near the base of P. pringlei stems, and, despite detailed anatomical reviews of the Cactaceae (Gibson, 1978 ; Gibson and Nobel, 1986 ), no anatomical information that could account for the nonlinear trend in wood stiffness was available. Variation in a number of anatomical features is known to influence (or at least correlate with) plant tissue stiffness, which is generally assumed to increase with the volume fraction of cell wall materials, cell wall lignification, and symplast turgor pressure, and assumed to decrease with fiber cell length and the volume fraction of air-filled spaces (Record, 1934 ; Falk, Hertz, and Virgin, 1958 ; Seibt, 1964 ; Carlquist, 1975 ; Wainwright et al., 1976 ; Niklas, 1992 ). However, in the absence of detailed study, the specific anatomical feature(s) possibly accounting for the trend in P. pringlei wood stiffness remain(s) problematic.

In this paper, we re-examine the longitudinal variation in P. pringlei wood samples drawn from another representative plant in the context of a detailed anatomical and biomechanical investigation. Our objective was to determine whether the previously reported trend in wood stiffness could be reproduced, and, if so, to determine which among the contending anatomical features of the wood could account for this trend. The biomechanical protocol previously used to investigate the longitudinal variation in P. pringlei wood was repeated using the main vertical stem of a plant comparable in height and diameter to those of the two previously examined plants. The stem of the newly examined specimen was dissected as were the previous two stems to remove representative and widely spaced woody vascular bundles that were then individually tested in bending to determine their bulk tissue stiffness (Young's modulus E) measured in the radial and tangential directions with respect to the grain of the wood. Smaller but anatomically representative tissue samples were removed from some of the tested bundle segments and anatomically and biomechanically examined to determine which among the many tissue properties were correlated with wood stiffness.

Another objective was to determine whether self-loading and external environmental factors may influence the properties of P. pringlei wood along the axis of the stem by indirectly affecting the development of the derivatives of the vascular cambium. Any columnar stem exerts compressive stresses on its tissues and is subject to chronic mechanical perturbation, which is known to alter stem and leaf morphology and tissue stiffness (see Telewski, 1995 , and references therein). It is possible, therefore, that the development of P. pringlei stem wood is influenced by the magnitudes of the stresses generated by the increasing weight of the stem and by periodic or aperiodic mechanical disturbance, both of which have the potential to alter the anatomy and thus the mechanical properties of wood. Since the vascular cambium is located away from the centroid axis of the stem where bending stresses reach high (but not their highest) levels and since the magnitude of these stresses measured at the same location with respect to the center of a vertical stem generally increases toward the base of a columnar support member, we speculated that self-loading and differential wind-induced bending stresses may serve as developmental cues for a longitudinal variation in wood stiffness, especially since stem growth in height is determinate for this species. This hypothesis, which was not tested directly for technological reasons, was examined indirectly by calculating the stresses experienced by the intact P. pringlei stem resulting from its weight and wind acting normal to the stem surface.

The data and calculations we present are argued to provide strong circumstantial evidence that P. pringlei wood stiffness is significantly and positively correlated with the volume fraction and the extent of lignification of axial tissues, less so with fiber wall thickness, and not at all with fiber cell length, which varies across tissue samples in the conventional manner for woody species. Our calculations likewise provide good evidence that self-loading and wind-induced stem flexure influence the development of wood such that the less stiff and more extensible wood prevents abrupt increases in axial compressive stresses and reduces the probability of shearing failure at the interface between any two tissues differing in their material properties (i.e., wood development in this species is adaptively responsive to self-loading and differentially applied external mechanical forces).

MATERIALS AND METHODS

Study site and plant selection
The field site was on a west-facing bajada of the Sierra Seri located at Rancho El Sacrificio (29E 05.82'N, 112E 08.00'W), which is in the coast of the state of Sonora, Mexico, in an area that belongs to the Central Gulf Coast vegetational subdivision of the Sonoran Desert (Shreve, 1964 ; Felger and Moser, 1985 ). The plant selected for study measured 5.22 m in height and ~0.21 m in basal stem diameter, and differed in no noticeable way from conspecifics of similar size. It was selected for study because of its healthy appearance and size, which was intermediate between two previously examined specimens (measuring 3.67 m and 5.89 m in height), for which we have biomechanical data (see Niklas, Molina-Freaner, and Tinoco-Ojanguren, 1999 ).

Dissection protocol
The main stem of this plant was cut into five stem segments of nearly equivalent length (~1.02 m). These segments were labeled A–E in an acropetal sequence from the base to the top of the stem. The outlines of the transverse surface of each segment and of each of the 14 vascular bundles running the length of entire segment and of each of the 14 vascular bundles running the length of entire stem were drawn to scale for future reference. The cut ends of each segment were also labeled to record their proximal-distal orientation, and individual vascular bundles were assigned consecutive numbers (1–14), which were consistent among the five stem segments. Each stem segment was then dissected to remove its vascular bundles for mechanical testing. During this process, the smaller lateral strands joining the larger neighboring vascular bundles were purposefully broken and removed to obtain prismatic beams that were, on average, 1.02 m long.

The five prismatic segments of each of four vascular bundles (numbers 2, 5, 9, and 13) were tested in bending (N = 20 vascular bundle segments). These four vascular bundles were selected for detailed study because they were located at the corners of an imaginary square drawn on the transverse surface of each of the five stem segments. Prior research indicated that the cross-section geometry and size of vascular bundles can vary as a function of location in tilted or curved stems. Even though the stem studied here appeared to be perfectly vertical, this protocol was used to avoid as best as possible any bias in tissue stiffness resulting from wood developing under the influence of tensile or compressive stresses.

Biomechanical protocol
Bending tests were used to determine the vascular bundle tissue stiffness (Young's modulus E) measured in the radial and tangential directions (E_R and E_T, respectively). The flexural rigidity EI of each tissue sample was also determined. Young's modulus E is a measure of the ability of a material to resist bending; it is a size-independent parameter. Flexural rigidity EI is a measure of the ability of a structure to resist bending; it is a size- and shape-dependent parameter because the second moment of area I is a measure of the contribution made by the transverse geometry and size of the material used to fabricate a structure to the ability of the structure to resist bending. The determination of E and I is necessary therefore because the material properties and transverse shape and size of vascular bundles are not uniform throughout the stems of P. pringlei. Pristmatic segments from each of the four vascular bundles were placed between two vertical supports and then loaded by placing bags of sand varying in weight attached at the midlength of each segment. A horizontally oriented needle was sighted against a metric ruler to measure the midlength vertical deflection resulting from the load. Young's modulus was computed from the formula E = PL³/48I, where P is a mass-force of the load and L is the free length of the vascular bundle segment. Second moments of area were computed on the basis of morphometric measurements of transections taken at the bottom, middle, and upper thirds of each sample. Different formulas for I were used depending on the transverse geometry of the tissue samples and the orientation of the sample's cross section with respect to the plane of bending (see Fig. 3). For further details, see Niklas, Molina-Freaner, and Tinoco-Ojanguren (1999) .

View larger version (19K): [in this window] [in a new window]   Fig. 1. Mean ± SE of wood stiffness (Young's modulus E) measured in the radial and tangential directions (ER and ET, respectively) plotted as functions of the location of five segments (segments A–E) of four vascular bundles with respect to the top of the Pachycereus pringlei stem

View larger version (130K): [in this window] [in a new window]   Fig. 2. Transverse sections of wood showing the alternation of ray and axial tissues. (A) Sample from segment A. Rays (lighter) and axial tissues (darker with light vessel lumens) fan outward in the section. Number of alternating panels increases outward with the formation of new rays from within the axial system. Bar = 10 mm. (B) Sample from segment E at the same magnification (see bar in A) shows difference in size and overall morphology of the bundle as seen in transverse section at the two locations. At this level of sampling no new rays have originated and divergence in the outward direction is limited. (C) Vessel elements (V) in the axial tissue (A) are embedded in paratracheal parenchyma and a matrix of thick-walled libriform fibers. Rays (R) are composed of relatively thin-walled parenchyma cells. Bar = 100 µm

View larger version (25K): [in this window] [in a new window]   Fig. 3. Wood stiffness (Young's modulus E) measured in the tangential direction (ET) plotted as a function of wood stiffness measured in the radial direction (ER) for 20 segments isolated from four vascular bundles of a Pachycereus pringlei stem. Solid line and formula are for ordinary least squares regression analysis

Three vascular bundles (2, 5, 13) of the four bundles tested biomechanically were evaluated for features of the axial and radial systems. In bundle 5, coordinated sampling furnished information on volume fraction of axial vs. ray systems, volume fraction of fibers, fiber wall thickness, and fiber and vessel element cell length. Bundles 2 and 13 were used as replicates for determining the volume fraction of axial vs. ray systems. In the context of the vascular cylinder of the plant, bundles 2 and 5 were separated by two intervening bundles, as were bundles 2 and 13.

Bundle 5 furnished transverse sections (20–80 µm thick), taken on a sliding microtome, from samples at the midregion of each segment, A–E. One set of sections were stained with phloroglucinol-HCl to develop pink to red coloration in lignified cell walls, and photographed with a digital camera and transmitted light to produce prints at ~10x magnification. The photographic print of each section (or the montage in the case of a larger section) was photocopied, the photocopy was divided into ray system vs. axial system using scissors, and the relative proportions of the two systems by weight was taken as an indication of their volume fractions.

Using an arbitrary band width that was fully occupied by the secondary xylem of segment E, photocopies of segments A–D were divided into strips parallel to the locus of the vascular cambium, so that volume fractions of axial and ray systems could be estimated as a function of distance from the cambium. The layer closest to the cambium was designated as layer 1.

Other sets of transverse sections were stained with 1% toluidine blue in water, dehydrated, and mounted in synthetic resin. Digital photographs (at 230x) taken through the microscope were assembled as montages to record images of the axial system in each segment in transverse section along the radius. Photocopies of these assemblies were used to separate pore space and associated parenchyma cells from the groundmass of fibers, so that relative abundance of fibers could be estimated at the midpoints of segments A–E along the axis, and along the radius of segment A, as was done for the relative abundance of the axial system itself.

Fiber wall thickness was measured on digital photographs (740x) taken with the microscope from transverse sections to evaluate layer 1 in segments A–E. A minimum of 250 measurements was taken from the sample for each segment. Wall thickness was measured from the middle lamella to the lumen at approximately two locations for each cell that was evaluated.

Finally, for bundle 5, samples of wood for macerations were taken from locations near the midline of the bundle for evaluation of cell lengths. After treatment with macerating fluid, the 2-cm long samples were stained in bulk with 1% basic fuchsin in 95% ethanol. As a basis for replication of the measurements of the lengths of fibers and vessel elements, three fragments of wood were selected from separate locations in a sample and prepared as three separate slides by dehydration, dissection, and mounting in synthetic medium.

Cell lengths were measured using a 10x lens of the compound microscope, which just accommodated the longest fibers in the field of view, and a drawing tube positioned above a digitizing tablet under the control of a microcomputer. Typically 80–95 cells were measured on each slide. Fibers were measured from tip to tip in layer 1 of segments A–E, and at six equally spaced locations along the centerline of segment A, across layers 1–13. Vessel element lengths were measured in layer 1 of segments B and E. Measurements were from the center of the transverse to oblique perforation plate at one end to the center of the perforation plate at the opposite end of the cell, to exclude as much as possible the effect of apical intrusive growth on the length of vessel elements.

For bundles 2 and 13, in each of the five 8-cm samples from the midregion of segments A–E, the two transverse ends were ground smooth with Carborundum papers and photographed in reflected light with a 35-mm camera. Photographs at ~10x were photocopied, and the relative proportions of axial vs. ray system were estimated as for bundle 5 (above), but using both ends of a sample to estimate volume fractions, as a function of distance along the axis. Bundle 13 furnished small beams that were used in additional bending experiments. The beams were selected to represent six locations spanning the radius of segment A, with three replicates from layer 1. Each end of each beam was photographed using a stereomicroscope, and photocopies of prints at 25x were used to determine volume fraction of axial vs. ray systems, as above.

Lignin analysis protocol
The lignin content of wood samples was analyzed using the protocol of Müsel et al. (1997) modified after Bruce and West (1989) . Wood samples weighing 8 g were removed from the 8 milled prismatic beams taken from segment A and from the most recently formed growth layers in segments B–E (all samples were from vascular strand 13). Each sample was frozen in liquid nitrogen for ~60 s, pulverized, and subsequently thawed in 2.0 mL homogenization buffer (50 mmol/litre Tris-HCL, 10 g/L Triton X-100, 1 mol/L NaCl; pH 8.3). The suspension was vortexed and then centrifuged (at 2000 g for 10 min). The recovered cell-wall pellet was washed twice with 4 mL of the homogenization buffer, 80% acetone, and pure acetone, and subsequently lyophilized. Each pellet was then treated with 0.4 mL thioglycolic acid + 2 mL 2 mol/L HCl for 4 h at 95°C, after which it was centrifuged (at 15 000 g for 10 min) and washed three times with distilled water. The lignothioglycolic acid (LTGA) from each pellet was extracted with 2 mL 0.5 mol/L NaOH (agitating for 16 h at 20°C); the supernatants (collected after a first and second centrifugation during which the pellets were re-extracted with 0.8 mL NaOH) were combined and acidified with 0.4 mL concentrated HCl. LTGA was precipitated for 3.5 h at 4°C, recovered by centrifugation (at 15 000 g for 20 min), and dissolved in 1 mL 0.5 mol/L NaOH. Aborbance was measured against a NaOH blank in the range of 220–320 nm. The amount of lignin was calculated from the aborbance at 280 nm using a specific absorbance coefficient of 6.0 L·g^-1·cm^-1 using a conversion to relative units based on the relationship: absorbance of 100 µg lignin in 1 mL = 0.60 A₂₈₀ in a 1-cm cell. Because the 6.0 L·g^-1·cm^-1 specific absorbance coefficient is an approximate conversion (the absorbance of LTGA from different sources can vary considerably; see Doster and Bostock, 1988 ), the specimen with the highest lignin content among the 12 samples (i.e., the wood removed from segment B) was used as an internal standard to express the percent lignin content of the other wood samples.

Stress and bending moment computations
We calculated the stresses produced by the weight of stem tissues (self-loading, compressive stresses) based on the formula _i = [ (·g·A_i·_i)]/{A_i + [(E_s/E_c - 1)A_s]}, where is the bulk stem tissue density, g ~ 9.8 kg·m^-1·s^-2, _i is stem length measured from the top of the stem (where _{i = 0}), A_i is stem cross-sectional area at i, E_s is vascular strand stiffness at i, E_c is bulk stiffness of the nonwoody tissues at i, and A_s is the combined cross-sectional area of all vascular strands at i (see Timoshenko and Gere, 1961 ; Lin and Burns, 1981 ; Niklas, 1992 ). The term (·g·A_i·_i) computes the "running sum" of stem weight above any cross section i; the term {A_i + [(E_s/E_c - 1)A_s]}, or "the transformed-section," is the stem cross-sectional area adjusted for the relative stiffness and cross sectional area of the vascular strands with respect to those of their surrounding tissues (see Appendix). A numerical value of E_c = 0.115 GN/m² was used (i.e., the average wood stiffness measured for segment E); however, any value for E_c obtains the same relative stress magnitudes provided that E_c is more or less constant along the stem.

We modeled the effects of hypothetical longitudinal variations in vascular strand stiffness on stem self-loading stresses by stipulating that E_s increases linearly from the top to the bottom of the stem based either on the measured stiffness of the strands segments A, D, and E (model 1) using the linear regression formula E_s = 0.86 - 0.15 d, where d is distance from ground level, or the wood stiffness measured for segments B, C, D, and E to predict the stiffness of the wood in segment A (model 2) using the linear regression formula E_s = 0.2.02 - 0.41 d. Model 1 predicts less stiff wood for segments B and C; model 2 predicts higher wood stiffness in segment A than that which actually occurs. In tandem, the two models define the lower and upper limits for the longitudinal wood stiffness gradient that was actually observed.

In order to evaluate the consequences of wind-induced stem flexure, we measured stem diameter d_i at different distances x_i from the top of the stem (x = 0), and computed the surface area each stem element i (any imaginary section of the stem with finite length) projected toward the on-coming wind as the product of its diameter d_i and effective length x_i - x_j (where x_j denotes the distance from the tip of the stem to the top of the element i). The drag force D_f acting at the base of element i resulting from a wind speed u acting normal to the stem surface was then computed from the formula D_f = 0.5u²_i [d_i·(x_i - x_j)]C_D, where is the density of air (taken as 1.205 kg/m³) and C_D is the drag coefficient (taken as 1.0). A logarithmic wind speed profile was used to specify values of u_i at different heights above ground such that the maximum wind speed occurred at the top of the stem u_top (arbitrarily set equal to 10 m/s) and progressively decreased to zero at ground level, i.e., the wind speed profile was calculated on the basis of the formula, u_i = [u_top/ln(h/z_o)] ln[(h - x_i)/z_o], where h is the height of the cactus stem (~5.2 m) and z_o is the roughness height (set equal to 0.75 m based on the surrounding vegetation). The magnitude of the drag force acting locally on any stem element i thus decreases toward the base of the stem but the bending moment and stresses it creates increase basipetally toward ground level. The bending moment M_i resulting from the drag force for any element i was computed on the basis of the formula

Statistics
ANOVA and Model Type I and II regression analyses were used to determine whether E or EI varied significantly and predictably as a function of distance from the top of the stem and to determine the extent to which biomechanical and anatomical parameters were correlated. Given the objectives of this study, we emphasized statistical comparisons between wood stiffness measures in the radial and tangential directions and the volume fraction of axial tissues, fiber wall thickness, and fiber cell length. All analyses were performed using the software package JMP©(SAS Institute, Inc.) on a Power Macintosh 8100/80.

Results

General biomechanical phenomenology
The biomechanical properties observed during our study of the third P. pringlei stem do not differ in any substantive way from those previously reported for two other stems examined from this species (Niklas, Molina-Freaner, and Tinoco-Ojanguren, 1999 ).

Tissue stiffness measured in either the radial or tangential direction increased from the top to the base of each bundle but decreased near the base of the stem in either segment A or B (Fig. 1), where large quantities of secondary xylem had accumulated. Wood stiffness measured in the radial direction was greatest in segment B (mean ± SE = 1.67 ± 0.35 GN/m²) the midpoint of which was located ~1.5 m from ground level; wood stiffness measured in the tangential direction was greatest in segment C (mean ± SE = 1.09 ± 0.16 GN/m²) the midpoint of which was located ~2.5 m from ground level. The disparity between the locations where the stiffest wood measured in the radial and tangential direction was found (segment B and C, respectively) may be a consequence of experimental error resulting from difficulties in orienting the larger vascular bundle segments with respect to the direction of the bending force. Anatomical observations indicated that the axial and ray tissue systems of the older parts of vascular bundles "fan" outward toward the vascular cambium when viewed in the transverse plane (Fig. 2); this anatomy is more reliably oriented (and thus more reliably tested in bending to determine its stiffness) with respect to a radial rather than a tangential acting bending force.

Despite the apparent discrepancy between where radial and tangential wood stiffness reached their maximum values with respect to location from the top of the stem, a statistically significant and positive correlation was found for E_R and E_T: r² = 0.55, P > |t| = 0.002 (Fig. 3). Reduced major axis (Model Type II) regression analysis showed that tangential wood stiffness increases at a slower rate with respect to rate at which radial wood stiffness increases (i.e., _RMA = E_T/E_R = 0.49). On average, the stiffness of the wood measured in the radial and tangential direction was 0.94 ± 0.17 GN/m² and 0.56 ± 0.08 GN/m², respectively (N = 20). The wood was thus mechanically anisotropic in its behavior (i.e., its resistance to a bending force depended markedly on the direction of an externally applied bending force; see Niklas, Molina-Freaner, and Tinoco-Ojanguren, 1999 ).

The flexural rigidity EI of the vascular bundles increased exponentially toward the base of the stem and was significantly larger when measured in the radial than in the tangential direction (Fig. 4). The exponential increase in flexural rigidity was attributed to the accumulation of wood in older portions of the vascular bundles and the attending increase in the axial second moment of area I. The higher values for EI measured in the radial direction as opposed to the tangential direction was attributed to the, on average, greater stiffness of the wood measured in the radial direction, and to the fact that the cross-sectional shapes of the vascular bundles tended to be more amplified in the radial than in the tangential direction as wood is added over the course of growth and development (Fig. 2A, B). Calculations (not shown) revealed that the mechanical anisotropy of the wood (i.e., E_R > E_T) was not the over-riding factor in determining differences in the flexural rigidity measured in the radial and tangential directions (i.e., changes in cross-sectional shape and size attending the accumulation of wood in the vascular bundles had the largest influence on differences in EI).

View larger version (25K): [in this window] [in a new window]   Fig. 4. Mean ± SE of flexural stiffness (EI) measured in the radial and tangential directions (EIR and EIT, respectively) plotted as functions of the location of five segments (segments A–E) of four vascular bundles with respect to the top of the Pachycereus pringlei stem. Shaded outlines, which are drawn to scale, represent transverse geometries of representative segments; orientation of these sections correspond to the direction of the applied bending force used to measure E, which is here arbitrarily defined in the vertical direction with respect to each graph

Layering was best expressed in samples from the distal segment of the axis. It was confirmed that the spacing and degree of differentiation of layers were duplicated among bundles in the distal segment, and that the layers expressed therein were represented by corresponding layers that were somewhat more weakly expressed in the more proximal segments of the axis.

The volume fraction of axial tissues (expressed as a percentage of the total wood volume) varied along the radial transect through the various wood growth layers within any one vascular bundle segment. The highest percent volume fraction determined any where in one segment occurred in the youngest wood nearest the vascular cambium. In segments C, D, and E, the lowest percent volume fraction of axial tissues occurred in the oldest wood farthest away from the vascular cambium, but, in segments A and B, the oldest wood had a percent volume fraction of axial tissues that was slightly higher than wood nearer to the vascular cambium (Fig. 5). The percent volume fraction of axial tissues determined along much of the radial transect through the wood in segment A was numerically equivalent to the percent volume fraction determined for axial tissues in segment E.

View larger version (32K): [in this window] [in a new window]   Fig. 5. Relationship between the percent volume fraction of axial tissues in wood and relative distance d of wood sample from the vascular cambium for five segments (A–E) drawn from a vascular bundle of a Pachycereus pringlei stem. The cartoon shown at lower right of figure denotes the transverse geometry of segment A and shows the relationship between d and the vascular cambium at the top of the cartoon

View larger version (21K): [in this window] [in a new window]   Fig. 6. Mean ± SE of percent volume fraction of axial tissues (A) and fiber wall thickness t (B) plotted as a function of the location of five segments (A–E) drawn from four vascular bundles of a Pachycereus pringlei stem. For further details, see text

Model Type I regression analyses indicated that the mean values for wood stiffness (measured in the radial and tangential directions) measured for large segments of the vascular bundles significantly correlated in a positive and linear manner with the mean percent volume fraction of axial tissues (despite the small sample size; N = 10), but the wood stiffness did not correlate with the mean values of fiber wall thickness (Fig. 7A and B, respectively). Based on analyses of residuals and R² values, multiple regression analyses confirmed that mean fiber wall thickness detracted from rather than augmented the ability to predict wood stiffness based on the joint operation of mean percent axial tissue volume and mean fiber wall thickness. We note, however, that the failure to find a statistically significant correlation between wood stiffness and fiber wall thickness or a correlation between wood stiffness and the joint effects of these two anatomical parameters was principally due to the higher than expected value observed for fiber wall thickness in segment E (see Fig. 6B). When the data point representing the mean fiber wall thickness in segment E was removed from our regression analyses, the correlation between wood stiffness and either fiber wall thickness or fiber wall thickness x percent axial tissue volume was found to be statistically significant at the 5% level.

View larger version (22K): [in this window] [in a new window]   Fig. 7. Mean wood stiffness measured in the radial and tangential directions (ER and ET, respectively) plotted against mean percent volume fraction of axial tissues (A) and mean fiber wall thickness (B) determined for corresponding tissue samples. Solid lines and formulas are for ordinary least squares regression analyses

View larger version (27K): [in this window] [in a new window]   Fig. 8. Stiffness (Young's modulus E) measured in the radial and tangential directions (ER and ET, respectively) for small, milled prismatic samples of wood isolated from segment A (the most proximal segment) of a Pachycereus pringlei vascular bundle plotted as a function of percent volume fraction of axial tissues. Solid lines denote ordinary least squares regression curves for these data

View larger version (21K): [in this window] [in a new window]   Fig. 9. Relationships among percent volume fraction of axial tissues, wood stiffness (Young's modulus), and wood lignin content for tissue samples from eight milled prismatic beams of wood removed from segment A and for the most recently formed wood in segments B–E. (A) Percent volume fraction of axial tissues plotted as a function of lignin content expressed as a percentage of the absolute lignin content of the youngest wood produced in segment A (percent lignin content). (B) Wood stiffness measured in the radial and tangential direction plotted against percent lignin content. Solid lines are ordinary least squares regression curves. (C) Percent volume fraction of axial tissues and percent lignin content of wood samples drawn from the most recently formed growth layers in segments A–E plotted as a function of segment location along stem length. See text for further details

Self-loading and wind-induced bending stresses
The magnitude of the stresses resulting from the self-loading computed on the basis of the actual stiffness of the vascular strands (see Fig. 1) and their combined cross-sectional areas increased in a basipetal direction and, neglecting the solid woody base of the stem, reached maximum intensity in segment A (Fig. 10A). In contrast, two models, each of which stipulated a basipetal but linear increase in wood stiffness such that the stiffness of the wood in segments B and C was underestimated (model 1) or the stiffness of the wood in segment A was overestimated (model 2), predicted that the self-loading stresses would reach their maximum in either segment B or segment C (models 1 and 2, respectively) (Fig. 10A). A statistically strong, exponential relationship was found for the flexural rigidity of the vascular strands EI and the self-loading stresses computed on the basis of the empirically determined values for wood EI (Fig. 10B), whereas the correlations between EI and the stresses predicted by models 1 or 2 were significantly less strong (r² 0.63). The less stiff wood produced in segment A (or, conversely, the more stiff wood produced in segments B and C) thus obviated a steep "stress-rise" anywhere along the length of the stem and the resistance afforded by the vascular strands to bending under the stem's self-load was proportional to the stresses resulting from self-loading.

View larger version (26K): [in this window] [in a new window]   Fig. 10. Self-loading stresses and flexural rigidity of vascular strands. (A) Self-loading stresses in stem segments A–E plotted as a function of distance from ground level. Actual stresses (bold curve) for segments A–E computed on the basis of the empirically determined longitudinal variations in the stiffness of the vascular strands using the formula shown at upper right. The stresses resulting from models 1 and 2 are based on the assumption that wood stiffness increases linearly toward the base of the stem. Model 1 is based on a linear regression formula using the stiffness of wood in segments A, D, and E; model 2 is based on a linear regression formula using the stiffness of wood in segments B–E. Both models predict that self-loading stresses will reach their maximum intensity in stem segments other than segment A. (B) Flexural rigidity of the vascular strands measured in the radial and the tangential directions plotted as a function of the actual self-loading stresses (data taken from Fig. 10A; see bold curve). Solid lines are ordinary least squares regression curves. For further details, see text

View larger version (23K): [in this window] [in a new window]   Fig. 11. Relationships among bending moment M and rate of change of the bending moment M with respect to distance from ground level d and between mean wood stiffness measured in the radial direction ER and the bending moment and the rate of change of the bending moment computed for the Pachycereus pringlei stem from which wood samples were examined. (A) Bending moment and rate of change of the bending moment (computed on the basis of morphometric measurements of the diameter and effective length of stem elements and a curvilinearly decreasing wind profile) plotted as a function of distance from ground level. The distance of the midpoints of vascular bundle segments A–E are indicated for reference. Solid curved line connects the points at which the bending moment was actually computed. (B) Flexural rigidity EI measured in the radial and tangential directions at the midpoints of segments A and B plotted as a function of the bending moment (see Fig. 11A). (C) Wood stiffness measured in the radial and tangential directions (ER and ET, respectively) plotted as a function of the rate of change of the bending moment computed at the midpoints of vascular bundle segments A–E. Solid line denotes linear regression for mean wood stiffness; thinner lines are regression curves for ER and ET

Wood stiffness and anatomy
The relationship between the anatomical and mechanical properties of plant tissues has been the subject of considerable attention because, in addition to its physiological function(s), every tissue type provides some measure of mechanical support against the effects of gravity or wind movement (Schwendener, 1874 ; Carlquist, 1961, 1969, 1975 ; Esau, 1967 ; Wainwright et al., 1976 ; Niklas, 1992 ; Mauseth, 1988 ; Speck, 1994 ; Spatz et al., 1995 ). Prior studies show that a number of anatomical features influence the mechanical properties of any particular tissue, and that, all others things being equal, tissue stiffness is positively correlated with the apoplastic volume fraction and degree of cell wall lignification (Forsaith, 1929 ; Record, 1934 ; Carlquist, 1975 ; Seibt, 1964 ; Niklas, 1992 ).

The present study provides additional support for the hypothesis that the bulk stiffness of wood increases in proportion with the apoplastic volume fraction and the degree of lignification since a strong positive correlation exists between wood stiffness and the percent volume fraction of axial tissues and the extent to which cell walls are lignified in P. pringlei. Even though no strong correlation exists between wood stiffness and fiber wall thickness, we draw attention to three facts that suggest that the correlation should be stronger than is shown by our results. First, the stiffest wood in this species contains fibers that, on average, have the thickest cell walls as well as the highest percent volume fraction of axial tissues. Second, the correlation between tissue stiffness and the apoplastic volume fraction becomes statistically significant when the data from the youngest portion of the vascular bundles (i.e., segment E) are removed from consideration. And, third, the stiffness measured for tissue samples with small transverse areas is not representative of the stiffness of larger tissue samples because samples with small transverse areas have disproportionately more damaged cell walls, which reduces their effective stiffness compared to their larger counterparts. Similarly, tissue samples with small cross-sectional areas contain few cells per unit transverse surface area. This is important because the stiffness of any tissue sample increases, to a limit, as the number of adjoining transverse and radial cell walls increases.

When these three factors are considered collectively, we believe they point to the conclusion that fiber wall thickness is more relevant to the stiffness of P. pringlei wood than is indicated by our statistical analyses. We note further that the walls of the ray tissues are relatively thin throughout the length of the vascular bundles. In summary, we believe that the data affirm that the bulk stiffness of wood samples drawn from different locations along the length of the vascular bundles is significantly correlated with and an emergent mechanical property of cell wall lignification and the overall apoplastic volume fraction of the wood, which increases as a function of both the volume fraction of the axial tissues and fiber wall thickness.

This conclusion is further supported by the observation that wood stiffness measured in the radial and tangential directions are positively correlated with the volume fraction of axial tissues. If the hypothesis that stiffness is a mechanical correlate of the apoplastic volume fraction is correct, then we must expect stiffness measured in either of the orthogonal directions to be correlated with this anatomical feature. Nonetheless, our data show that wood stiffness measured in the tangential plane of anatomical reference is less perfectly correlated with the volume fraction of axial tissues than is wood stiffness measured in the radial direction. One possible explanation is that, in younger tissue samples, the ray and axial tissues are nearly parallel in their alignment when viewed in the transverse plane of section, whereas, in progressively older portions of the same vascular bundle, these two wood components increasingly diverge from a parallel alignment and assume an outwardly "flared" configuration as a result of the tangential (circumferential) expansion of the vascular cambium. In terms of experimental procedure, this "flared" anatomy makes it increasingly difficult to align externally applied bending forces in the tangential plane of sections through wood samples during bending experiments, and thus has the potential to produce experimental measurements of wood stiffness that represent a hybrid between the stiffness measured in the radial and tangential directions. In contrast, the transverse shape of even the oldest portion of a vascular bundle makes it easier to align bending forces in a near or pure radial direction, thereby making the determination of the radial stiffness of wood samples less ambiguous. Under any circumstances, stiffness measured in the radial and tangential directions correlates well with the volume fraction of axial tissues in wood samples, regardless of where they are drawn from along the length of vascular bundles, which lends credence to the hypothesis that the apoplastic volume fraction and the degree to which it is lignified have an overriding influence on wood stiffness.

Stem biomechanics
We conclude that the stiffness of P. pringlei vascular strands correlates significantly with the apoplastic volume fraction and lignin content of the wood and that these features vary along the length of individual growth layers and from one wood growth layer to another in individual vascular strands. Since they evince a high degree of repeatable spatial (and, presumably, temporal) ordering and have now been reported for three representative stems of this species, these variations in wood stiffness cannot be reasonably ascribed to tissue fatigue brought about by chronic stem flexure or disease, but rather lend support to the plausibility that regulatory factors affecting the vascular cambium and its derivatives are sensitive and responsive to the force gradients established by stem self-loading and externally applied loads.

In the absence of direct experimental manipulation of stem development, this hypothesis can be inductively explored, first, by establishing the nature of the force and stress gradients existing in the columnar stems of P. pringlei based on engineering first principles, and, second, by determining whether the variations in wood anatomy and stiffness observed in stems correlate with these gradients in a manner that suggests developmental modifications occur and are functionally adaptive. The nature of the force and stress gradients experienced by P. pringlei stems follows directly from engineering first principles. Any vertical support member must support its own weight (self-loading) and the lateral loads exerted on it by drag forces (wind-loads) (Timoshenko and Gere, 1961 ; Wainwright et al., 1976 ; Vogel, 1981 ; Niklas, 1992 ). Both of these loading regimes are easily evaluated in the biological context of the comparatively simple morphology of P. pringlei stems. Because these stems are massive in girth relative to their height, they have a large axial second moment of area everywhere along their length. Calculations show that this "geometric contribution" to the ability to resist bending is more than sufficient to cope with the weight of the stem. However, this ability is augmented significantly by the longitudinal variations in the cross-sectional area and the stiffness of the vascular strands. The basipetal increase in the combined cross-sectional area of all the vascular strands and the nonlinear, complex variation in their stiffness produce a steady basipetal increase in axial (self-loading) stresses. In the absence of the observed pattern in wood stiffness, calculations show that self-loading stresses would reach maximum intensity near or just below the stem's midspan (i.e., in segments B or C; see Fig. 10A). Such a "stress-rise" could result in the compressive failure of thin-walled tissues, since the magnitudes of the stresses that would result in the absence of the less stiff wood in segment A exceed the compressive yield stress of parenchyma. Thus, in terms of self-loading, there is a clear mechanical benefit conferred by the production of less stiff wood in segment A.

The less stiff wood in segment A may also be beneficial in terms of wind-loading. A large wind-induced bending moment has the potential to uproot a massive stem in the absence of a strong anchoring root system. Based on the specific dimensions of the P. pringlei stem examined here, the location of the less stiff wood in segment A corresponds to where the magnitude of any wind-induced bending moment reaches near maximum intensity and where the rate of change of any wind-induced bending moment decreases significantly (see Fig. 11A).

These observations afford a plausible biomechanical explanation for the formation of less stiff wood in vascular strands (in the distal portions of segment A) just above the region in the stem where continuous growth layers of wood establish a solid core of wood (in the proximal portions of segment A). This explanation assumes that the basipetal increase in the cross-sectional area of the vascular stands contributes to the mechanical stability of a self-loaded stem. Under these circumstances, the presence of less stiff and more flexible wood at the location where the rate of change of bending moments is low (and where bending moments and stresses nearly reach their maximum intensity) permits a massive P. pringlei stem to elastically flex yet simultaneously preserves the interface of adjoining tissues differing in material properties to remain intact and thus avoid failure in shearing (Fig. 12). Although even substantial elastic stem flexure does not significantly reduce the wind-induced bending stresses or moments (e.g., 16° stem-tilt would reduce the bending stresses by <10% and the bending moment by <2%), any column will bend to some degree in the wind and thus experience bending shear stresses.

View larger version (38K): [in this window] [in a new window]   Fig. 12. Biomechanical model for a self- and wind-loaded P. pringlei stem (left and right longitudinal cutaways, respectively) in relation to the flexural rigidity EI and stiffness E measured at five locations (A–E) along the lengths of its vascular strands (graphs). In the absence of high lateral wind speeds, the stem can maintain its vertical growth posture and self-loading in part by the virtue of the exponential increase in the EI of vascular strands toward the base of stem. However, when subjected to lateral wind speeds incurring high drag forces, the vertical stem will elastically bend downwind and its tissues will experience compressive and tensile bending stresses (- and +, respectively), and shear stresses will develop at the interface between adjoining tissues differing in their bulk material properties (see insert). Shear stresses will reach their maximum intensities near the base of the stem above the region where vascular bundles become fused together due to the accumulation of secondary xylem because this portion of the stem acts as a mechanical pivot point. The low stiffness E and comparatively high extensibility 1/E of wood produced in the region of the pivot point (segment A) permits large shear strains and thus reduces the likelihood of the rupture of cells interfacing with the wood

The location of this joint just above the woody stem foundation is more or less ideal because it reduces the strains experienced by the stem foundation, which is attached to a mechanically ineffective root system. Our field observations indicate that the root systems of plants the size studied here are laterally extensive, yet shallow and weak when placed in tension or compression. As such, the root system of comparatively young plants may provide little in the way of mechanical support (except perhaps immediately near its junction with the stem) and would serve as a ground-level pivot point in the absence of a more distal and flexible "joint" along the length of the stem. Older, more massive plants may increasingly depend on their root systems for anchorage, such that the flexible joint may become less useful over time.

The mechanical stability of P. pringlei stems is fostered by their determinate growth in height and the ability to establish longitudinal and radial gradients in wood stiffness. Much like the stems of the saguaro cactus (Niklas and Buchmann, 1994 ), those of P. pringlei grow in height at a steadily decreasing rate and thus essentially stop growing in height after they achieve a certain size. In theory, this affords a developmental mechanism that can assure a suitable factor of safety against mechanical failure provided that mature stem size and anatomy are developmentally prefigured (Niklas, 1992, 1994 ; Niklas and Buchmann, 1994 ). Our data clearly indicate that the P. pringlei vascular cambium and the pattern of maturation in its derivatives can produce wood in a single growth layer that differs in stiffness along the length of the stem. The bulk stiffness of a vascular strand at any particular location along its length can also be adjusted by adding less or more stiff wood (see Fig. 5). Since the relative difference in the stiffness of wood added in each growth layer can be conserved as a stem increases in height, longitudinal gradients in P. pringlei wood stiffness can be established in the juvenile condition and maintained as a stem grows to reach its final height. Likewise, since stiffer wood can be added at each location along the length of a growth layer as a stem grows, the bulk stiffness of the vascular strands can be modified over time to mechanically accommodate increases in stem weight and height. Thus, P. pringlei stem development has the ability to prefigure longitudinal gradients in the material properties of its woody vascular stands as growth proceeds, yet preserves the capacity to adjust the absolute magnitudes of these properties as the stem increases in weight and height.

This phenomenology, which is described here for the first time, plays an important role in the optimization of a number of anatomical and morphological features, some of which are less conducive to mechanical stability than others. The stems of P. pringlei function well mechanically but clearly within the constraints imposed on them by their manifold functional obligations and their apparently specialized growth and development. Moreover, optimization should be viewed in a broader context. Our biomechanical analyses demonstrate that mechanical stability in terms of self-loading and wind-induced stem flexure is fostered by the production of a disproportionately large volume fraction of ray tissues and a reduction in the lignin content of secondary vascular tissues near the base of P. pringlei stems. However, because these advantages are a consequence of a variety of wood anatomical features that are developmentally correlated and that undoubtedly affect many biological functions, they cannot be judged to be a consequence of natural selection operating directly or exclusively on mechanical stability, although it is clear that selection acting on one aspect of wood anatomy will have consequences on other correlated anatomical features. In this regard, we note that among 77 surveyed P. pringlei plants, lateral branches generally emerge ~1 m from the base of the central stem, and that the number of branches increases as plants age. Therefore, the reduction in wood stiffness in this vicinity correlates with general plant morphology. Preliminary observations reveal that the widest rays accommodate vascular traces. The preponderance of wide rays in a sample reduces the value obtained for % axial tissue. Further investigations may reveal that the support of lateral branches is facilitated by a superabundance of large rays in the region of reduced vascular stiffness.

FOOTNOTES

¹ The authors thank Prof. James D. Mauseth (University of Texas) who, as an Associate Editor of the American Journal of Botany, supervised the reviewing process and served as Editor-in-Chief for this manuscript; the owners of El Sacrificio who provided access to their property; Ivan Romo for logistical support; Recardo Clark, Daniel Morales, Grethel Ramirez, and Martin Villegas for assistance in the field; and Prof. P. Schopfer (Institut für Biologie II der Universität, Freiburg) for sharing his expertise in lignin analyses. Field work was supported by funds from the operating budget of the Instituto de Ecologis UNAM to FMF. This research was also supported by Hatch Act Awards 185-403 (KJN) and 185-406 (DJP), and a von Humboldt Forschungspreis (KJN).

⁴ Author for correspondence (phone: 607 255 8727; FAX 607 255 5407; e-mail: kjnz{at}cornell.edu ).

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