American Journal of Botany 89(1): 12±21. 2002.

THE BIOMECHANICS OF PRINGLEI ROOT SYSTEMS1

KARL J. NIKLAS,2,4 FRANCISCO MOLINA-FREANER,3 CLARA TINOCO-OJANGUREN,3 AND DOMINICK J. PAOLILLO,JR.2

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

We report on the root system of the large columnar species Pachycereus pringlei to explore the hypothesis that increasing plant size decreases the ability to resist wind-throw but increases the capacity to absorb and store nutrients in roots (i.e., plant size limits the performance of these functions and may shift the performance of one function in favor of another as size increases). Based on 18 differing in size, the root system is characterized by a broad and deep bayonet-like root central to a shallow and extensive lateral system of root elements bearing sinker roots near the stem base. All root types have a living secondary cortex and contain wood with a large volume fraction of ray tissues that increases toward the stem base. Wood stiffness and tensile strength are correlated negatively with the ray tissue volume fraction and thus decrease toward the stem base in lateral and bayonet roots. Calculations show that the ability of the bayonet and proximal lateral root elements to resist wind-throw decreases with increasing plant size, whereas the nutrient absorption/storage capacity of the total root system increases with plant size (i.e., a size-dependent shift between these two root functions occurs).

Key words: biomechanics; Cactaceae; plant anatomy; roots; wind drag; wood.

Much of root biomechanics is phenomenologically expli- data and laboratory experiments were used to determine the cable in terms of the degree to which shoots transmit me- load capabilities (maximum bending and tensile stresses) of chanical forces to their roots (e.g., Pfeffer, 1893; Dittmer, root and stem tissues, and engineering theory was then used 1937; Stolzy and Barley, 1968; Nass and Zuber, 1971; Neeman to calculate the ability of root systems differing in size to cope and Spencer-Smith, 1975; Coutts, 1986; Anderson et al., 1989; with wind-throw over a range of ambient wind speeds (see Ennos and Fitter, 1992; Ennos, 1993, 2000; Gartner, 1994; Whitaker, 1970; Casada, Walton, and Swetnam, 1980; Niklas, Stokes, Fitter, and Coutts, 1995; Crook and Ennos, 1996; 1992; Niklas and Spatz, 2000). Size-dependent (allometric) Stokes and Mattheck, 1996; Stokes et al., 1996, 1997; Niklas, trends in wind-induced bending and counter-resisting moments 1999). The interplay between the effects of shoot morphology were evaluated to determine the minimum factor of safety and environmental conditions (and their effect on the trans- against wind-throw (see Appendix). mission of mechanical forces to the root system) are contin- gent on plant size as well as a number of ecological factors MATERIALS AND METHODS that may require a shift in emphasis among the various func- tional obligations of roots. Study site and plant selectionÐThe study site was on a west-facing bajada of the Sierra Seri located at Rancho El Sacri®cio (29.05Њ82Ј N, 112.08Њ00Ј Here we report on the size-dependent relationship between W) on the coast of the state of Sonora, MeÂxico, in an area belonging to the anchorage and nutrient absorption/storage for the root systems Central Gulf Coast vegetational subdivision of the Sonoran Desert (Shreve, of the columnar cactus species Pachycereus pringlei (see Nik- 1964; Felger and Moser, 1985). A healthy plant growing in an open site with las, Molina-Freaner, and Tinoco-Ojanguren, 1999; Niklas et a size and general appearance similar to previously studied plants was selected al., 2000). The root morphology of this species combines for intensive study (see Niklas, Molina-Freaner, and Tinoco-Ojanguren, 1999; plate, tap, and ®brous root system features (see Preston, 1900; Niklas et al., 2000). However, 17 plants differing in size were examined in Wilson, 1975; Coutts, 1983; Ennos, 2000). We speci®cally ex- the ®eld to determine root±stem allometric relationships. An additional 117 plore the hypothesis that the basal bayonet root of these root plants were measured to determine the allometry of shoot height with respect systems is the principal anchorage device, that the bulk of the to basal stem diameter. lateral root system provides for nutrient absorption and below- ground storage, and that a size-dependent shift in the perfor- Dissection protocolÐAll of the root anatomical information reported here mance of these two functions occurs. was derived from the study of the largest plant in our data set, which was This hypothesis could not be tested directly. Instead, ®eld selected for study because of its correspondence in size and general appear- ance to those previously studied and because this specimen was the extremum 1 Manuscript received 10 May 2001; revision accepted 26 July 2001. in the statistical size range of the species (see Gaines and Denny, 1993). The The authors thank Dr. Aaron M. Ellison (Mount Holyoke College, MA) stem of this plant was cut 0.40 m above ground and dissected into ®ve seg- who, as an Associate Editor of the American Journal of Botany, supervised ments measuring 0.80 m in length with the exception of the most distal seg- the review process and served as the acting Editor-in-Chief for this manu- ment, which measured 1.0 m in length. The segments were labeled A to E script; Jose Martinez, Jose Luis Ibarra, and Norma Vidales (Instituto de Ecol- from the base to the top of the plant. The orientation of each segment with ogia) for assistance in the ®eld; and Kenneth C. Cheung (Cornell) for labo- respect to the intact stem was noted and four representative vascular bundles, ratory assistance. Field work was supported by funds from the operating bud- get of the Instituto de Ecologia UNAM to FMF and CTO. This research was labeled I to IV, were dissected from the surrounding primary tissues in each also supported by Hatch Act Awards 185-403 to KJN and 185-406 to DJP, of the ®ve stem segments. A specimen of wood measuring 0.20 m in length Jr. was removed from the mid-span of each of these 20 vascular strands, wrapped 4 Author for reprint requests (Phone: 607 255-8727; Fax: 607 255-5407; e- in moist paper, placed in a zip-lock plastic bag, and saturated with FAA for mail: [email protected]). mechanical testing. 12 January 2002] NIKLAS ET AL.ÐROOT SYSTEM BIOMECHANICS 13

Fig. 1. Root (A±C) and stem morphology (D) of the largest Pachycerous pringlei specimen examined. (A) Polar view of lateral root elements (1L±3L). Root diameter (in centimeters) indicated for speci®c locations denoted by short lines. (B) Polar view of lateral roots (1L±3L) and sinker roots (denoted by S; e.g., 1L1S1). Depth of burial (in centimeters) indicated by numbers; distance (in meters) from stem base given in parentheses. (C) Vertical silhouette of bayonet- like root emerging from stem base (location indicated by black circle in A). (D) Vertical silhouette of stem. Grid system for A and B is 1 ϫ 1m.

Sixty-®ve root segments were extensively studied in the following way. and depth of burial were measured and recorded systematically as were the After photographing all exposed roots, a 1 ϫ 1 m grid system of nylon cord dimensions and locations of ``sinker'' roots (designated as S, e.g., 1L1S1). A anchored to the ground at various locations was constructed using the stem total of 22 segments were collected from seven of the largest of these roots base as its center and the four compass directions to align the grid sides. This located for mechanical testing. These root samples were preserved as previ- grid system was used to map root location, diameter, and depth at various ously described for stem vascular traces. locations (see Fig. 1). Measurements were taken at each location with a mi- crocaliper reading to the nearest millimeter. Three large lateral roots diverged Determination of relative volumes of axial vs. ray tissuesÐTo conserve from the stem base (labeled 1L, 2L, and 3L) and branched (e.g., 1L1). The specimens for mechanical testing, nondestructive sampling was used to mea- base of each of these roots was cut transversely leaving short stumps on the sure axial and ray system volume fractions. The points used for measurement stem base, which were labeled to record the absolute orientation of the rest mostly coincide with the transverse surface cuts of root segments made in the of the root system. Additional excavation revealed the base of a deep (1.15 ®eld. These surfaces were trimmed using a razor saw and polished with 400 m) vertical bayonet-like root (labeled VR) that bifurcated ϳ0.25 cm below mesh silicon carbide paper, or a thin disc was cut from the ®eld-cut surface ground level (labeled VR1 and VR2), which was removed and sectioned trans- and polished. Ethanol (70%) was used as a lubricant and to prevent drying. versely into ten segments for further study. Surfaces were photographed by re¯ected light using 12ϫ objectives of a ste- A total of 33 segments measuring 0.20 m in length was removed sequen- reomicroscope and a 3CCD color video camera interfaced to a computer tially from the four prominent lateral root components 1L1, 1L3, 2L, and 3L1 equipped with image capture/processing software. after painting their dorsal surfaces to record their orientation. Their diameter Print ®les of large specimens were assembled into a montage. The orien- 14 AMERICAN JOURNAL OF BOTANY [Vol. 89 tation of the surface painted in the ®eld was maintained with the aid of a pin inserted into the root axis. Some images were inverted so that their orientation was in all cases consistent with viewing the planes of sectioning from the root base. On montages of lateral roots, vertical and horizontal axes were recorded midway across the width and height of the secondary xylem, re- spectively, and four sampling areas (top, bottom, left, right) were centered on the four points of intersection of the vertical and horizontal axes with the perimeter of the secondary xylem. The width of the sample (arc along the perimeter) was uniformly represented by 10±12 repeating axial and ray system units along the perimeter line, with half the units on each side of the center point. The radial depth of the sample was chosen to provide ample tissue for the measurements and to coincide with a growth layer boundary that could be traced throughout the section. Thus, tissues of the same age in different quadrants were sampled. Because of eccentric growth, the four samples were of unequal areas. However, since eccentricity was not consistent with refer- ence to absolute directions, no systematic bias occurred in area sampled in each quadrant across samples. Sampling in vertical roots followed the same guidelines, but the surface painted in the ®eld only provided a means to align successive transverse images. The relative masses of cutouts of axial and ray Fig. 2. Root taper t plotted as a function of distance d from stem base tissue system images were used to determine volume fractions. for lateral roots 1L1 and 1L3 (see Fig. 1). Transformed data are log-log linear (not shown). Ordinary least squares regression curve and 95% con®dence Mechanical testingÐRoot and stem wood samples where tested in three- intervals are indicated by thick and thin lines, respectively; slope of the re- point bending to determine Young's elastic modulus (E) and in tension until duced major axis regression ␣RMA and coef®cient of correlation of RMA re- gression are indicated. failure to determine the tensile breaking stress (␴B) (see Niklas, 1999). Sur- gically removed specimens were trimmed to obtain prismatic beams with more or less square cross sections of side s and length L with L/s Ն 20. Each beam was oriented horizontally and bent using different loads (P) placed at (Fig. 2). These features varied little across an additional 17 beam mid-length. E was computed from the fromula E ϭ Pl3/48␦I, where l plants differing in size. Bayonet roots were invariably deep is beam free length (ϽL), ␦ is vertical displacement, and I is the axial second and appeared established before lateral root proliferation and moment of area (i.e., I ϭ s4/12 for a square cross section; see Niklas, 1992, extension (Fig. 3). Lateral root length and basal diameter were p. 136). A microscope with an ocular micrometer was used to measure ␦. both correlated with plant size (see below). Ethanol (70%) was used to prevent drying. Each beam was then mounted with two felt-lined clamps in the operating head of an Instron universal testing Root anatomyÐTransverse sections of all three types of Ϫ1 machine and subjected to axial tension at a strain rate of 0.001 sec until it roots revealed a core of wood and a ``peripheral complex'' broke. Readings from force and distance transducers were logged by a com- consisting of secondary phloem, cortex, and periderm. The puter using an a/d-transformer interface. Data from specimens breaking near root wood was differentiated into axial and ray systems with or at clamps were rejected; when possible, these specimens were retrimmed weakly de®ned growth layers differentiated in both systems and re-tested. Tensile breaking stresses, ␴B, were computed using the formula F/s2, where F is maximum (tensile) force and s was measured after failure. (Fig. 4A). The number of alternating ray and axial tissue pan- Clamp effects and specimen extension were monitored, but minor effects els in the xylem and phloem increased toward the vascular cambium, indicating that, as in the stem, rays increase in num- could not be excluded. Minimum values for ␴B are assumed. After testing, the two ends of each beam were photographed under re¯ected light, images ber as secondary growth proceeds. The parenchymatous phlo- were projected onto a ¯at surface to draw axial and ray tissues, and the two em rays were dilated; their cell pattern revealed the occurrence tracings from each beam were cut out and weighed to determine the mean of tangential growth and cell proliferation (Fig. 4B). Ray and tissue volume fractions. These data and morphometric data were used to cal- living peripheral complex tissues contained large quantities of culate the ability of roots to resist wind-throw (see Appendix). starch. The strands of axial secondary phloem were capped with RESULTS ®bers that matured as the phloem aged. A pattern of disruption occurred tangentially across these caps; the discontinuities that Root morphologyÐThe root system of P. pringlei is later- separated the fragments, were occupied by parenchyma cells ally extensive but shallow (Fig. 1). The largest of the three (Fig. 4C). The cell net showed that these cells grow and pro- lateral roots (1L) diverged into four root elements (1L1±1L4), liferate to relieve the stresses causing fractures. This growth the largest of which (1L1) measured ϳ5.15 m in length and included radial displacement of the secondary phloem frag- 0.064 m in diameter at its base; lateral roots 2L and 3L mea- ments. The secondary phloem thus contributed to the radial sured 3.89 m and 4.11 m in length and 0.09 m and 0.10 m in expansion of the peripheral complex. The proportion of the basal diameter, respectively. The depth of burial of the prox- peripheral complex consisting of secondary phloem varied imal and most distal lateral root elements varied between 0.05 widely. m and 0.20 m, respectively. In contrast, the bayonet root mea- A parenchymatous cortical tissue containing druses sur- sured 0.18 m in diameter at the stem junction and was 1.15 rounded the secondary phloem. Radial longitudinal sections m deep. The depth of sinker roots ranged between 0.31 and revealed that the square to upright cortical parenchyma cells 0.72 m. Root taper t was uniform and approximated by the were sometimes arranged in tiers (Fig. 4D). Although the ra- reduced major axis regression formula t ϭ 0.484dϪ0.75 (n ϭ dial tiers suggested growth from a cambium, there was no 2 45, r ϭ 0.918, F ϭ 279.7, P Ͻ 0.0001, ␣OLS ϭϪ0.716 Ϯ evidence in transverse sections that the entire cortex originated 0.05), where t ϭ (Db Ϫ Dd)/Dbd, and Db and Dd are diameter from one cambium. Rather, growth appeared generalized, with measured at the base and distance (d) from Db, respectively the image of tiers generated by a lack of cell elongation and January 2002] NIKLAS ET AL.ÐROOT SYSTEM BIOMECHANICS 15

Fig. 3. Polar views of the lateral root elements and vertical silhouettes of stems and bayonet like roots differing in size (compare with Fig. 1). Lateral roots drawn to scale (1 ϫ 1 m grid); position of stem base denoted by shaded circle. Stem and bayonet-like root silhouettes not drawn to scale but proportionally represented (stem height h indicated for each specimen). Ground-level for each silhouette shown by transverse grid lines.

the predominance of tangential longitudinal divisions among by the network of cortical vascular strands. Multiple vascular cells related to one other. The cortex was surrounded on the bundles entered the otherwise parenchymatous sur®cial exterior by a periderm consisting of a persistent phellogen, a bumps. Traces to shed roots were absent in the thicker parts single layer of phelloderm, and numerous layers of phellum of the bayonet root axis, suggesting that these traces can be (Fig. 4E). attenuated and lost with growth and time. The peripheral complex contained an anastomosing network An uneven distribution of growth in the secondary xylem of vascular strands (Fig. 4F) that extended from the outer lim- produced transverse sections that varied from circular to ellip- its of the secondary phloem (Fig. 4C) to within one to a few tical to ¯attened and indented. In lateral roots, the orientation cells from the periderm. The anastomoses extended both tan- of the least developed portion of the wood occurred in all gentially and radially, and the network contained xylem and sectors (top, bottom, left, right) of the transverse sections. phloem. The vertical strands were spaced apart tangentially so Based on sections that were suf®ciently close together, the that they varied from scarce to abundant in individual radial intersection of the shortest radius with the perimeter of the sections. The vessel elements in the network were pitted (Fig. wood appeared to travel along the axis in a spiral-helical path. 4G), and stretched protoxylem was absent. There was no in- The ratio of lengths of radii along the diameter of the wood dication of cell disruption around these strands. The length and that included the smallest radius varied from 1.6 to 14.7 (XÅ arrangement of vascular elements (Fig. 4G±H) suggested cells Ϯ SE ϭ 5.4 Ϯ 1.2). Although the cortex was also eccentric, were recruited from surrounding parenchyma to establish and the eccentricity of the whole axis was more closely related to augment the strands of vascular tissue. that of the wood than that of the cortex (r2 ϭ 0.94 vs. r2 ϭ In addition to the anastomosing vascular tissue network, the 0.63). peripheral complex contained occasional root traces with ra- dial trajectories extending from the secondary xylem to the Tissue volume fractionsÐThe absolute area of the wood root surface. In the dry-season collections used for this study, and the cortex in a section was greatest at the base of a root, there were no feeder roots attached to the lateral roots. But and typically, the contribution of the cortex to transverse sec- each root trace entered a bump on the surface of the lateral tional area was greater than that of the wood. Although the root (Fig. 4I). The locations of these bumps matched the oc- slope of decrease in absolute area with distance from the base casional large rays of the secondary xylem containing root of a root was greater for the cortex than for the wood, the traces that were clearly visible on the outer surface of the absolute preponderance of cortex was such that the ratio of wood (Fig. 4J). The root traces were linked to and surrounded cortex to wood actually increased with distance along the axis. 16 AMERICAN JOURNAL OF BOTANY [Vol. 89

Except near the root tips, this ratio was much lower along the Allometric trendsÐRoot anchorage was inversely propor- axis in the bayonet root than in a lateral or sinker root. We tional to plant size, whereas lateral root surface area increased interpret this result to mean that, in comparison to a lateral with respect to stem size and surface area. For bayonet roots, root, the growth of the bayonet-like root emphasizes expansion the relationships between stem height h and root depth L and 1.74 of the axis as a function of distance from the root tip and that maximum diameter dr were given by the formulas h ϭ 36L 2 expansion of the woody axis is favored over the expansion of (n ϭ 18, r ϭ 0.971, F ϭ 531.7, P Ͻ 0.0001, ␣OLS ϭ 1.72 Ϯ 1.26 2 the peripheral complex. 0.07) and h ϭ 3.37dr (n ϭ 18, r ϭ 0.916, F ϭ 175.3, P For spatially and chronologically equivalent samples of the Ͻ 0.0001, ␣OLS ϭ 1.20 Ϯ 0.09) (Fig. 7A±B). youngest growth layers of wood, the axial tissue volume frac- Maximum lateral root length ᐉ increased but disproportion- tion VF increased, on average, toward the tip of lateral, bay- ately so with respect to basal stem diameter D and bayonet onet, and sinker roots (Fig. 5). For example, regression of VF root depth L. Speci®cally, ᐉ ϭ 24.8D1.23 (n ϭ 18, r2 ϭ 0.879, against distance d measured from the base of lateral root 1L1 F ϭ 115.9, P Ͻ 0.0001, ␣OLS ϭ 1.16 Ϯ 0.11) and ᐉ ϭ 2 1.55 2 gave VF ϭ 50.4 ϩ 5.95d (r ϭ 0.636, n ϭ 11, F ϭ 15.73, P 3.59L (n ϭ 18, r ϭ 0.898, F ϭ 140.7, P Ͻ 0.0001, ␣OLS Ͻ 0.003), whereas, across all wood samples, VF ϭ 46.6 ϩ ϭ 1.47 Ϯ 0.12) (Fig. 7C±D). In contrast, ᐉ decreased with 7.60d (r2 ϭ 0.350, n ϭ 26, F ϭ 12.94, P Ͻ 0.001). At any respect to h: ᐉ ϭ 1.27h0.89 (n ϭ 18, r2 ϭ 0.947, F ϭ 284.1, distance from the base of all three types of roots there was a P Ͻ 0.0001, ␣OLS ϭ 0.865 Ϯ 0.05) (Fig. 7E). Thus, the al- trend toward higher VF in the radial direction inward (data lometry of lateral root length with respect to bayonet root not shown). Thus, the longitudinal trend is likely explained by depth provides additional anchorage, but not commensurate the radial trend, since early secondary growth produces wood with increases in stem size. with higher VF. Bayonet roots tended to have lower VF than The ability of lateral root elements to provide nutrient ab- lateral and sinker roots. The anatomical similarities among the sorption or storage increased signi®cantly with respect to three types of roots and the abundance of rays in their wood growth in stem size. Total lateral root surface area vs. stem 2.38 bespeak a similarity in function with respect to water absorp- height was approximated by the formula SAroot ϭ 0.369h 2 tion and nutrient storage. (n ϭ 18, r ϭ 0.941, F ϭ 238.0, P Ͻ 0.0001, ␣OLS ϭ 2.31 Ϯ 0.15); the relationship between stem and lateral root surface 1.40 2 Wood biomechanicsÐAnalyses of the bending stiffness of areas was given by SAroot ϭ 0.488SAstem (n ϭ 18, r ϭ the vascular strands removed from the largest plant indicated 0.922, F ϭ 176.9, P Ͻ 0.0001, ␣OLS ϭ 1.34 Ϯ 0.10). The that the stem wood stiffness increased toward the stem base failure to excavate all small lateral root elements would in- but sharply decreased ϳ0.5 m above ground level as previ- crease the values of these scaling exponents. Moreover, lateral ously described for other P. pringlei plants of equivalent size root volume scaled anisometrically with respect to stem vol- 1.41 2 (see Niklas et al., 2000). ume: Vroot ϭ 1.02Vstem (n ϭ 18, r ϭ 0.899, F ϭ 135.6, P Across all root wood samples, VF correlated positively with Ͻ 0.0001, ␣OLS ϭ 1.34 Ϯ 0.12). Thus, overall root volume E and ␴B such that the data from all three root types could be increased, on average, with respect to that of stem volume pooled. Regression analyses of these pooled data gave E ϭ (Fig. 7F). Ϫ0.49 ϩ 0.02VF (r2 ϭ 0.975, n ϭ 20, F ϭ 195, P Ͻ 0.0001) Finally, data from 117 additional plants indicate that the 2 and ␴B ϭϪ0.02 ϩ 0.003VF (r ϭ 0.972, n ϭ 20, F ϭ 632, relationship between h and basal stem D is log-log nonlinear P Ͻ 0.0001) (Fig. 6A±B). The root cortical complex E also and that growth in height decreases with increasing plant size: 2 2 increased toward root bases, possibly as a consequence of the log10h ϭ 1.01 ϩ 0.506 log10D Ϫ 0.347 log10D (r ϭ 0.968, accumulation of vascular traces, which increase in number and F ϭ 2602, P Ͻ 0.0001). Thus, plants are essentially deter- thickness as a function of age. minant in their growth in height, as reported for other species Calculations showed that the basipetal reduction in E was of columnar cacti (see Niklas, 1994; Niklas and Buchmann, compensated for by wood quantity. Using orthogonal stele di- 1994). ameters, we calculated the axial second moment of area I (ϭ0.25a3b, where a is the major semiaxis and b is the minor Root safety factorsÐCalculations based on engineering the- semiaxis of the stele in each root element) for lateral root 1L1 ory (see Appendix) showed that the ability to resist wind- and the bayonet root elements VR1 and VR2; I increased to- throw decreases with increasing plant height due to a dispro- ward the stem base (i.e., d ϭ 0) as did EI (Fig. 6C±D). Thus, portional relationship between stem height and bayonet root although wood stiffness decreased basipetally, the ability to depth such that MB increased with respect to MR. Using a resist wood deformation was compensated by the production parabolic vertical wind speed pro®le generated by umax ϭ 10 of large amounts of wood. m/s at h ϭ 5 m, the relationships among h, MB, and MR were

→

Fig. 4. Anatomy of lateral root 1L1. Parts A, I, and J were taken using re¯ected light and a stereomicroscope. Parts B±H are from unstained hand sections, using a compound microscope. (A) Transversely cut surface showing eccentric wood core, alternating axial and ray tissues, and growth layers. Main ®gure ϫ3.7, insert ϫ6.8. (B) Tangential section of dilated ray showing that cell net reveals lateral expansion (dilation) of the ray. Axial phloem ®bers are seen at the left and right. ϫ40. (C) Transverse section of secondary phloem showing overview (inset) and detail (main ®gure) of fragmentation of ®ber strands. The periphery of the root is beyond the tops of these ®gures. The asterisk in the inset indicates the location of the enlarged image. Each of the two displaced fragments (arrows in the inset) once capped three conjoined ®ber strands. Portions of the vascular network in the peripheral complex (four arrows in main ®gure) have differentiated in the outer limits of the secondary phloem. Main ®gure ϫ58.5, insert ϫ6. (D) Radial section showing tiers of cells in the cortex. The axis of the ®gure is vertical and the periderm is to the right. ϫ25. (E) Inner portion of periderm and outermost cell layer of the cortex, as seen in radial section. The axis of the root is vertical in the ®gure. The persistence of the phellogen is indicated by the radial ®les of cells in the periderm. These do not match the cell ®les in the cortex. ϫ175. (F) Radial section showing anatomosing cortical network of vascular tissue in the cortex. The axis of the root is vertical in the ®gure. The dark image at the extreme right in the ®gure is that of secondary phloem ®bers. Periderm was just beyond the left edge of the ®gure. The January 2002] NIKLAS ET AL.ÐROOT SYSTEM BIOMECHANICS 17

two arrows at the left indicate the least visible portion of the network that was present in this section. ϫ40. (G) Radial section of a portion of the vascular network showing short, pitted vessel elements. The axis of the root is horizontal in the ®gure. ϫ250. (H) Tangential section of a slender strand of vascular tissue in the cortex. The end walls of vessel elements (arrows) match the ends of cells in the cortex. The root axis is horizontal in the ®gure. ϫ145. (I) Pro®le surface view of three bumps on the surface of the root. The axis of the root is horizontal in the ®gure. Bumps also occur singly, but multiple bumps allow for more convincing demonstration of corresponding large xylem rays that each contain a root trace. ϫ5.3. (J) Root traces in large rays at the surface of the wood match the locations of the bumps. The axis of the root is horizontal in the ®gure. ϫ5.3. 18 AMERICAN JOURNAL OF BOTANY [Vol. 89

Fig. 5. Relationship between the axial tissue volume fraction VF and dis- tance from stem base d for lateral, bayonet, and sinker roots (see insert).

3.71 2 h ϭ 0.263MB (n ϭ 18, r ϭ 0.999, F ϭ 10 884, P Ͻ 0.0001, 0.51 2 ␣OLS ϭ 3.71 Ϯ 0.04) and h ϭ 0.182MR (n ϭ 18, r ϭ 0.972, F ϭ 565.5, P Ͻ0.0001, ␣OLS ϭ 0.512 Ϯ 0.02). As a conse- quence, stem height and the safety factor were inversely re- Ϫ1.81 2 lated: h ϭ 108(MR/MB) (n ϭ 18, r ϭ 0.968, F ϭ 489.8, P Ͻ 0.0001, ␣OLS ϭϪ1.81 Ϯ 0.08). Thus, the susceptibility to wind-throw increased rapidly with stem-height growth. We also calculated the maximum wind speed that each plant could sustain without roots failing. For the largest plant (h ϭ

4.6 m), the bayonet root's MR ϭ 535.6 N´m. Over a broad range of maximum wind speeds, the relationship between MB 2 2 and maximum wind speed was MB ϭ 0.83umax (n ϭ 8, r ϭ 2 1.0). Thus, MR/MB ϭ 535.6/0.83umax such that MR/MB Յ 1 when umax ϳ 25 m/s (Fig. 8). In this regard, meteorological data collected between January 1980 and October 1999 (pro- Fig. 7. Allometric relationships among root system and stem features. vided by the Comision Nacional del Agua) for Empalme (lo- Ordinary least squares regression curve and 95% con®dence intervals for cated at the southern limit of P. pringlei in Sonora) indicate log10-transformed data are indicated by thick and thin lines, respectively; slope of the reduced major axis regression and coef®cient of correlation of that u ϭ 26 m/s (August 1997). Thus, the largest plant was ␣RMA max RMA regression are indicated for each bivariate graph. (A) Stem height h vs. depth of burial of bayonet-like root L. (B) Stem height h vs. diameter of

bayonet-like root measured at stem base dr (C) Length of largest lateral root ᐉ vs. basal stem diameter D. (D) Lateral root length ᐉ vs. depth of burial of bayonet-like root L. (E) Lateral root length ᐉ vs. stem height h. (F) Total

lateral root volume Vroot vs. stem volume Vstem.

estimated to fail by wind-throw, assuming that its bayonet root pivoted at L/2 (see Appendix). If pivoting occurred at L due

to lateral and sinker root element restraint, MR ϭ l1 071 N´m and umax ϭ 36 m/s. This wind speed approaches hurricane/ tropical storm proportions. However, these calculations assume stem bending stresses do not exceed stem tissue breaking stresses and that plants lack large lateral branches (which would increase stem sail area, wind-induced drag forces, and bending moments).

DISCUSSION With increasing plant size, Pachcereus pringlei root systems provide progressively less resistance to wind-throw but afford a greater capacity to absorb and store nutrients. The bayonet root, which characterizes the root system regardless of plant age, fails to grow in girth and depth in a manner that me- Fig. 6. Relationship among elastic modulus E and breaking stress ␴B, chanically compensates for the increasing bending moments axial tissue volume fraction VF, and axial second moments of area I for root exerted on stems by wind. The lateral and sinker root elements wood. (A) E vs. VF. (B) ␴ vs. VF. (C) Log -transformed data for I vs. B 10 may contribute to anchorage by forcing the bayonet root to transformed data for distance from stem base d. (D) Log10-transformed data for EI (¯exural stiffness) vs. transformed data for distance from stem base d. pivot closer to ground level (see Appendix). This scenario is Data from bayonet roots and lateral roots are shown by squares and ϫ's, mechanically reasonable (see Ennos, 1993), especially in light respectively. of unequal lateral root expansion (due to the uneven accu- January 2002] NIKLAS ET AL.ÐROOT SYSTEM BIOMECHANICS 19

along all root axes. Moreover, the volume fraction of root ray tissues increases toward the stem base, further reducing wood stiffness and strength. This feature also occurs in P. pringlei stems where it reduces the probability of tissue strain incom- patibilities (Niklas et al., 2000). However, living tissues also have the ability to store water during the rainy season (Mau- seth, 1993) and those in P. pringlei roots contain large quan- tities of starch, which can be hydrolyzed and recruited to change tissue osmotic potentials when soil-water is available. Allometric analysis also shows that total root system surface area increases signi®cantly with increasing plant size, which increases the number of feeder root loci that can be potentially formed. In passing, we surmise that the formation of new ®ne (feed- er) roots of P. pringlei resembles that reported for species not adapted to arid, desert conditions (e.g., alfalfa and parsnip; see Jones, 1943; Warning, 1934, respectively). These feeder roots form in secondary tissues of the parent root axis, at locations determined by the previous emergence of endogenously formed branch roots. These ®ne roots typically atrophy. But their traces are maintained or augmented as secondary cortical parenchyma cells are recruited to form new vascular tissues. Subsequent crops of adventitious feeder roots attach to these older vascular networks. Arguably, the repeated use of the same root formation loci, which resembles the formation of root spurs in the primary tissues of Opuntia (Boke, 1979), on established lateral roots evincing secondary growth may be deemed an adaptive feature, since it improves the ability of suberized roots to obtain and store water and soil nutrients (see North, Huang, and Nobel, 1993). Further research into the mechanical, morphological, and anatomical features of desert-adapted species is required to determine whether the features reported here for P. pringlei are representative of columnar cactus species in general, which is our impression. Nonetheless, this study expands the growing Fig. 8. Estimated stem bending moments M , root counter-resisting mo- B body of literature that reveals generalizations about root sys- ments MR, and factors of safety against anchorage failure MR/MB for plants differing in height h. All estimated are based on the assumption that the tem functions must be couched in terms of potentially complex bayonet-like root providing the MR pivots at a point equal to 1/2 its depth of anatomical, biometric, mechanical, and environmental rela- burial (ᐉ ϭ L/2; see Appendix Fig. 1A). (A) Bending and counter-resisting tionships (e.g., Ennos, 1993; North, Huang, and Nobel, 1993; moments are plotted as a function of different stem heights, assuming a ver- Stokes, Fitter, and Couts, 1995; Stokes and Mattheck, 1996; tical wind speed pro®le created by a maximum wind speed u of 10 m/s max Niklas, 1999). measured at h ϭ 5 m. (B) Stem bending moment and factor of safety esti- mated for the largest plant in the data set (h ϭ 4.6 m) are plotted as functions of a range of maximum wind speeds measured at h ϭ 5 m. The minimum LITERATURE CITED factor of safety against wind-throw (MR/MB ϭ 1) is shown by the horizontal line. Stem failure is predicted to occur when umax ϳ 25 m/s. ANDERSON, C. J., M. P. COUTTS,R.M.RITCHIE, AND D. J. CAMPBELL. 1989. Root extraction forces measurements for Sitka spruce. Forestry 62: 127± 137. mulation of secondary tissues) that, in tandem with the het- BOKE, N. H. 1979. Root glochids and root spurs of Opuntia arenaria (Cac- erogeneity of wood stiffness, may differentially compact the taceae). American Journal of Botany 66: 1085±1092. surrounding soil, i.e., root development may establish auger- BROMS, B. B. 1964. Lateral resistance of piles in cohesive soils. Journal of like growth that reduces the probability of soil-root shear fail- the Soil Mechanics and Foundation Division, Proceedings of the Amer- ure (see, however, North and Nobel, 1997). Yet, the allometry ican Society of Civil Engineers SM2 90: 27±63. of P. pringlei clearly results in a steady erosion of the safety CASADA, J. H., L. R. WALTON, AND L. D. SWETNAM. 1980. Wind resistance of Burely tobacco as in¯uenced by depth of plants in soil. Transactions factor against wind-throw, which is consistent with the de- of the American Society of Agricultural Engineers 23: 1009±1011. mographics of dead plants (F. Molina-Freaner, personal obser- COUTTS, M. P. 1983. Root architecture and tree stability. Plant and Soil 71: vation). 171±188. In contrast, the allometry of P. pringlei root anatomy and COUTTS, M. P. 1986. Components of tree stability in Sitka spruce on peaty morphology favors water absorption and nutrient storage as gley soil. Forestry 59: 173±197. plants increase in size. Even though the absolute cross sec- CROOK, M. J., AND A. R. ENNOS. 1996. The anchorage mechanics of mature larch Larix europea ϫ L. japonica. Journal of Experimental Botany 47: tional areas of root wood and cortex increase toward the stem 1509±1517. base (with concomitant increases in the root axial second mo- DITTMER, H. J. 1937. A quantitative study of the roots and root hairs of ment of areas and anchorage), the contribution of the cortex winter a rye plant (Secale cereale). American Journal of Botany 24: 417± to transverse sectional area is greater than that of the wood 420. 20 AMERICAN JOURNAL OF BOTANY [Vol. 89

ENNOS, A. R. 1993. The scaling of root anchorage. Journal of Theoretical nutrition: effects on biomass allocation, root development, and resistant Biology 161: 61±75. to bending. Canadian Journal of Forest Research 27: 1049±1057. ENNOS, A. R. 2000. The mechanics of root anchorage. Advances in Botanical STOLZY, L. H., AND K. P. BARLEY. 1968. Mechanical resistance encountered Research 33: 133±157. by roots entering compact soils. Soil Science 105: 297. ENNOS,A.R.,AND A. H. FITTER. 1992. Comparative functional morphology VOGEL, S. 1981. Life in moving ¯uids. Willard Grant Press, Boston, Mas- of the anchorage systems of annual dicots. Functional Ecology 6: 71± sachusetts, USA. 78. WARNING, W. C. 1934. Anatomy of the vegetative organs of the parsnip. FELGER,R.S.,AND M. B. MOSER. 1985. People of the desert and the sea. International Journal of Plant Biology (formerly the Botanical Gazette) Ethnobotany of the Seri Indians. University of Arizona Press, Tucson, 96: 44±72. Arizona, USA. WILSON, B. F. 1975. Distribution of secondary thickening in tree root sys- GAINES, S. D., AND M. W. DENNY. 1993. The largest, smallest, highest, low- tems. In J. G. Torrey and D. T. Clarkson [eds.], The development and est, longest and shortestÐextremes in ecology. Ecology 74: 1677±1692. function of roots, 197±219. Third Cabot Symposium. Academic Press, GARTNER, B. L. 1994. Root biomechanics and whole plant allocation pat- London, UK. terns: responses of tomato to simulated wind. Journal of Experimental WHITAKER, T. 1970. The design of piled foundations. Pergamon Press, Ox- Botany 45: 1645±1654. ford, UK. HATANAKA, M., AND A. UCHIDA. 1995. Effects of test methods on the cyclic deformation characteristics of high quality undisturbed gravel samples. In M. D. Evans and R. J. Fragaszy [eds.], Static and dynamic properties APPENDIX of gravelly soils, 136±151. Geotechnical Special Publication No. 56. American Society of Civil Engineers, New York, New York, USA. JONES, F. R. 1943. Growth and decay of the transient (noncambial) roots of alfalfa. Journal of the American Society of Agronomy 35: 625±634. A wind-induced pressure force F acting along the length of a shoot with KEÂ ZDI,AÂ . 1974. Handbook of soil mechanics, vol. 1, Soil physics. Elsevier height h produces a bending moment MB resulting in the rotational moment Scienti®c, Amsterdam, The Netherlands. in a vertical basal root with radius r and length L. To avoid wind-throw, the MAUSETH, J. D. 1993. Water-storing and cavitation-preventing adaptations in root restoring moment MR must ՆMB. In the absence of lateral root restraint, wood of cacti. Annals of Botany 72: 81±89. the vertical root will pivot at distance l below ground (see Fig. A1A) and the NASS,H.G.,AND M. S. ZUBER. 1971. Correlation of corn (Zea mays L.) sorrounding soil will fail plastically, resisting sideways motion with a unit roots early in development to mature root development. Crop Science force dFB per unit root length dᐉ such that dFB ϭ 18␶rdᐉ, where ␶ is soil 11: 655±658. shear strength, which varies across soil types and conditions (Broms, 1964; NEEMAN, M., AND J. L. SPENCER-SMITH. 1975. An analysis of the problem KeÂzdi, 1974; Hatanaka and Uchida, 1995). In the case where the root pivots

of lodging with particular reference to wheat and barley. Journal of Ag- at ᐉ ϳ L/2, the restoring moment MR acting along L is given by the formula L/2 2 ricultural Science 85: 495±507. MR ϭ #ϪL/2 18␶rᐉ dᐉ ϭ 9␶r(L /2) (see Niklas, 1992; Ennos, 1993). If additional NIKLAS, K. J. 1992. Plant biomechanics. University of Chicago Press, Chi- cago, Illinois, USA. NIKLAS, K. J. 1994. Plant allometry. University of Chicago Press, Chicago, Illinois, USA. NIKLAS, K. J. 1999. Variations of the mechanical properties of Acer sac- charum roots. Journal of Experimental Botany 50: 193±200. NIKLAS, K. J., AND S. L. BUCHMANN. 1994. The allometry of height. American Journal of Botany 81: 1161±1168. NIKLAS, K. J., F. MOLINA-FREANER, AND C. TINOCO-OJANGUREN. 1999. Bio- mechanics of the columnar cactus Pachycereus pringlei. American Jour- nal of Botany 86: 767±775. NIKLAS, K. J., F. MOLINA-FREANER,C.TINOCO-OJANGUREN, AND D. J. PAOL- LILO,JR. 2000. Wood biomechanics and anatomy of Pachycereus prin- glei. American Journal of Botany 87: 469±481. NIKLAS,K.J.,AND H.-C. SPATZ. 2000. Wind-induced stresses in cherry trees: evidence against the hypothesis of constant stress levels. Trees, Structure and Function 14: 230±237. NORTH,G.B.,AND P. S. NOBEL. 1997. Drought-induced changes in soil contact and hydraulic conductivity for roots of Opuntia ®cus-indica with and without rhizosheaths. Plant and Soil 191: 249±258. NORTH, G. B., B. HUANG, AND P. S. NOBEL. 1993. Changes in structure and hydraulic conductivity for root junctions of desert succulents as soil- water varies. Botanical Acta 106: 126±135. PFEFFER, W. 1893. Druck- und Arbeitsleistung durch Waschende Plfanzen. Abhandlungen der Koniglich Sachsischen Gesellschaft der Wissenschaf- ten 33: 235±474. Fig. A1. Mechanical forces and moments hypothesized for Pachycereus PRESTON, C. E. 1900. Observations on the root system of certain Cactaceae. pringlei root system and stem. (A)±(B) A stem of height h experiences a International Journal of Plant Biology (formerly the Botanical Gazette) wind-induced (drag) force F acting perpendicular to its longitudinal axis. This 30: 348±351. force induces a stem bending moment that is transmitted at the stem base to SHREVE, F. 1964. Vegetation and ¯ora of the Sonoran Desert. Stanford Uni- a bayonet-like root that pivots at some distance ᐉ along its length L. The

versity Press, Stanford, California, USA. rotation of the bayonet-like root creates a counter-resistance moment MR as STOKES, A., J. BALL,A.H.FITTER,P.BRIAN, AND M. P. COUTTS. 1996. An root rotation is resisted by the soil (which results in a rhomboid stress distri- experimental investigation of the resistance of model root systems to bution along root surface shown by arrows of varying length). The maximum

uprooting. Annals of Botany 78: 415±421. MR is provided when ᐉ ϭ L. This condition can be obtained provided that STOKES, A., A. H. FITTER, AND M. P. COUTTS. 1995. Responses of young lateral root elements provide anchorage at the stem base (B). (C) The mag- trees to wind and shading: effects on root architecture. Journal of Ex- nitude of F is dependent on the wind speed pro®le generated by the maximum

perimental Botany 46: 1139±1146. wind speed umax and the vertical distribution of local wind speeds ui acting at STOKES, A., AND C. MATTHECK. 1996. Variation of wood strength in tree distances x along the length of the stem. The wind-induced (drag) force F is

roots. Journal of Experimental Botany 47: 693±699. also dependent on the local stem sail area: (xi Ϫ xj)(di ϩ dj)/2, where d is

STOKES, A., B. C. NICHOLL,M.P.COUTTS, AND A. H. FITTER. 1997. Re- stem diameter. Stem bending moment MB induced by F increases toward stem sponses of young Sitka spruce clones to mechanical perturbation and base. January 2002] NIKLAS ET AL.ÐROOT SYSTEM BIOMECHANICS 21

roots contribute to anchorage (Fig. A1B), the extremum is ᐉ ϭ L and MR ϭ wind bending moments thus decrease toward the stem base, whereas the total L 2 bending moment increases toward the stem base where it reaches maximum #0 18␶rᐉ dᐉ ϭ 9␶rL . intensity Mmax. Turning to MB, the wind pressure (drag) force F on any stem element i is given by F 0.5 u2 S C , where is air density ( 1.2 kg/m3), u is local Numerical solutions of Mi are required, since ui and d¯ i vary as a function i ϭ ␳ i i D ␳ ϳ i 1/2 of L. We modeled ui using the formula ui ϭ umax[1 Ϫ (xi/h)] (see Niklas wind speed, Si is stem element i sail area, and CD is the drag coef®cient (ϳ1.0 and Spatz, 2000), where umax is maximum wind speed speci®ed for an arbitary for a cylinder; see Vogel, 1981; Niklas, 1994). For a tapered cylindrical stem, distance above ground (see Fig. A1C). Based on ®eld measurements of plants Si ϭ d¯ iLi, where d¯ i ϭ (di ϩ dj)/2, Li ϭ xi Ϫ xj, and xi and xj are the distances differing in size (0.09 m Յ h Յ 4.6 m), we computed MB and its correspond- measured from the top of the stem to d and d , respectively (see Fig. A1C). i j ing MR (using umax ϭ 10 m/s at 5 m above ground), estimated the maximum 2 Since Fi ϭ 0.5␳u id¯ i(xi Ϫ xj), the MB on stem element i is given by the formula wind speed each plant could sustain before wind-throw, and assessed the i 2 Mi ϭ ⌺jϭ1 [0.5␳u id¯ i(xi Ϫ xj)](h Ϫ xi) (see Niklas and Spatz, 2000). Localized factor of safety using the quotient MR/MB.