| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
Biomechanics |
2Department of Plant Biology, Cornell University, Ithaca, New York 14853-5908 USA; and 3Instituto de Ecologia UNAM, Apartado Postal 1354, Hermosillo, Sonora CP83000, México
Received for publication May 10, 2001. Accepted for publication July 26, 2001.
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXLITERATURE CITED |
|---|
Key Words: biomechanics • Cactaceae • plant anatomy • roots • wind drag • wood
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXLITERATURE CITED |
|---|
; Dittmer, 1937
; Stolzy and Barley, 1968
; Nass and Zuber, 1971
; Neeman and Spencer-Smith, 1975
; Coutts, 1986
; Anderson et al., 1989
; Ennos and Fitter, 1992
; Ennos, 1993, 2000
; Gartner, 1994
; Stokes, Fitter, and Coutts, 1995
; Crook and Ennos, 1996
; Stokes and Mattheck, 1996
; Stokes et al., 1996, 1997
; Niklas, 1999
). The interplay between the effects of shoot morphology and environmental conditions (and their effect on the transmission of mechanical forces to the root system) are contingent on plant size as well as a number of ecological factors that may require a shift in emphasis among the various functional obligations of roots.
Here we report on the size-dependent relationship between anchorage and nutrient absorption/storage for the root systems of the columnar cactus species Pachycereus pringlei (see Niklas, Molina-Freaner, and Tinoco-Ojanguren, 1999
; Niklas et al., 2000
). The root morphology of this species combines plate, tap, and fibrous root system features (see Preston, 1900
; Wilson, 1975
; Coutts, 1983
; Ennos, 2000
). We specifically explore the hypothesis that the basal bayonet root of these root systems is the principal anchorage device, that the bulk of the lateral root system provides for nutrient absorption and belowground storage, and that a size-dependent shift in the performance of these two functions occurs.
This hypothesis could not be tested directly. Instead, field data and laboratory experiments were used to determine the load capabilities (maximum bending and tensile stresses) of root and stem tissues, and engineering theory was then used to calculate the ability of root systems differing in size to cope with wind-throw over a range of ambient wind speeds (see Whitaker, 1970
; Casada, Walton, and Swetnam, 1980
; Niklas, 1992
; Niklas and Spatz, 2000
). Size-dependent (allometric) trends in wind-induced bending and counter-resisting moments were evaluated to determine the minimum factor of safety against wind-throw (see Appendix).
|
MATERIALS AND METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXLITERATURE CITED |
|---|
; Felger and Moser, 1985
). A healthy plant growing in an open site with a size and general appearance similar to previously studied plants was selected for intensive study (see Niklas, Molina-Freaner, and Tinoco-Ojanguren, 1999
; Niklas et al., 2000
). However, 17 plants differing in size were examined in the field to determine root–stem allometric relationships. An additional 117 plants were measured to determine the allometry of shoot height with respect to basal stem diameter.
Dissection protocol
All of the root anatomical information reported here was derived from the study of the largest plant in our data set, which was selected for study because of its correspondence in size and general appearance to those previously studied and because this specimen was the extremum in the statistical size range of the species (see Gaines and Denny, 1993
). The stem of this plant was cut 0.40 m above ground and dissected into five segments measuring 0.80 m in length with the exception of the most distal segment, which measured 1.0 m in length. The segments were labeled A to E from the base to the top of the plant. The orientation of each segment with respect to the intact stem was noted and four representative vascular bundles, labeled I to IV, were dissected from the surrounding primary tissues in each of the five stem segments. A specimen of wood measuring 0.20 m in length was removed from the mid-span of each of these 20 vascular strands, wrapped in moist paper, placed in a zip-lock plastic bag, and saturated with FAA for mechanical testing.
Sixty-five root segments were extensively studied in the following way. After photographing all exposed roots, a 1 x 1 m grid system of nylon cord anchored to the ground at various locations was constructed using the stem base as its center and the four compass directions to align the grid sides. This grid system was used to map root location, diameter, and depth at various locations (see Fig. 1). Measurements were taken at each location with a microcaliper reading to the nearest millimeter. Three large lateral roots diverged from the stem base (labeled 1L, 2L, and 3L) and branched (e.g., 1L1). The base of each of these roots was cut transversely leaving short stumps on the stem base, which were labeled to record the absolute orientation of the rest of the root system. Additional excavation revealed the base of a deep (1.15 m) vertical bayonet-like root (labeled VR) that bifurcated 
0.25 cm below ground level (labeled VR1 and VR2), which was removed and sectioned transversely into ten segments for further study.
|
Determination of relative volumes of axial vs. ray tissues
To conserve specimens for mechanical testing, nondestructive sampling was used to measure axial and ray system volume fractions. The points used for measurement mostly coincide with the transverse surface cuts of root segments made in the field. These surfaces were trimmed using a razor saw and polished with 400 mesh silicon carbide paper, or a thin disc was cut from the field-cut surface and polished. Ethanol (70%) was used as a lubricant and to prevent drying. Surfaces were photographed by reflected light using 12x objectives of a stereomicroscope and a 3CCD color video camera interfaced to a computer equipped with image capture/processing software.
Print files of large specimens were assembled into a montage. The orientation of the surface painted in the field 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, respectively, 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 reference 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 field only provided a means to align successive transverse images. The relative masses of cutouts of axial and ray tissue system images were used to determine volume fractions.
Mechanical testing
Root and stem wood samples where tested in three-point bending to determine Young's elastic modulus (E) and in tension until failure to determine the tensile breaking stress (
B) (see Niklas, 1999
). Surgically removed specimens were trimmed to obtain prismatic beams with more or less square cross sections of side s and length L with L/s 
20. Each beam was oriented horizontally and bent using different loads (P) placed at beam mid-length. E was computed from the fromula E = Pl3/48
I, where l is beam free length (<L), is vertical displacement, and I is the axial second moment of area (i.e., I = s4/12 for a square cross section; see Niklas, 1992
, p. 136). A microscope with an ocular micrometer was used to measure . 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 machine and subjected to axial tension at a strain rate of 0.001 sec–1 until it broke. Readings from force and distance transducers were logged by a computer using an a/d-transformer interface. Data from specimens breaking near or at clamps were rejected; when possible, these specimens were retrimmed 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. Clamp effects and specimen extension were monitored, but minor effects could not be excluded. Minimum values for B are assumed. After testing, the two ends of each beam were photographed under reflected light, images were projected onto a flat surface to draw axial and ray tissues, and the two tracings from each beam were cut out and weighed to determine the mean tissue volume fractions. These data and morphometric data were used to calculate the ability of roots to resist wind-throw (see Appendix).
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXLITERATURE CITED |
|---|
5.15 m in length and 0.064 m in diameter at its base; lateral roots 2L and 3L measured 3.89 m and 4.11 m in length and 0.09 m and 0.10 m in basal diameter, respectively. The depth of burial of the proximal and most distal lateral root elements varied between 0.05 m and 0.20 m, respectively. In contrast, the bayonet root measured 0.18 m in diameter at the stem junction and was 1.15 m deep. The depth of sinker roots ranged between 0.31 and 0.72 m. Root taper t was uniform and approximated by the reduced major axis regression formula t = 0.484d–0.75 (n = 45, r2 = 0.918, F = 279.7, P < 0.0001, 
OLS = –0.716 ± 0.05), where t = (Db – Dd)/Dbd, and Db and Dd are diameter measured at the base and distance (d) from Db, respectively (Fig. 2). These features varied little across an additional 17 plants differing in size. Bayonet roots were invariably deep and appeared established before lateral root proliferation and extension (Fig. 3). Lateral root length and basal diameter were both correlated with plant size (see below).
|
|
|
A parenchymatous cortical tissue containing druses surrounded the secondary phloem. Radial longitudinal sections revealed that the square to upright cortical parenchyma cells were sometimes arranged in tiers (Fig. 4D). Although the radial tiers suggested growth from a cambium, there was no evidence in transverse sections that the entire cortex originated from one cambium. Rather, growth appeared generalized, with the image of tiers generated by a lack of cell elongation and the predominance of tangential longitudinal divisions among cells related to one other. The cortex was surrounded on the exterior by a periderm consisting of a persistent phellogen, a single layer of phelloderm, and numerous layers of phellum (Fig. 4E).
The peripheral complex contained an anastomosing network of vascular strands (Fig. 4F) that extended from the outer limits of the secondary phloem (Fig. 4C) to within one to a few cells from the periderm. The anastomoses extended both tangentially and radially, and the network contained xylem and phloem. The vertical strands were spaced apart tangentially so that they varied from scarce to abundant in individual radial sections. The vessel elements in the network were pitted (Fig. 4G), and stretched protoxylem was absent. There was no indication of cell disruption around these strands. The length and arrangement of vascular elements (Fig. 4G–H) suggested cells were recruited from surrounding parenchyma to establish and augment the strands of vascular tissue.
In addition to the anastomosing vascular tissue network, the peripheral complex contained occasional root traces with radial trajectories extending from the secondary xylem to the root surface. In the dry-season collections used for this study, there were no feeder roots attached to the lateral roots. But each root trace entered a bump on the surface of the lateral root (Fig. 4I). The locations of these bumps matched the occasional large rays of the secondary xylem containing root traces that were clearly visible on the outer surface of the wood (Fig. 4J). The root traces were linked to and surrounded by the network of cortical vascular strands. Multiple vascular bundles entered the otherwise parenchymatous surficial bumps. Traces to shed roots were absent in the thicker parts of the bayonet root axis, suggesting that these traces can be attenuated and lost with growth and time.
An uneven distribution of growth in the secondary xylem produced transverse sections that varied from circular to elliptical to flattened and indented. In lateral roots, the orientation of the least developed portion of the wood occurred in all sectors (top, bottom, left, right) of the transverse sections. Based on sections that were sufficiently close together, the intersection of the shortest radius with the perimeter of the wood appeared to travel along the axis in a spiral-helical path. The ratio of lengths of radii along the diameter of the wood that included the smallest radius varied from 1.6 to 14.7 ( ± SE = 5.4 ± 1.2). Although the cortex was also eccentric, the eccentricity of the whole axis was more closely related to that of the wood than that of the cortex (r2 = 0.94 vs. r2 = 0.63).
Tissue volume fractions
The absolute area of the wood and the cortex in a section was greatest at the base of a root, and typically, the contribution of the cortex to transverse sectional area was greater than that of the wood. Although the slope of decrease in absolute area with distance from the base of a root was greater for the cortex than for the wood, the absolute preponderance of cortex was such that the ratio of cortex to wood actually increased with distance along the axis. Except near the root tips, this ratio was much lower along the axis in the bayonet root than in a lateral or sinker root. We interpret this result to mean that, in comparison to a lateral root, the growth of the bayonet-like root emphasizes expansion of the axis as a function of distance from the root tip and that expansion of the woody axis is favored over the expansion of the peripheral complex.
For spatially and chronologically equivalent samples of the youngest growth layers of wood, the axial tissue volume fraction VF increased, on average, toward the tip of lateral, bayonet, and sinker roots (Fig. 5). For example, regression of VF against distance d measured from the base of lateral root 1L1 gave VF = 50.4 + 5.95d (r2 = 0.636, n = 11, F = 15.73, P < 0.003), whereas, across all wood samples, VF = 46.6 + 7.60d (r2 = 0.350, n = 26, F = 12.94, P < 0.001). At any distance from the base of all three types of roots there was a trend toward higher VF in the radial direction inward (data not shown). Thus, the longitudinal trend is likely explained by the radial trend, since early secondary growth produces wood with higher VF. Bayonet roots tended to have lower VF than lateral and sinker roots. The anatomical similarities among the three types of roots and the abundance of rays in their wood bespeak a similarity in function with respect to water absorption and nutrient storage.
|
0.5 m above ground level as previously described for other P. pringlei plants of equivalent size (see Niklas et al., 2000
).
Across all root wood samples, VF correlated positively with E and B such that the data from all three root types could be pooled. Regression analyses of these pooled data gave E = –0.49 + 0.02VF (r2 = 0.975, n = 20, F = 195, P < 0.0001) and B = –0.02 + 0.003VF (r2 = 0.972, n = 20, F = 632, P < 0.0001) (Fig. 6A–B). The root cortical complex E also increased toward root bases, possibly as a consequence of the accumulation of vascular traces, which increase in number and thickness as a function of age.
|
Allometric trends
Root anchorage was inversely proportional to plant size, whereas lateral root surface area increased with respect to stem size and surface area. For bayonet roots, the relationships between stem height h and root depth L and maximum diameter dr were given by the formulas h = 36L1.74 (n = 18, r2 = 0.971, F = 531.7, P < 0.0001, OLS = 1.72 ± 0.07) and h = 3.37dr1.26 (n = 18, r2 = 0.916, F = 175.3, P < 0.0001, OLS = 1.20 ± 0.09) (Fig. 7A–B).
|
increased but disproportionately so with respect to basal stem diameter D and bayonet root depth L. Specifically, = 24.8D1.23 (n = 18, r2 = 0.879, F = 115.9, P < 0.0001, OLS = 1.16 ± 0.11) and = 3.59L1.55 (n = 18, r2 = 0.898, F = 140.7, P < 0.0001, OLS = 1.47 ± 0.12) (Fig. 7C–D). In contrast, decreased with respect to h: = 1.27h0.89 (n = 18, r2 = 0.947, F = 284.1, P < 0.0001, OLS = 0.865 ± 0.05) (Fig. 7E). Thus, the allometry of lateral root length with respect to bayonet root depth provides additional anchorage, but not commensurate with increases in stem size.
The ability of lateral root elements to provide nutrient absorption or storage increased significantly with respect to growth in stem size. Total lateral root surface area vs. stem height was approximated by the formula SAroot = 0.369h2.38 (n = 18, r2 = 0.941, F = 238.0, P < 0.0001, OLS = 2.31 ± 0.15); the relationship between stem and lateral root surface areas was given by SAroot = 0.488SAstem1.40 (n = 18, r2 = 0.922, F = 176.9, P < 0.0001, OLS = 1.34 ± 0.10). The failure to excavate all small lateral root elements would increase the values of these scaling exponents. Moreover, lateral root volume scaled anisometrically with respect to stem volume: Vroot = 1.02Vstem1.41 (n = 18, r2 = 0.899, F = 135.6, P < 0.0001, OLS = 1.34 ± 0.12). Thus, overall root volume increased, on average, with respect to that of stem volume (Fig. 7F).
Finally, data from 117 additional plants indicate that the relationship between h and basal stem D is log-log nonlinear and that growth in height decreases with increasing plant size: log10h = 1.01 + 0.506 log10D – 0.347 log10D2 (r2 = 0.968, F = 2602, P < 0.0001). Thus, plants are essentially determinant in their growth in height, as reported for other species of columnar cacti (see Niklas, 1994
; Niklas and Buchmann, 1994
).
Root safety factors
Calculations based on engineering theory (see Appendix) showed that the ability to resist wind-throw decreases with increasing plant height due to a disproportional relationship between stem height and bayonet root depth such that MB increased with respect to MR. Using a parabolic vertical wind speed profile generated by umax = 10 m/s at h = 5 m, the relationships among h, MB, and MR were h = 0.263MB3.71 (n = 18, r2 = 0.999, F = 10 884, P < 0.0001, OLS = 3.71 ± 0.04) and h = 0.182MR0.51 (n = 18, r2 = 0.972, F = 565.5, P <0.0001, OLS = 0.512 ± 0.02). As a consequence, stem height and the safety factor were inversely related: h = 108(MR/MB)–1.81 (n = 18, r2 = 0.968, F = 489.8, P < 0.0001, OLS = –1.81 ± 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 = 4.6 m), the bayonet root's MR = 535.6 N·m. Over a broad range of maximum wind speeds, the relationship between MB and maximum wind speed was MB = 0.83umax2 (n = 8, r2 = 1.0). Thus, MR/MB = 535.6/0.83umax2 such that MR/MB 
1 when umax 25 m/s (Fig. 8). In this regard, meteorological data collected between January 1980 and October 1999 (provided by the Comision Nacional del Agua) for Empalme (located at the southern limit of P. pringlei in Sonora) indicate that umax = 26 m/s (August 1997). Thus, the largest plant was 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 = l1 071 N·m and umax = 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 |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXLITERATURE CITED |
|---|
), especially in light of unequal lateral root expansion (due to the uneven accumulation of secondary tissues) that, in tandem with the heterogeneity of wood stiffness, may differentially compact the surrounding soil, i.e., root development may establish auger-like growth that reduces the probability of soil-root shear failure (see, however, North and Nobel, 1997
). Yet, the allometry of P. pringlei clearly results in a steady erosion of the safety factor against wind-throw, which is consistent with the demographics of dead plants (F. Molina-Freaner, personal observation).
In contrast, the allometry of P. pringlei root anatomy and morphology favors water absorption and nutrient storage as plants increase in size. Even though the absolute cross sectional areas of root wood and cortex increase toward the stem base (with concomitant increases in the root axial second moment of areas and anchorage), the contribution of the cortex to transverse sectional area is greater than that of the wood 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 incompatibilities (Niklas et al., 2000
). However, living tissues also have the ability to store water during the rainy season (Mauseth, 1993
) and those in P. pringlei roots contain large quantities 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 significantly 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 fine (feeder) 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 fine 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 body of literature that reveals generalizations about root system functions must be couched in terms of potentially complex anatomical, biometric, mechanical, and environmental relationships (e.g., Ennos, 1993
; North, Huang, and Nobel, 1993
; Stokes, Fitter, and Couts, 1995
; Stokes and Mattheck, 1996
; Niklas, 1999
).
|
APPENDIX |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXLITERATURE CITED |
|---|
MB. In the absence of lateral root restraint, the vertical root will pivot at distance 
below ground (see Fig. A1A) and the sorrounding soil will fail plastically, resisting sideways motion with a unit force dFB per unit root length d such that dFB = 18
rd, where is soil shear strength, which varies across soil types and conditions (Broms, 1964
; Kézdi, 1974
; Hatanaka and Uchida, 1995
). In the case where the root pivots at L/2, the restoring moment MR acting along L is given by the formula MR = 
L/2–L/2 18r d = 9r(L2/2) (see Niklas, 1992
; Ennos, 1993
). If additional roots contribute to anchorage (Fig. A1B), the extremum is = L and MR = L0 18r d = 9rL2.
|
u2iSiCD, where is air density (1.2 kg/m3), ui is local wind speed, Si is stem element i sail area, and CD is the drag coefficient (1.0 for a cylinder; see Vogel, 1981
; Niklas, 1994
). For a tapered cylindrical stem, Si = diLi, where di = (di + dj)/2, Li = xi – xj, and xi and xj are the distances measured from the top of the stem to di and dj, respectively (see Fig. A1C). Since Fi = 0.5u2idi(xi – xj), the MB on stem element i is given by the formula Mi = 
ij=1 [0.5u2idi(xi – xj)](h – xi) (see Niklas and Spatz, 2000
). Localized wind bending moments thus decrease toward the stem base, whereas the total bending moment increases toward the stem base where it reaches maximum intensity Mmax.
Numerical solutions of Mi are required, since ui and di vary as a function of L. We modeled ui using the formula ui = umax[1 – (xi/h)]1/2 (see Niklas and Spatz, 2000
), where umax is maximum wind speed specified for an arbitary distance above ground (see Fig. A1C). Based on field measurements of plants differing in size (0.09 m h 4.6 m), we computed MB and its corresponding MR (using umax = 10 m/s at 5 m above ground), estimated the maximum wind speed each plant could sustain before wind-throw, and assessed the factor of safety using the quotient MR/MB.
|
FOOTNOTES |
|---|
4 Author for reprint requests (Phone: 607 255-8727; Fax: 607 255-5407; kjn2{at}cornell.edu
).
|
LITERATURE CITED |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXLITERATURE CITED |
|---|
Boke N. H. 1979 Root glochids and root spurs of Opuntia arenaria (Cactaceae). American Journal of Botany 66: 1085-1092[CrossRef][ISI]
Broms B. B. 1964 Lateral resistance of piles in cohesive soils. Journal of the Soil Mechanics and Foundation Division, Proceedings of the American Society of Civil Engineers SM2 90: 27-63
Casada J. H. L. R. Walton L. D. Swetnam 1980 Wind resistance of Burely tobacco as influenced by depth of plants in soil. Transactions of the American Society of Agricultural Engineers 23: 1009-1011
Coutts M. P. 1983 Root architecture and tree stability. Plant and Soil 71: 171-188
Coutts M. P. 1986 Components of tree stability in Sitka spruce on peaty gley soil. Forestry 59: 173-197
Crook M. J. A. R. Ennos 1996 The anchorage mechanics of mature larch Larix europea x L. japonica. Journal of Experimental Botany 47: 1509-1517
Dittmer H. J. 1937 A quantitative study of the roots and root hairs of winter a rye plant (Secale cereale). American Journal of Botany 24: 417-420[CrossRef][ISI]
Ennos A. R. 1993 The scaling of root anchorage. Journal of Theoretical Biology 161: 61-75[CrossRef]
Ennos A. R. 2000 The mechanics of root anchorage. Advances in Botanical Research 33: 133-157
Ennos A. R. A. H. Fitter 1992 Comparative functional morphology of the anchorage systems of annual dicots. Functional Ecology 6: 71-78
Felger R. S. M. B. Moser 1985 People of the desert and the sea. Ethnobotany of the Seri Indians. University of Arizona Press, Tucson, Arizona, USA
Gaines S. D. M. W. Denny 1993 The largest, smallest, highest, lowest, longest and shortest—extremes in ecology. Ecology 74: 1677-1692[CrossRef][ISI]
Gartner B. L. 1994 Root biomechanics and whole plant allocation patterns: responses of tomato to simulated wind. Journal of Experimental Botany 45: 1645-1654
Hatanaka M. 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 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
Kézdi Á. 1974 Handbook of soil mechanics, vol. 1, Soil physics. Elsevier Scientific, Amsterdam, The Netherlands
Mauseth J. D. 1993 Water-storing and cavitation-preventing adaptations in wood of cacti. Annals of Botany 72: 81-89
Nass H. G. M. S. Zuber 1971 Correlation of corn (Zea mays L.) roots early in development to mature root development. Crop Science 11: 655-658
Neeman M. J. L. Spencer-Smith 1975 An analysis of the problem of lodging with particular reference to wheat and barley. Journal of Agricultural Science 85: 495-507
Niklas K. J. 1992 Plant biomechanics. University of Chicago Press, Chicago, 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 saccharum roots. Journal of Experimental Botany 50: 193-200
Niklas K. J. S. L. Buchmann 1994 The allometry of saguaro height. American Journal of Botany 81: 1161-1168[CrossRef][ISI]
Niklas K. J. F. Molina-Freaner C. Tinoco-Ojanguren 1999 Biomechanics of the columnar cactus Pachycereus pringlei. American Journal of Botany 86: 767-775
Niklas K. J. F. Molina-Freaner C. Tinoco-Ojanguren D. J. Paollilo Jr 2000 Wood biomechanics and anatomy of Pachycereus pringlei. American Journal of Botany 87: 469-481
Niklas K. J. 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[ISI]
North G. B. P. S. Nobel 1997 Drought-induced changes in soil contact and hydraulic conductivity for roots of Opuntia ficus-indica with and without rhizosheaths. Plant and Soil 191: 249-258[CrossRef][ISI]
North G. B. B. Huang 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 Wissenschaften 33: 235-474
Preston C. E. 1900 Observations on the root system of certain Cactaceae. International Journal of Plant Biology (formerly the Botanical Gazette) 30: 348-351
Shreve F. 1964 Vegetation and flora of the Sonoran Desert. Stanford University Press, Stanford, California, USA
Stokes A. J. Ball A. H. Fitter P. Brian M. P. Coutts 1996 An experimental investigation of the resistance of model root systems to uprooting. Annals of Botany 78: 415-421
Stokes A. A. H. Fitter M. P. Coutts 1995 Responses of young trees to wind and shading: effects on root architecture. Journal of Experimental Botany 46: 1139-1146
Stokes A. C. Mattheck 1996 Variation of wood strength in tree roots. Journal of Experimental Botany 47: 693-699
Stokes A. B. C. Nicholl M. P. Coutts A. H. Fitter 1997 Responses of young Sitka spruce clones to mechanical perturbation and nutrition: effects on biomass allocation, root development, and resistant to bending. Canadian Journal of Forest Research 27: 1049-1057[CrossRef]
Stolzy L. H. K. P. Barley 1968 Mechanical resistance encountered by roots entering compact soils. Soil Science 105: 297[ISI]
Vogel S. 1981 Life in moving fluids. Willard Grant Press, Boston, Massachusetts, USA
Warning W. C. 1934 Anatomy of the vegetative organs of the parsnip. International Journal of Plant Biology (formerly the Botanical Gazette) 96: 44-72
Wilson B. F. 1975 Distribution of secondary thickening in tree root systems. In J. G. Torrey and D. T. Clarkson [eds.], The development and function of roots, 197–219. Third Cabot Symposium. Academic Press, London, UK
Whitaker T. 1970 The design of piled foundations. Pergamon Press, Oxford, UK
This article has been cited by other articles:
|
|
 |
|
  L. X. Dupuy, T. Fourcaud, P. Lac, and A. Stokes A generic 3D finite element model of tree anchorage integrating soil mechanics and real root system architecture Am. J. Botany, September 1, 2007; 94(9): 1506 - 1514. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
K. J. Niklas and H.-C. Spatz Allometric theory and the mechanical stability of large trees: proof and conjecture Am. J. Botany, June 1, 2006; 93(6): 824 - 828. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 K. J. NIKLAS Modelling Below- and Above-ground Biomass for Non-woody and Woody Plants Ann. Bot., January 2, 2005; 95(2): 315 - 321. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. G. Dubrovsky and L. F. Gomez-Lomeli Water deficit accelerates determinate developmental program of the primary root and does not affect lateral root initiation in a Sonoran Desert cactus (Pachycereus pringlei, Cactaceae) Am. J. Botany, June 1, 2003; 90(6): 823 - 831. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
D. J. Paolillo Jr and R. W. Zobel The formation of adventitious roots on root axes is a widespread occurrence in field-grown dicotyledonous plants Am. J. Botany, September 1, 2002; 89(9): 1361 - 1372. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||
