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Ecology |
2Department of Plant Biology, Cornell University, Ithaca, New York 14853-5853 USA 3Botanischer Garten der Albert-Ludwigs-Universität, Freiburg i. Br., D-79104 Germany
Received for publication August 15, 2000. Accepted for publication November 7, 2000.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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The highest factors of safety were calculated among the most ancient rhyniophyte and zosterophyllophyte species examined (e.g., Rhynia and Gosslingia), and, on average, decreased among the taller and geologically younger species. The tallest species examined (e.g., Archaeopteris and Diaphorodendron) had safety factors equal to or higher than those of some of their presumed ancestors (e.g., Psilophyton and Leclercqia). These trends were statistically more robust among rhyniophytes and their presumed descendants.
Even though the results comply with the hypothesis, numerous limitations of our protocol exist (e.g., the requirement for reliable whole-plant reconstructions). These are discussed in terms of our theory. Nonetheless, we believe our theory and protocol afford a reasonable opportunity to explore the effects of wind on early plant evolution.
Key Words: biomechanics • factors of safety • fossil plants • mechanical stability • wind-loading
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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; Chaloner and Sheerin, 1979
; Gensel and Andrews, 1984
; Stewart and Rothwell, 1993
; Taylor and Taylor, 1993
; Niklas, 1997
). During this time interval, the morphological repertoire of the sporophyte generation expanded from the comparatively simple open-dichotomous branching patterns characterizing the leafless axes of the earliest vascular plants to include anisotomous, pseudomonopodial, and monopodial branching patterns supporting micro- and megaphylls as well as a variety of different kinds of reproductive organs (Banks, 1968
; Chaloner and Sheerin, 1979
; Gensel and Andrews, 1984
).
This period of morphological diversification was attended by an equally impressive anatomical diversification (Banks, 1968
; Chaloner and Sheerin, 1979
; Gensel and Andrews, 1984
; Stewart and Rothwell, 1993
; Taylor and Taylor, 1993
). The vegetative axes of most, if not all, Silurian vascular plants were apparently mechanically supported by an undifferentiated parenchymatous cortex surrounding a centrally located strand of primary vascular tissues (Speck and Vogellehner, 1988, 1994
; Niklas, 1990, 1992
). By middle Devonian times, many vascular plants relied on stiffer and stronger primary tissues (e.g., collenchyma and sclerenchyma) or secondary tissues for mechanical support. This anatomical diversification permitted an increase in plant stature (Chaloner and Sheerin, 1979
; Niklas, 1997
). The most ancient sporophytes measured only a few centimeters in height, whereas the height of many late Devonian species rivaled that of some of tallest plants today (Mosbrugger, 1990
; Niklas, 1992, 1997
; Taylor and Taylor, 1993
; Bateman et al., 1998). Considerable attention has been paid to the evolution of plant biomechanics, particularly with regard to the capacity for self-support. Studies of fossil and living plants indicate that the anatomical evolution of progressively stiffer and stronger primary tissues increased the ability of stems to resist the bending forces induced by gravity and thus permitted an increase in plant height, which benefits photosynthesis and long-distance spore dispersal (Niklas, 1992, 1993, 1994
; Speck, 1994
; Speck and Vogellehner, 1994
; Rowe and Speck, 1998
; Speck and Rowe, 1999a
). Studies likewise show that the acquisition of secondary growth permitted a basipetal increase in the cross-sectional area of stems. This resulted in a reduction in the magnitudes of bending stresses, as well as an increase the axial second moment of area, both of which enhance the ability of a stem to support its mass and that of attached organs (Niklas, 1992, 1997
; Speck, 1994
; Speck and Vogellehner, 1994
). There is ample evidence that the early evolution of plant anatomy was as much a consequence of natural selection acting on the mechanical behavior of stems as on their physiology (Niklas, 1992
; Bateman et al., 1998
).
In contrast, comparatively few studies have addressed the evolutionary response of plants to the mechanical effects of wind-loadings (see, however, Niklas, 2000
; Niklas and Spatz, 2000
), even though simple calculations show that the drag forces exerted on aerial stems by wind pressure typically exceed those generated by gravity (Alexander, 1971
; Vogel, 1981
). For example, the bending moment due to wind-induced drag Md acting at the base of an untapered cylindrical stem with length L and radius r is given by the formula Md = 0.5 
a u2 Sp CD L, where a is the density of air, u is ambient wind speed, Sp is projected area, and CD is the drag coefficient. Since the maximum projected surface area of a cylinder is given by the formula Sp = 2 r L, it follows that the maximum moment due to wind-loading equals Md = a u2 r L2 CD. For the same stem oriented at any angle 
with respect to the vertical, the bending moment resulting from self-loading Ms acting on the base is given by the formula Ms = [(
r2 L2/2) ( – a) g sin ], where is the bulk density of the stem and g is the acceleration due to gravity (=9.81 m/sec2). Since the density of most plant tissues is 1000 times that of air, a rough approximation is Ms 
r2 L2 g sin /2. The quotient of these two moments Md/Ms equals 2 a u2 CD/ r g sin , which shows that the moment due to wind-loading exceeds that of self-loading even for comparatively modest wind speeds (e.g., calculations indicate that Md/Ms 2 when u = 3 m/sec and = 2°, assuming that a = 1.2 kg/m3, = 1000 kg/m3, CD = 1.0, and r = 0.01 m). Similar calculations for entire trees indicate that the stresses produced in stems by wind exceed those caused by the self-mass of stems for wind speeds between 1 and 5 m/sec, depending on the geometrical parameters used to model the tree (Speck, Spatz, and Vogellehner, 1990
).
Since the bending moments created by gravity and wind are additive, stems that are more than sufficient to support their own mass may mechanically fail when subjected to modest to large wind-induced drag. For example, the maximum bending stress 
M that develops in a cylindrical stem with length L and radius r is given by the formula M = 4 MT / r3, where MT = Md + Ms a u2 r L2 CD + ( r2 L2 g sin ) /2 = r L2 [a u2 CD + ( r g sin )/2]. Thus, max = (4 L2/ r2) [a u2 CD + ( r g sin )/2]. Assuming that a = 1.2 kg/m3, = 1000 kg/m3, CD = 1.0, and r = 0.01 m and assuming a tissue-breaking stress b of 10 MN/m2, calculations indicate that a horizontally cantilevered stem measuring one meter in length will mechanically fail by tissue rupture when u = 25 m/sec (i.e., M > b). It is thus reasonable to believe that early land plant evolution was as much influenced by the effects of wind as by the effects of gravity on stems and other aerial organs.
We explore this hypothesis by calculating the maximum bending stresses M produced by drag forces acting on the aerial portions of a constellation of early Paleozoic plants and by using the magnitudes of these stresses in tandem with those of empirically determined tissue-breaking stresses b of anatomically comparable, modern-day plants to estimate the factors of safety SF ("mechanical reliability") against wind-induced stem failure (i.e., SF = b/M). For each plant, we mathematically simulate a vertical wind speed profile, determine the plant surface area projected toward the wind as a function of height above ground, calculate the drag forces and the resulting bending moments and stresses acting on different portions of the plant body, and then compute the factors of safety based on the breaking stress of the tissue believed to serve as the principal stiffening agent at the base of each species (see Niklas, 2000
; Niklas and Spatz, 2000)
. Our objective is to evaluate whether the mechanical reliability of fossil plants adaptively changed during the early phases of land plant evolution.
This research agenda requires information about plant community structure (to estimate within-canopy speed profiles), the morphology of each species (to calculate projected areas), and stem anatomy (to select the appropriate tissue-breaking stress to compute a factor of safety). Clearly, for many fossil species, much uncertainty surrounds each of these requirements. Many aspects of fossil community structure are often poorly preserved; whole-plant reconstructions are always subject to revision as new information comes to light; and the basal anatomy of some species is either unknown or the subject of continued debate.
However, recent studies indicate that estimates of the drag-induced bending stresses acting in the base of plants are far more sensitive to variations in plant size and morphology than to the "geometry" of wind-speed profiles (Niklas, 2000
; Niklas and Spatz, 2000)
. By the same token, differences in the breaking stresses of unlignified primary plant tissues (e.g., parenchyma and collenchyma) are comparatively small and differ significantly from those of thick-walled, lignified primary or secondary tissues (e.g., sclerenchyma and secondary xylem) (Niklas, 1992
). Thus, errors in judgement concerning which wind-speed profile or tissue-breaking stress should be used in the analysis of wind-induced stem failure have far less effect on the conclusions drawn than errors resulting from the use of morphologically unrepresentative whole-plant reconstructions.
Nonetheless, we are aware of the limitations imposed by the fossil record on the protocol used in this study. The following is presented more as a theoretical than as an empirical evaluation of whether wind-induced bending stresses played a significant role in shaping early land plant morphology and anatomy.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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The silhouette of each reconstruction was darkened by hand and then scanned into the memory of a desktop computer equipped with the program WinDrag (developed by KJN; unpublished program) (see Fig. 1 for examples). The size of each "element" of the reconstruction (i.e., sporangia, axes, and leaves, if present) was then scaled with respect to the maximum height published in the literature (designated by HP) and the maximum stem diameter (designated here as D) reported in the literature for each species. The projected surface area Sp of each element i with scaled diameter di and length 
i was automatically computed by WinDrag based on the quotient of the number of pixels creating the image of the element and the total number of pixels falling in a portion of a grid system that was superimposed on the entire scanned image (Fig. 2). WinDrag also calculated one or more stem "path lengths" (i.e., the distance dt of each element i from the tip of an interconnected series of branches) for each species based on points of attachment ("nodes") entered into the computer's memory by the operator. The locations of nodes were determined by visual inspection of each reconstruction.
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For these and other reasons, we scaled the absolute size of each fossil plant reconstruction using two different techniques to estimate plant height as well as using the maximum plant height reported in the literature by different authors. The first of these two techniques used the empirically determined allometric relationships between height and basal stem diameters observed for a broad spectrum of extant plant species with nonwoody and woody axes or stems (e.g., moss sporophytes, pteridophytes, and arborescent palm, dicot, and gymnosperm species). This "allometric" technique has successfully predicted the height (= length) of representative intact fossil stems based on their basal stem diameters (see Niklas, 1994
). Allometrically determined plant heights are designated as HA throughout this paper.
The second technique estimated the height of fossil plant species by calculating the critical buckling height Hcrit (see Greenhill, 1881)
of stems based on their reported maximum basal stem diameter and dividing this height by a factor of safety SF against mechanical failure due to self-loading equal to 2.5. This "safety factor" height for self-loading is designated as HSF throughout this paper (i.e., HSF = Hcrit/SF = Hcrit/2.5; see Speck and Vogellehner, 1992, 1994
; Speck, 1994
; Speck and Rowe, 1999b
). This technique was successfully "tested" by calculating the known heights of extant herbaceous species based on their basal stem diameters. We note in passing that the use of Hcrit calculated in this fashion is not subject to the criticism of "circular logic," since these estimates of plant height are based on static loading conditions, whereas the factors of safety we calculate based on wind-induced bending moments and stresses are for dynamic loading conditions.
These two techniques were used to introduce a degree of internal consistency among all of the estimated plant heights used in our study, and as the basis of a "sensitivity" analysis that could highlight "problem taxa," that is, species for which height estimates vary widely depending on the technique used.
Drag-force and bending moment computations
The magnitude of the drag force Df exerted on each element i of a whole-plant reconstruction was calculated based on the formula Df = 0.5 Ui2 Sp CD, where is the density of air (taken at 1.2 kg/m3), Ui is the wind speed measured for each element i, CD is the drag coefficient (taken as 1.0), and Sp = di i.
The drag-induced bending moment acting on any series of elements i connected by nodes was computed using the formula Md = 
(0.5 a Ui2 Sp CD) dt = (0.5 a Ui2 di i CD) dt. This formula gives a "running sum," such that the bending moment increases basipetally toward the base of each series of interconnected elements and reaches its maximum value at the base of the plant.
Wind-speed profiles
The wind speeds used to calculate drag forces were computed based on a maximum wind speed of 10 m/sec at 10 m above ground. The wind speed at any distance h above ground for an open terrain was computed by means of the formula Uh = 10 m/sec (h/10 m)0.5. Within-canopy wind speeds Ui were then calculated based on the formula Ui = UH exp [a (hi/H – 1)], where UH is the wind speed at the top of a canopy with height H (i.e., UH = Uh when H = h), a is a scaling factor that increases from 1 to 5 as the number of plants in a community increases, and hi is the distance above ground measured anywhere within the canopy (Fig. 3). Thus, regardless of their different canopy heights and geological ages, this protocol assures each species "sees" the same above-canopy wind speed profile (i.e., the speed at the top of each canopy was scaled in the same manner with respect to absolute plant height). For the purposes of this study, each plant species was assumed to have grown in a densely packed community composed of plants of equivalent height (i.e., a = 5).
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for any element i of radius r reach their maximum intensities at the element's surface and are given by the formula = Md r/I, where I is the axial second moment of area. For a terete cylindrical element, this moment of area is given by the formula I = r4/4 such that = 4 Md/ r3 1.273 Md/r3. However, since the maximum bending stresses along the entire length of any stem occur at the base, where the maximum bending moment MM occurs, the maximum bending stresses M for an entire plant is given by the formula M = (32/ D3) (0.5 a Ui2 Sp CD) H (10/D3) (0.5 a Ui2 Sp CD) H, where D is maximum (basal) stem diameter and H is estimated plant height (i.e., either HP or HSF). This formula emphasizes that estimates of overall plant size (D and H) exert a powerful influence on estimates of stress, since D and H are used to scale the size of all elements i to compute projected surface area and thus drag forces and since D is raised to the third power to calculate stresses.
Factors of safety
The factor of safety was computed using the formula b/M, where b is the breaking stress of the plant tissue believed to serve as the principal stiffening agent at the base of each fossil species. For the purposes of our analyses, no distinction was made between tissue-breaking stress and the yield stress because any loading condition that exceeds the breaking stress will result in catastrophic mechanical failure and because any loading condition that results in tissue yielding will produce permanent plastic deformation, either of which can severely impair or kill a plant.
The values for the tissue-breaking stresses used to calculate the factor of safety were taken either from the primary literature or determined experimentally based on bending tests of tissue samples surgically removed from a variety of living plants (data are available upon request). The specific values used for b are as follows: parenchyma = 5 MN/m2, collenchyma = 7 MN/m2, primary tracheids = 25 MN/m2, sclerenchyma = 75 MN/m2, and secondary xylem = 80 MN/m2. These values are conservative in that they are neither the highest breaking stresses reported in the literature nor the highest determined by us experimentally for each of these tissues. For example, the breaking stresses of the hypodermal sterome in the basal parts of Equisetum giganteum and E. hyemale aerial stems, which consists either of collenchyma or nonlignified sclerenchyma, range between 30 MN/m2 and 80 MN/m2 (Spatz, Köhler, and Speck, 1998
; Speck et al., 1998
). Likewise, subepidermal lignified sclerenchyma isolated from the leaf stalk or midrib of Musa textilis has tensile breaking stresses that range between 35 MN/m2 and 80 MN/m2 depending on their location within the leaf.
We studied and analyzed thin sections and peels of many of the plants treated in this study (Speck, 1994
; Speck and Vogellehner, 1994
) and, in addition, surveyed the literature to determine the tissue composition of each fossil treated in this study. In most cases, exceptionally well preserved axes provided unambiguous anatomical information about which breaking stress should be used to compute the factor of safety (e.g., the cortex of Aglaophyton major and Rhynia gwynne-vaughanii is composed of parenchyma). However, in some cases, stem anatomy is either questionable or unknown. For example, it is not clear whether the outer cortex of Drepanophycus spinaeformis is composed of collenchyma or parenchyma, whereas the cortical tissues of Cooksonia spp. are essentially unknown. In these cases, the lower breaking stress among those of candidate tissues was used (e.g., the breaking stress of parenchyma was used to calculate the factor of safety for D. spinaeformis and Cooksonia spp.). For some other species, though having well preserved axes, it was impossible to decide in the fossil material whether the hypodermal sterome was built of collenchyma or sclerenchyma fibres (see Speck and Vogellehner, 1994
). In these cases, the lower breaking stress among the possible tissues was used (e.g., the breaking stress of collenchyma was used to calculate the factor of safety for Zosterophyllum llanoveranum, Gosslingia breconensis, and Psilophyton dawsonii). For this reason, the factors of safety reported here are likely to be conservative estimates of mechanical reliability.
Within-plant (longitudinal) variation in factors of safety
In addition to determining the factor of safety at the base of each plant fossil, we also determined the extent to which the factors of safety varied as a function of distance above ground along the length of each plant fossil reconstruction. Points of stem attachment were entered manually into computer memory and WinDrag computed the bending moments and stresses as well as the factor of safety at each attachment site based on estimates of local wind speed and scaled stem diameter and length (see above). A representative "path length" for each plant was then selected (i.e., a series of representative attached stems ascending from the base to the most elevated and distal portion of each reconstruction), and the factors of safety were plotted as a function of normalized (relative) plant height HN (where HN = 1.0 and 0.0 at the top and base of the plant, respectively).
Factors of safety were computed for different parts of the plant body assuming either a uniform tissue-breaking stress in the case of species lacking the capacity for secondary growth or different tissue-breaking stresses as a function of stem location in the case of species known to produce secondary tissues. For example, the breaking stress of parenchyma was used to compute the factors of safety for all portions of the branching infrastructure of Rhynia major and Asteroxylon mackiei, and for the more distal stems of Diaphorodendron vasculare and Archaeopteris, whereas the breaking stresses of sclerenchyma and wood were used to compute the factors of safety for the older, more proximal portions of the latter two species. The selection of which tissue-breaking stresses should be assigned to which portions of a woody plant body was, once again, conservative and based on anatomical inspection of well-preserved stems differing in size (and thus location).
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Plant size and wind speeds
A statistically significant relationship was found between estimated above-canopy wind speed UH and maximum stem diameter D for the 17 species, regardless of the technique used to estimate plant height. Regression of the log10-transformed data for UH (computed on the basis of HSF) against basal stem diameter gave log UH = 1.2 + 0.40 log D – 0.002 (log D)2 (r2 = 0.85, P < 0.0001). Regression of the log10-transformed data for UH (computed on the basis of HA) against basal stem diameter gave log UH = 1.5 + 0.30 log D – 0.24 (log D)2 (r2 = 1.0) (Fig. 5). Both of these relationships indicate that, on average, above-canopy wind speed is not expected to increase in direct proportion to an increase in basal stem diameter, especially for the tallest species in the data set (e.g., Archaeopteris, Diaphorodendron, and Psaronius). We interpret these relationships to indicate that an evolutionary increase in plant height was attended by a disproportionate increase in basal stem diameter, presumably as a mechanical adaptation to increases in above-canopy wind speeds resulting from an evolutionary increase in plant height.
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M varied curvilinearly or linearly as a function of estimated plant height depending on whether plant height was estimated allometrically, HA, or on the basis of a 2.5 safety factor against self-loading failure, HSF. However, regardless of the technique used to estimate plant height, bending stresses were predicted to increase among nonwoody species with increased height and to decrease relative to plant height among the taller species in the data set. Specifically, ordinary least squares regression analysis indicated that a second-order polynomial curve best fit the data when height was estimated on the basis of a 2.5 factor of safety, log M = 4.2 + 0.80 log HSF – 0.24 (log HSF)2 (r2 = 0.64, P < 0.0007), indicating that taller species in the data set experienced smaller bending stresses than their shorter counterparts relative to their absolute height (Fig. 6A). Likewise, regression analysis obtained a linear best fit between the maximum bending stress and plant height estimated allometrically, log M = 4.1 + 0.73 log HA (r2 = 0.76, P < 0.0001), indicating that the magnitude of the maximum bending stress decreased relative to plant height as absolute plant height increased across the species examined (Fig. 6B). Owing to the smaller sample size, similar regression analyses for each of the two species groups (rhyniophytes and related species, n = 9, and zosterophyllophytes and lycopods, n = 8) indicated weaker statistical correlations between the maximum bending stress and HA or HSF (0.36 
r2 0.59). However, in each case, the trend observed within each of the two groups agreed with the general trend observed when the two species groups were pooled.
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M = 5.5 + 0.76 log D (r2 = 0.75, P < 0.0001), indicating that M tends to decrease relative to D as plant height increases across species (Fig. 7A), whereas regression of the maximum bending stresses computed on the basis of HA gave log M = 5.3 + 0.37 log D – 0.12 (log D)2 (r2 = 0.77, P < 0.0001), indicating, once again, that M tends to be smaller relative to D for the taller species in the data set (Fig. 7B). Due to the smaller sample sizes, similar regression analyses for the two species groups (rhyniophytes and related species, n = 9, and zosterophyllophytes and lycopods, n = 8) indicated weaker statistical correlations between the maximum bending stress (computed on the basis of HSF or HA) and maximum stem diameter (0.21 r2 0.62). In each case, however, the trend observed for each of the two species groups agreed with the trend observed for the pooled species (n = 17).
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b/M decreased among progressively taller nonwoody species and then increased among progressively taller woody plant species. Based on HSF, ordinary least squares regression of the log10-transformed data for the 17 species gave log (b/M) = 2.7 – 0.26 log HSF + 0.55 (log HSF)2 (r2 = 0.35). Although not statistically robust (P < 0.048), the trend across species indicated that the tallest species had larger factors of safety than many species other than their smallest counterparts (Fig. 8A). Based on HA, regression of the log10-transformed data gave log (b/M) = 2.8 – 0.35 log HA + 0.25 (log HA)2 (r2 = 0.52), which is statistically significant (P < 0.0056) (Fig. 8B). Although regression analyses of the data from the two species groups failed to identify highly statistically significant relationships between the factor of safety and plant height, the trends observed for each of the two groups complied with that observed for the pooled data.
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b/M) = 2.9 + 0.62 log D + 0.30 (log D)2 (r2 = 0.50, P < 0.008), indicating that the safety factor decreased among progressively larger nonwoody species and then increased among the larger species in the data set (Fig. 9B). This correlation was a consequence of the data for rhyniophytes and related species, since regression gave log (b/M) = 2.8 + 0.61 log D + 0.30 (log D)2 (r2 = 0.54, P < 0.095) for these species. Nonetheless, the general trend in the data indicated that the factors of safety for the largest among the species examined were comparable to those of many of the smaller species in the data set. For example, the factor of safety (computed on the basis of a 2.5 factor of safety against self-loading failure) for Archaeopteris was comparable to that of Rhynia and not significantly above Zosterophyllum llandoveranum (see Fig. 9A).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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. Likewise, much remains to be learned concerning the community structure of many fossil plants, especially the spacing among neighboring conspecifics, which influences estimates of within canopy wind speeds (see Remy, Remy, and Hass, 1997
). For these reasons, attempts to quantify the wind speeds profiles and the bending moments and stresses resulting that influence early land plant evolution must be viewed with as much or more skepticism than we have tried to convey. However, as a theoretical exercise, we believe the approach presented here has merit, since it uses the same mathematical tools that have been successfully applied to study the effects of wind on living plants, which are consistent with those reported here. Even so, the following discussion is presented largely in the context of a theoretical treatment of the affects of wind-loading on early Paleozoic land plant evolution. Taken at face value, the results of this study are consistent with the hypothesis that the factor of safety against wind-induced mechanical failure decreased as plant height increased during the early stages of land plant evolution only to increase with the subsequent evolutionary origin of secondary growth among the rhyniophytes and their presumed descendant species. The data for the zosterophyllophytes and lycopods are less clear, since only very weak correlations were found between the factor of safety and plant height or stem diameter for the species of this group represented in our data set. Nonetheless, the largest lycopod in our data set, Diaphorodendron, is estimated to have had a substantial factor of safety compared to some of its herbaceous antecedents (e.g., Gosslingia), which is once again consistent with the hypothesis that arborescent species were adapted to substantial wind-loadings.
However, the data set used to evaluate whether factors of safety against wind-induced mechanical failure evidenced an evolutionary trend was heavily skewed in terms of sampling Devonian taxa. Only two Carboniferous taxa (Diaphorodendron and Psaronius) and only one Triassic species (Pleuromeia longicaulis) were represented among the 17 species examined by us. This bias in the age distribution of species, which was in part due to the availability of reliable whole-plant reconstructions, prevented us from drawing statistically meaningful conclusions regarding an evolutionary trend in the factors of safety. Qualitatively, however, an inverse relationship between plant size (measured either in terms of maximum stem diameter or estimated plant height) and the factor of safety (computed either on the basis of the bending stresses associated with HSF or HA) was observed (Fig. 11). This relationship accorded with the hypothesis that the evolutionary advent of the arborescent growth habit and the attending increase in plant size across species nonetheless either maintained or increased the factor of safety against wind-induced mechanical failure.
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Analyses of the factors of safety within the branched architecture of fossil arborescent taxa, such as Archaeopteris and Diaphorodendron, are also consistent with the hypothesis that plant evolution has responded to the effects of wind- as well as self-loading. Our analyses indicate that the factor of safety varies along the lengths of woody plants and reaches equivalently local minima among a constellation of smaller, more distal branches (see also Niklas, 2000)
. Similar patterns in the longitudinal variation of the factor of safety are reported for extant arborescent species (see Niklas and Spatz, 2000)
. Since peripheral portions of the arborescent plant body are the most susceptible to mechanical failure and since failure at the base of a tree is arguably more devastating, it is reasonable to suggest that some of the distant and most recent descendants of the earliest land plants have evolved adaptations to progressively larger wind-loadings as plant size increased such that they "self-prune" when subject to exceptionally high wind speeds. The loss of some younger stems can reduce drag and thus bending moments and stresses and in this way reduce the likelihood of trunk failure.
In contrast, our analyses of nonwoody early Paleozoic fossil plants indicates that their factors of safety decreased in a step-wise manner from the base to the top of the plant body. This pattern is unquestionably the consequence of their iso-dichotomous branching geometry and anatomical homogeneity, since each step-wise decrease in the factor of safety corresponds to the location of a bifurcation in the branching geometry at which point the wind-induced bending stresses experienced by the two more distal stems are additively transmitted to the subtending stem sharing much the same anatomical configuration and size. The resulting step-wise pattern of safety factors cannot be maintained indefinitely as overall plant size increases, since the most distal elements of the plant body, which support sporangia in the case of many species, would have safety factors approaching or dropping below unity. It is thus reasonable to conclude that the changes in the branching geometry attending the evolutionary transformation of nonwoody to woody plants were functionally adaptive in terms of coping with the larger drag forces taller plants typically experience.
From first principles, we know that the drag forces exerted by wind on the aboveground portions of plants increase as the density of neighboring plants decreases or as plant height, projected surface area, or wind speed increases. Previous studies also indicate that estimates of the drag forces acting on plants are far less sensitive to the shape of the wind-speed profile (and thus, to a limited degree, on estimates of community density) than to plant morphology (e.g., the frequency of branching and the manner in which stems taper). For this reason, we believe that precise knowledge of community structure and the shape of the wind speed profile is less essential than reliable morphological information when attempting to estimate the relative differences among the drag forces acting on different fossil plants.
Clearly, however, the absolute magnitudes of wind speeds are critical to estimating drag forces, since these forces are computed on the basis of the square of ambient wind speeds. In this regard, community structure and the locations of individuals are critical, since closely space conspecifics will reduce ambient wind speeds that will vary as a function of location within the same community. Individuals growing at the perimeter of a dense community are likely to experience higher wind speeds than those sheltered by others within the community as a whole. It is notable, however, that most extant plant species are thigmomorphogenetic such that individuals that experience chronic mechanical perturbation are reduced in size and produce more flexible organs compared to those that are sheltered from the wind. This response to wind reduces the drag forces exerted on individuals exposed to higher wind speeds (and thus increases the factor of safety for wind-loading) by reducing the surface area projected toward the wind, since absolute size is reduced and since organs can bend in the wind and thereby reduce their projected areas. Unfortunately, even though there is no reason to believe that thigmomorphogenesis did not evolve by early Paleozoic times, we have little information from the fossil record regarding the degree to which different species were capable of adjusting their size and the material properties of their tissues or organs in response to wind-induced mechanical perturbations.
From a theoretical perspective, it is clear that plant stature cannot increase without evoking large deformations or buckling unless stem diameter or tissue stiffness increases. This conclusion holds true for wind- as well as self-loading, because the magnitudes of bending forces increase nonlinearly and rapidly as a function of distance above ground due to an increase in wind speeds or the additive mass of the plant body. Even a small increase in stem diameter will dramatically increase the mechanical stability of a vertical plant stem, because the axial second moment of area (which is a measure of the contributions that absolute size, shape, and geometry make to the ability of a beam or column to resist bending) increases exponentially as a function of diameter. Likewise, for any force F, the magnitude of the resulting stress is reduced with even a modest increase in the diameter d of a terete stem, since = 4 F/ d2. The mechanical advantages of increased stem diameter are thus obvious and help to explain why plant height correlates so well with basal stem diameter across a broad taxonomic spectrum of extant plant species.
It is equally obvious that any increase in stem diameter increases the magnitude of self- and wind-loadings by increasing the mass and projected area elevated above ground. The benefits of evolving stiffer tissues and locating these agents at or just below the perimeter of the stem cross section are clear (since stiffer tissues can sustain higher bending stresses before they yield or break and because bending stresses reach their highest intensities at the surface of a flexed stem). Our data agree with this supposition. Taken at face value, they indicate that the most ancient vascular land plants had extremely large factors of safety. Their small stature and comparatively sparsely branched morphologies exposed them to comparatively low wind speeds and drag forces, which was more than adequate to compensate for the comparatively low breaking stresses of their parenchymatous or collenchymatous cortical tissues and the absence of secondary growth. However, with increasing height and branching, the factor of safety, on average, steadily declined (albeit not to potentially dangerous levels) despite the appearance of more stiff and strong cortical tissues (e.g., sclerenchyma). This trend of decreasing mechanical reliability was reversed with the appearance of species capable of manufacturing wood or of deploying and accumulating sclerified organs around the base of their stems (e.g., the adventitious roots of Psaronius), either of which could produce a broad stem base.
We believe that the protocol presented here is useful and holds the potential to shed light on the consequences of morphological and anatomical elaboration on the mechanical stability of terrestrial plants.
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FOOTNOTES |
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4 Author for correspondence (Phone: 607-255-8727; FAX: 607-255-5407; kjn2{at}cornell.edu)
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LITERATURE CITED |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Banks H. P. 1968 The early history of land plants. In E. T. Drake [ed.], Evolution and environment, 73–107. Yale University Press, New Haven, Connecticut, USA
———, P. M. Bonamo J. D. Grierson 1972 Lerclercqia complexa gen. et sp. nov., a new Lycopod from the Late Middle Devonian of eastern New York. Review of Palaeobotany and Palynology 14: 19-40[CrossRef][Web of Science]
———, S. Leclercq F. M. Hueber 1975 Anatomy and morphology ofPsilophyton dawsonii sp.n. from the Late Lower Devonian of Quebec (Gaspé), and Ontario, Canada. Palaeontographica Americana 8: 77-127
Bateman R. M. P. R. Crane W. A. Dimichele P. R. Kenrick N. P. Rowe T. Speck W. E. Stein 1998 Early evolution of land plants: phylogeny, physiology, and ecology of the primary terrestrial radiation. Annual Review of Ecology and Systamatics 29: 263-292
Beck C. B. 1962 Reconstructions of Archaeopteris and further consideration of its phylogenetic position. American Journal of Botany 49: 373-382
———. 1981 Archaeopteris and its role in vascular plant evolution. In K. J. Niklas [ed.], Paleobotany, paleoecology and evolution, vol. 1, 193–230. Praeger Press, New York, New York, USA
Bonamo P. M. H. P. Banks J. D. Grierson 1988 Lerclercqia, Haskinsia, and the role of leaves in delineation of Devonian Lycopod genera. International Journal of Plant Science (formerly Botanical Gazette) 149: 222-239
Chaloner W. G. A. Sheerin 1979 Devonian macrofloras. In M. R. House, C. T. Scrutton, and M. G. Bassett [eds.], The Devonian system Special papers in Palaeontology 23: 145-161
Croft W. N. W. H. Lang 1942 The Lower Devonian flora of the Senni Beds of the Monmouthshire and Breconshire. Philosophical Transactions of the Royal Society of London B 231: 131-163[CrossRef]
DiMichelle W. A. 1981 Arborescent lycopods of Pennsylvanian age coals: Lepidodendron, with description of a new species. Palaeontographica B 175: 85-125
———. 1985 Diaphorodendron, gen. nov., segregate from Lepidodendron (Pennsylvanian age). Systematic Botany 10: 453-458
———, and T. L. Phillips 1977 Monocyclic Psaronius from the Lower Pennsylvanian of the Illinois Basin. Canadian Journal of Botany 55: 2514-2524
Edwards D. 1969 Further observations on Zosterophyllum llanoveranum from the Lower Devonian of South Wales. American Journal of Botany 56: 201-210[CrossRef][Web of Science]
———. 1970a Further observations on the Lower Devonian plant, Gosslinigia breconensis Heard. Philosophical Transactions of the Royal Society of London B 258: 225-243[CrossRef]
———. 1970b Fertile Rhyniophytina from the Lower Devonian of Britain. Palaeontology 13: 451-461
———, K. L. Davies L. Aex 1992 A vascular conducting strand in the early land plant Cooksonia. Nature 357: 683-685
———, U. Fanning J. B. Richardson 1986 Stomata and sterome in early land plants. Nature 323: 438-440[CrossRef]
———, and E. C. W. Rogerson 1979 New records of fertile Rhyniophytina from the late Silurian of Wales. Geological Magazine 116: 93-98[Abstract]
Edwards D. S. 1980 Evidence for the sporophytic status of the Lower Devonian plant Rhynia gwynne-vaughanii Kidston and Lang. Review of Palaeobotany and Palynology 29: 177-188[CrossRef]
———. 1986 Aglaophyton major, a non-vascular land-plant from the Devonian Rhynie Chert. Botanical Journal of the Linnean Society 93: 173-204
Eggert D. A. 1974 The sporangium of Horneophyton lignieri (Rhyniophytina). American Journal of Botany 61: 405-413
Fairon-Demaret M. 1971 Quelques charactères des Drepanophycus spinaeformis Göppert. C.R. Acad. Sci. Paris, Ser. D 273: 933-935
Gensel P. G. H. N. Andrews 1984 Plant life in the Devonian. Praeger Press, New York, New York, USA
Greenhill A. G. 1881 Determination of the greatest height consistent with stability that a vertical pole or mast can be made, and of the greatest height to which a tree of given proportions can grow. Proceedings of the Cambridge Philosophical Society 4: 65-73
Grierson J. D. 1976 Leclercqia complexa (Lycopsida, Middle Devonian): its anatomy, and the interpretation of pyrite petrifications. American Journal of Botany 63: 1184-1202
Hartman C. M. H. P. Banks 1980 Pitting in Psilophyton dawsonii, an early Devonian trimerophyte. American Journal of Botany 67: 400-412[CrossRef][Web of Science]
Kasper A. E. H. N. Andrews W. H. Forbes 1974 New fertile species of Psilophyton from the Devonian of Maine. American Journal of Botany 61: 339-359[CrossRef][Web of Science]
Kidston R. W. H. Lang 1917 On Old Red Sandstone plants showing structure, from the Rhynie chert bed, Aberdeenshire. Part I. Rhynia Gwynne-Vaughani, Kidston and Lang. Transactions of the Royal Society of Edinburgh 51: 761-784
———, and ———. 1920a On Old Red Sandstone plants showing structure, from the Rhynie chert bed, Aberdeenshire. Part II. Additional notes on Rhynia Gwynne-Vaughani, Kidston and Lang; with descriptions of Rhynia major, n.sp., and Hornea Lignieri, n.g., n.sp. Transactions of the Royal Society of Edinburgh 52: 603-627
———, and ———. 1920b On Old Red Sandstone plants showing structure, from the Rhynie chert bed, Aberdeenshire. Part III. Asteroxylon Mackiei, Kidston and Lang. Transactions of the Royal Society of Edinburgh 52: 643-680
———, and ———. 1921 On Old Red Sandstone plants showing structure, from the Rhynie chert bed, Aberdeenshire. Part IV. Restorations of the vascular cryptogams, and discussion of their bearing on the general morphology of the Pteridophyta and the origin of the organisation of land-plants. Transactions of the Royal Society of Edinburgh 52: 831-854
Lyon A. G. 1964 Probable fertile region of Asteroxylon mackiei K. and L. Nature 203: 1082-1083[Medline]
Meyer-Berthaud B. S. E. Scheckler J.-L. Bousquet 2000 The development of Archaeopteris: new evolutionary characters from the structural analysis of an Early Famennian trunk from southeast Morocco. American Journal of Botany 87: 456-492
Morgan J. 1959 The morphology and anatomy of American species of the genus Psaronius. Illinois Biological Monographs 27: 1-108
Mosbrugger V. 1990 The tree habit in land plants. Lecture Notes in Earth Sciences 28: 1-116
Niklas K. J. 1990 Biomechanics of Psilotum nudum and some early Paleozoic vascular sporophytes. American Journal of Botany 77: 590-606[CrossRef][Web of Science]
———. 1992 Plant biomechanics. The University of Chicago Press, Chicago, Illinois, USA
———. 1993 Influence of tissue-density specific mechanical properties on the scaling of plant height. American Journal of Botany 72: 173-179
———. 1994 Plant allometry. The University of Chicago Press, Chicago, Illinois, USA
———. 1997 The evolutionary biology of plants. The University of Chicago Press, Chicago, Illinois, USA
———. 2000 Computing factors of safety against wind-induced tree stem damage. Journal of Experimental Botany 51: 797-806
———, and H.-Ch. Spatz 2000 Wind-induced stresses in cherry trees: evidence against the hypothesis of constant stress levels. Trees, Structure and Function 14: 230-237[Web of Science]
Phillips T. L. W. A. Dimichelle 1992 Comparative ecology and life-history biology of arborescent Lycopsids in late Carboniferous swamps of Euramerica. Annals of the Missouri Botanical Gardens 79: 560-588[CrossRef][Web of Science]
Rayner R. J. 1984 New finds of Drepanophycus spinaeformis GÖPPERT from the Lower Devonian of Scotland. Transactions of the Royal Society of Edinburgh 75: 353-363
Remy W. D. Remy H. Hass 1997 Organisation, Wuchsform und Lebensstrategien früher Landpflanzen des Unterdevons. Bot. Jahrb. Syst 119: 509-562
Rettallak G. J. 1975 The life and times of a Triassic lycopod. Alcheringa 1: 3-29
Rowe N. P. T. Speck 1998 Biomechanics of plant growth forms: the trouble with fossil plants. Review of Palaeobotany and Palynology 102: 43-62
Schweitzer H.-J. 1979 Die Zosterophyllaceae des rheinischen Unterdevons. Bonner Paläobotanische Mitteilungen 3: 1-32
———. 1980 Über Drepanophycus spinaeformis. Bonner Paläobotanische Mitteilungen 7: 1-29
———. 1983 Die Unterdevonflora des Rheinlandes. 1. Teilung Paläontographica B 189: 1-138
———. 1990 Pflanzen erobern das Land. Kleine Senckenberg-Reihe Nr. 18, Frankfurt, Germany
Spatz H.-C. L. Köhler T. Speck 1998 Biomechanics and functional anatomy of hollow stemmed Sphenopsids: I. Equisetum giganteum. American Journal of Botany 85: 305-314
Speck T. 1994 A biomechanical method to distinguish between self-supporting and non self-supporting plants. Review of Palaeobotany and Palynology 81: 65-82[CrossRef]
———, and N. P. Rowe 1999a A quantitative approach for analytically defining size, form and habit in living and fossil plants. In M. H. Kurmann and A. R. Hemsley [eds.], The evolution of plant architecture, 447–479. Royal Botanic Gardens Kew, Kew, UK
———, and ———. 1999b Biomechanical analysis. In T. P. Jones and Rowe [eds.], Fossil plants and spores: modern techniques, 105–109. Geological Society, London, UK
———, H.-C. Spatz D. Vogellehner 1990 Contribution to the biomechanics of plants. I. Stabilities of plant stems with strengthening elements of different cross-sections against weight and wind forces. Botanica Acta 103: 111-122[Web of Science]
———, O. Speck A. Emanns H.-C. Spatz 1998 Biomechanics and functional anatomy of hollow stemmed sphenopsids: III. Equisetum hyemale. Botanica Acta 111: 366-376
———, and D. Vogellehner 1988 Biophysical examinations of the bending stability of various stele types and the upright axes of early "vascular" land plants. Botanica Acta 101: 262-268[Web of Science]
———, and ———. 1992 Biomechanics and maximum height of some Devonian land plants. In J. Kovar-Eder [ed.], Palaeovegetational development in Europe and regions relevant to its palaeofloristic evolution, 413–422. Museum of Natural History, Vienna, Austria
———, and ———. 1994 Devonische Landpflanzen mit und ohne hypodermales Sterom—Eine biomechanische Analyse mit Überlegungen zur Frühevolution des Leit- und Festigungssystems. Palaeontographica B 233: 157-227
Stewart W. N. G. Rothwell 1993 Paleobotany and the evolution of plants,. 2nd ed. Cambridge University Press, Cambridge, UK
Taylor T. N. E. L. Taylor 1993 The biology and evolution of fossil plants. Prentice Hall, Englewood Cliffs, New Jersey, USA
Vogel S. 1981 Life in moving fluids. Willard Grant Press, Boston, Massachusetts, USA
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