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Tropical Biology |
2Department of Geography, Concordia University, 1455 de Maisonnueve Boulevard, Montreal, Quebec, H3G 1M8; 3Centro de Investigaciones en Ecosistemas, Universidad Nacional Autónoma de México, Apartado Postal 27-3 (Xangari), 58089, Morelia, Michoacan, Mexico
Received for publication July 23, 2004. Accepted for publication February 21, 2005.
ABSTRACT
The aerodynamic constraints operating on the wind-dispersed, drag-producing diaspores of several species of the tropical family Bombacaceae were examined. Kapok (the drag-promoting appendage) was best characterized as a moderately flattened hemisphere impervious to air movement. The kapok shape was not isometric: kapok planform area was proportional to the kapok mass raised to the power 0.52 rather than to the 0.67 expected from isometry. Thus, necessarily, terminal velocity rises with seed mass much faster in this group than among taxa with winged seeds. Further, we derived the optimality argument to show that the kapok mass ought to be about 50% of the total diaspore mass (seed plus kapok). While seven of eight species had a lower kapok investment than this, and none were especially close to the theoretically optimal value, nonetheless the kapok investment values were hardly draws from a random distribution. Finally, the kapok fibers of these Bombacaceae species begin to bend at a drag of about 0.005 N, and this sets an upper limit on the efficient diaspore size of about 250 mg for the seed mass. This latter value is similar to the mass of the largest seed we know of in this family.
Key Words: aerodynamics • Bombacaceae • kapok • seed dispersal • seed size • wind
The idea that larger diaspores are necessarily more poorly dispersed by the wind (e.g., van der Pijl, 1982
) is of interest for two reasons. First, ignoring dispersal by animals, the notion contributes to the conventional idea of a trade-off in evolutionary ecology between juvenile survivorship (promoted by large seed size: e.g., Jurado and Westoby, 1992
; Greene and Johnson, 1998
; Nathan and Muller-Landau, 2000
; Willson and Traveset, 2000
) and dispersal capacity. Second, it underpins the standard explanation for why large-seeded species are typically animal-dispersed while wind dispersal is almost invariably limited to seed masses less than about 1 g (Augspurger, 1986
; Greene and Johnson, 1993
; Tackenberg et al., 2003
). For wind-dispersed seed populations, median dispersal distance is inversely related to terminal velocity (Kohlermann, 1950
; Greene and Johnson, 1989; Nathan, 2001
; Tackenberg, 2003
), and terminal velocity (vf), in turn, is related to seed mass (ms) as:
 | (1) |
), plume loading (Ap for the drag-producing pappus of Asteraceae as in Greene and Johnson [1990]
), or disk loading (AD as mentioned by Greene and Johnson [1990]
for a set of fibers contributing to such a high solidity that the appendage can be regarded as a solid disk). While the important role of terminal velocity in longer distance dispersal is clear (Nathan et al., 2002b
; Tackenberg, 2003
), the following questions arise: Why must terminal velocity increase with seed mass? Why do larger seeds not have a correspondingly larger investment in ma (and thus A)?
For one class of winged seeds (asymmetric samaras), Greene and Johnson (1993)
showed that aerodynamic stability required that the wing shape be maintained within certain limits, otherwise the wing would stall and stable autorotation would be lost as the diaspore plummeted. Thus with this imposed isometry, vf 
ms(1–b)/2 (where b is the allometric exponent relating appendage mass to area). Given isometry and simple mass/volume relations, necessarily b = 0.67 and vf m0.167. But, how does this relate to drag-producing diaspores? The fibers of Asteraceae or Bombacaceae and similar families need not, of course, avoid stalling, so what is the constraint? Greene and Johnson (1990)
hinted at the answer when they showed that the fibers of an artificially ballasted Asclepius would bend. This bending reduces A (the drag-producing area) and thus increases vf. For a given seed mass, there must then be a limiting drag at which fibers will bend and thus no amount of appendage augmentation can forestall an increase in terminal velocity. Our first objective therefore is to model the aerodynamics of several species of the family Bombacaceae to discover whether there are systemic limits to terminal velocity given a particular seed mass. Effectively, we want to know the drag at which the kapok fibers begin to bend as this sets an upper limit to efficient dispersal using this aerodynamic mode. (We assume here that selection is for the lowest possible terminal velocity and, thus, for the highest possible dispersal distance.)
A second objective, necessary for understanding optimization, involves the characterization of the area (A) in the loading value for Bombacaceae. Augspurger (1986)
measured A as AD (the planform area of the kapok mass, which we here are calling the disk loading but she referred to as the wing loading) for her drag-producing species and pointed out that the square root of disk loading led to a significant correlation when regressed against terminal velocity. By contrast, Greene and Johnson (1990)
in their study of a different drag-producing taxon, the Asteraceae, used Ap (the total projected area of all the fibers comprising the pappus). Thus, as we examine the aerodynamics of the Bombacaceae, a second line of inquiry involves a test to determine which conceptualization of area is more appropriate for this family.
A third objective concerns the slope of the regression line for vf as a function of the square root of the loading value. In the best study of this relationship among a large number of aerodynamic types, Augspurger (1986)
found that all the winged (lift-producing) categories had similar slopes (although some differed in intercept). By contrast, the drag-producing group (mainly her Bombacaceae) had a much steeper slope than the others. A possible explanation, to be explored here, is that the three-dimensional diaspores of the Bombacaceae have a "packaging" problem on the limited surface of the fruit. (Augspurger [1986]
provides line drawings of Bombacaceae diaspores.) While the essentially two-dimensional diaspores of winged species can be packed in a wide variety of ways (e.g., Jacaranda seeds neatly stacked within their hard disklike fruits or paired Acer samaras attached to peduncle clusters or Pinus samara pairs enclosed under the scales of an ovulate cone), the kapok must be expanded on an already-crowded surface. That is, the area adjacent to each kapok-seed unit is already filled with the kapok of the neighboring unit. Augmentation of the kapok can only result then in an elongation of the unit or a further increase in its density of fibers rather than as an increase in the planform area of the unit. Thus, Bombacaceae may be poorer at translating augmentation to the appendage mass into additional planform area. Simply, with A mkb (where mk is the kapok mass and A is the planform area), then b must be smaller for the Bombacaceae than for taxa with winged seeds (where b = 0.67).
A final issue concerns variation in the terminal velocities at the population scale. As pointed out by Nathan et al. (2002a)
, modelling seed dispersal by wind for tropical species requires that we understand the magnitude of the relative variation in terminal velocity (i.e., the coefficient of variation, CV) within a population. For mid-latitude species, the CV is so small relative to vertical turbulence that it can simply be ignored in modelling (Debain et al., 2003
; Nathan et al., 1996
; Greene and Johnson, 1992
). Greene and Johnson (1992)
went further, arguing that the CV of terminal velocity had to be greatly constrained because it was a function of two other factors (as before: diaspore mass and area) that lay inside a square-root term. Aside from Augspurger's (1986)
rather small samples (N = 3–15 specimens per species), there is little information available to compare the CV of tropical diaspores with the better-studied mid-latitude species. We intend, therefore, to measure it both within and among fruits of two Bombacaceae species.
MODELLING
The well-known equation relating terminal velocity (vf) to an areal (A) measure is
 | (1) |
is the density of air (assumed to be 1.2 kg/m3), A is the characteristic diaspore area (in m2), and CD is the drag coefficient.
How best to define the diaspore area of a species in the Bombacaceae? Following Greene and Johnson (1990)
in their study of the Asteraceae, one might characterize area as the projected area (Ap) of a set of cylinders:
and d are the length and diameter, respectively, of each of the N fibers, and 
is the angle of attack between the fiber and the horizontal. Unlike the Asteraceae, the kapok fibers of the Bombacaceae have a variety of values. For simplicity in what follows we will assume a uniform distribution of and use the resulting mean value for cos() of 0.64. (The unknown true mean cannot be far from this value, as inspection reveals no obvious preferred orientation for the fibers.)
The drag coefficient (CD) of a cylinder depends on the dimensionless Reynolds number (Re) as
 | (3) |
is the kinematic viscosity of air (0.000015 m2/s) and d is the cylinder diameter (in m). Under this conception, given that Re values will all be in the range of 1–3, we can use the empirical expression of Laws and Livesay (1978)
to define this drag coefficient:
 | (4) |
The alternative is to characterize the kapok not as an array of cylinders but as a solid object that deflects air around itself during descent. If so, the area of interest (A in equation 1) is AD, the projected outline of the kapok mass. In turn, the diameter (d) in the Re calculation (equation 3) becomes the diameter of the entire kapok mass. Prediction of the drag coefficient now requires that we characterize the shape of this mass (disk or sphere). Over our range of Re (now 1200 to 10 000), we expect
 | (2) |
), or
 | (3) |
). As we shall see, the kapok mass would best be idealized as a hemisphere with the planar side on the bottom. If so, then the conception of the kapok as a solid leads to an expected CD somewhat intermediate between a sphere and a disk: CD 
0.85.
Viewing the kapok as a mass investment (mk), let us recast equation 1 as:
 | (5) |
Given that terminal velocity is the single most important biological trait controlling seed dispersal by the wind (Tackenberg et al., 2003
), one asks: Are the allocations to kapok mass (mk) optimal; i.e., does the diaspore achieve the minimal terminal velocity possible with the investment of mk/mT given the ms? For any function such as this proportionality (5), vf is minimized when mk/mT is equal to 1–b.
Rewriting Equation 1 as a general argument for the minimal terminal velocity (vfmin) achievable granted a particular seed mass (ms) for any drag-producing diaspore, we have:
 | (6) |
MATERIALS AND METHODS
Study site
The study site is located in the central Pacific coast of Mexico within and surrounding the Chamela-Cuixmala Biosphere Reserve (ca. 19°30' N, 105°03' W). This 13 200-ha reserve is located halfway between Puerto Vallarta, Jalisco, and Manzanillo, Colima. The predominant vegetation type in this area is tropical dry forest. Average annual rainfall is 707 mm with a dry season from November through June. The majority of the tree species are deciduous, abscising their leaves and producing flowers during the dry season (Bullock and Solís-Magallanes, 1990
).
Study species
We concentrated on two Ceiba species on the west-central coast of Mexico. Ceiba aesculifolia is a Neotropical species distributed from Mexico to northern Costa Rica (Cascante-Marín, 1997
). Trees may grow up to 20 m in height and have diameters of 20–50 cm. Ceiba aesculifolia has large (10–16 cm) flowers with five brown pubescent petals and five white filaments with yellow stamens. Styles are on average 15 cm long and surpass the stamens by 1–2 cm. Ceiba aesculifolia blooms from April through July, with a peak in May. Bats are the main pollinators of this principally self-incompatible tree. Ceiba aesculifolia initiates fruit development at the end of the dry season and dehisce mature fruits during the following dry season. This pattern suggests that seed dispersal may be an important selective factor that constrains the flowering period of these Bombacaceous trees (Lobo et al., 2003
). Fruits are five-valved, woody, and dehiscent with abundant kapok fibers surrounding the seeds for wind dispersal (Cascante-Marín, 1997
). Each fruit contains an average of 100 seeds with a mean mass of 0.12 g.
Our second species, C. grandiflora, has only been reported from the states of Jalisco and Colima, Mexico, and thus appears to be endemic to the tropical dry forest in this region (Lott, 1993). This is a relatively short species (<12 m) with a diameter up to 60 cm. The actinomorphic flowers are cream-colored with petals approximately 9–12 cm long with five stamens with cream-colored filaments united at the base. Leaves are digitate compound and abscise prior to flowering in the dry season and produce new leaves in the rainy season. Ceiba grandiflora begins flowering in December, approximately 2 mo after the beginning of the dry season, and its extended flowering continues until the middle of June; peak flowering for this species was observed in April (Lobo et al., 2003
). The bats Glossophaga soricina, Leptonycteris curasoae, and Musonycteris harrisoni are the most common pollinators of this mainly self-incompatible tree (Quesada et al., 2003
). Fruits of C. grandiflora dehisce during the dry season after flowering (Lobo et al., 2003
). Fruits are five-valved, woody, and dehiscent with abundant kapok fibers surrounding the seeds for wind dispersal (Quesada et al., 2003
). Each fruit contains an average of 60 seeds with a mean seed mass of 0.26 g.
Seeds and kapok were obtained from eight mature but unopened fruits collected from eight different C. aesculifolia trees in January 2003 and nine mature but unopened fruits from seven C. grandiflora trees collected in May 2003.
Additionally, we sampled five diaspores of Pseudombombax ellipticum taken from a single fruit found on an individual in the Chamela area.
Seed release from fruits
To insure that we did not modify the kapok in any way, we attached seeds to a wooden post inside an empty swimming pool and let the wind (or in some cases a fan) abscise the diaspores. The high walls of the pool forced the seeds to remain inside this enclosure. After the fruit was clearly emptied of seeds, we randomly selected about 30 seeds on the floor of the pool from each C. aesculifolia fruit and 15 seeds from each C. grandiflora fruit, ignoring any seeds that were clearly small aborts. Subsequent mass measurements and cutting tests would allow us to detect which of the apparently normal seeds were actually empty; these empty seeds were not included in the samples in Table 2.
|
, we adopted the handy formula of Clements (1977)
:
 | (4) |
We also examined the effect of artificially compressing the kapok of a C. aesculifola diaspore, thus increasing its disk loading. Each specimen had two terminal velocity measurements: first as a normal diaspore and then with its kapok compressed (after forcing it into a square wooden frame). Kapok planform area (AD) was measured before and after compression.
To test the drag limits where fiber bending begins, we also worked with empty-seeded and modified C. aesculifola specimens. For a sample of apparently normal diaspores, we glued pieces of solder, varying in size, to each seed. For a smaller sample of diaspores, we clipped off small parts of the kapok but did not modify the diaspore in any other way. The next year (2004) we filmed the descent of some specimens with solder glued to the seed to determine more directly the drag at which bending began. The film was running at a speed of 30 frames/s.
Masses of kapok and seed (or modified seed) were determined on an electronic balance. For C. grandiflora, we determined kapok area as did Augspurger (1986)
as the apparent area given by the longest diameter. This measure, as she originally pointed out, exaggerated the apparent kapok area. For two fruits of C. aesculifolia, we estimated area in this way but also in a second, more accurate, way. After the terminal velocity measurements were completed, we traced the outline of the kapok as closely as possible. On average, this more accurate measurement yielded an apparent area 15% smaller than the Augspurger (1986)
approach; i.e., the projected circumference was not perfectly circular. In what follows all the area measurements of C. grandiflora and Auguspurger's (1986)
, five Bombacaceae species were multiplied by 0.85.
Augspurger (1986)
gives mean values for total mass for each species, but they are not subdivided into kapok vs. seed mass. However, Augspurger (1988)
for the same species on Barro Colorado Island provides the mass allocation. While the specimens in this latter paper are not the same individual specimens in the first paper, nonetheless, the mean values for total mass and for area are similar to those of Augspurger (1986)
with most of the means within a few percentages of one another.
Measurements on individual fibers
We measured kapok fiber diameters of C. aesculifolia and P. ellipticum (but not C. grandiflora) using our specimens. We used fibers from herbarium specimens for the five species of Augspurger (1986)
(see Table 1). We also measured length and (using groups of fibers) density (in kg/m3) based on these herbarium specimens from the Missouri Botanical Garden (St. Louis, Missouri, USA).
|
Preabscission changes in Ceiba diaspore morphology
A Ceiba fruit has a thick exocarp that turns from green to brown as the seeds mature on the tree. Longitudinal separation layers develop on the drying exocarp, which then splits into five segments that separately fall from the remaining fruit. These five segments correspond to the original five locules of the ovary. Each locule of the fruit contains two rows of about 16 seeds each in C. aesculifolia or about 12 seeds in C. grandiflora. In C. aesculifolia, less than 3% of the seeds per fruit are either shriveled aborts or unfilled. In C. grandiflora, about half of these seeds are aborts. Concentrated around each seed are bundles of kapok fibers, with around five fibers per bundle and each fiber a few centimeters long. Most bundles are tenuously attached to the segment, but a few are attached to the seed. These damp fibers are initially matted against the placenta, but drying after the loss of the exocarp leads to their expansion, a process that is especially rapid if they are exposed to direct sunlight. The ends of the fibers of separate bundles intertwine, causing many of the bundles (as well as the seed) to detach from the fruit. At this point, each diaspore is essentially a flattened hemisphere of interlocking fiber bundles with a seed very loosely contained inside. Each diaspore is also interwoven (but more modestly) with neighboring diaspores. The drag exerted by high-magnitude winds easily separates a diaspore from its neighbors, thus effecting abscission.
The preabscission diaspore development of P. ellipticum morphology is quite similar to that of Ceiba. The diaspore is a modestly flattened "ball" of kapok fibers surrounding the seed (see the line drawing in Augspurger [1986]
).
Choice of aerodynamic model
Rearranging equation 1 with area defined as Ap (a set of cylinders), we obtained CD for the eight species ranging from 0.09–0.54. By contrast, using the empirical formula of White (1974)
(equation 2), we obtained a range of expected CD values from 2.25–4.68 (Table 1: our three species plus five from Augspurger [1986]
). Because the predicted CD values were 6–24 times greater than the observed values, we conclude that the diaspores of these species cannot be regarded aerodynamically as an array of cylinders. With the area in equation 1 defined as AD (an impenetrable disk of kapok), the fit between predicted and observed was much better. The observed CD (Table 1) ranged from 0.5–1.06. Recall that if the diaspore was regarded as a sphere, we expected CD 0.5, while a disk would yield CD 1.2. Sensibly, our resulting CD (average = 0.80) lay almost exactly between these two extremes because we are dealing with what is best idealized as an oblate hemisphere.
Figure 1 restates the foregoing argument with the observed terminal velocity vs. the predicted value (based on equation 1 with CD = 0.8 and the observed mT and AD in Table 1). A regression of observed on predicted for these eight species of Bombacaceae was highly significant (r2 = 0.91; P < 0.05), with the intercept not significantly different from 0 nor the slope significantly different from 1.0 (t tests; P > 0.05).
|
, the angle of attack, would have to increase due to the compression.) What we see in Fig. 2 is a straightforward argument in support of the idealization of the diaspore as a solid. From equation 1, we expect
 | (5) |
|
), but the difference lies in the solidities Ap/AD (equivalent in Table 1 to the ratio of the CD for the cylinder concept to the CD for the solid). The solidities of five Asteraceae ranged from 0.08–0.16 whereas the Bombacaceae here were much denser, with solidities from 1.5–10.2. In conclusion, we can regard the diaspore as essentially a solid body with a CD roughly intermediate between an idealized sphere and an idealized disk. The observed mean CD for all eight species (Table 1) was 0.78, and we recommend this value of drag coefficient for any subsequent prediction of terminal velocity with members of the Bombacaceae.
Is the ratio of kapok mass to total diaspore mass near the optimum?
We obtained the relationship of AD to mk (kapok mass) for the diaspores of the two fruits of C. aesculifolia where we measured both quantities:
 | (6) |
 | (7) |
|
 | (7) |
The drag at which fibers begin to bend
Figure 4 shows the relationship between terminal velocity and a variant on the square root of disk loading. (Instead of disk area, which was not measured for these specimens, we measured the kapok mass.) The proxy we used in the denominator of disk loading was mk0.5, as in equation 5. These C. aesculifolia specimens were either hollow-seeded, had some kapok removed, or had the mass augmented with solder. From equation 1 (supplemented with the relationship between disk area and kapok mass in equation 7), we expected a linear relationship in Fig. 4, but it becomes modestly curvilinear at about a drag of about 0.004 N and decidedly curvilinear at a total mass value corresponding to a drag of about 0.005 N. The departure from linearity was due to bending of the kapok fibers for the diaspores with the greatest amount of attached solder: as the diaspore fell, the mass of kapok fibers streamlined in response to the increase in drag. When a heavily weighted seed struck the floor, the kapok, a moment later, "collapsed" around the seed as seen from above. The six ballasted specimens that we filmed showed very slight decreases in the diameter of the kapok mass for the four smallest masses, but much more pronounced streamlining for the two most heavily ballasted diaspores (Fig. 4). In short, up to a limiting drag the measured AD did not change. Beyond this drag, the AD was increasingly smaller than measured originally. Interestingly, this limiting value corresponds to a total mass (mT) of about 0.5 g, only a little larger than our largest diaspore in Table 1 (B. sessilis).
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Aerodynamically, the kapok is best regarded as a hemisphere with a drag coefficient about midway between a perfect sphere and a perfect disk. Unlike the pappus of Asteraceae, the kapok does not behave as a planar set of cylinders. This is because the kapok has a much higher solidity than a pappus; the difference in solidity is as much as 100-fold between B. sessilis (Table 1) and a composite such as Taraxacum officinale. Thus, as we showed, air is deflected around the kapok. For investigators interested in a quick calculation of terminal velocity for diaspores with morphologies similar to the Bombacaceae, one can use equation (1) with an intermediate drag coefficient of 0.8.
The relationship between planform area (AD) and appendage mass investment (mk) indicated that shape was not held constant with changes in diaspore size, and this was true both for C. aesculifolia fruits as well as among Bombacaceae species. This is unlike the case with a certain class of winged seeds (asymmetric samaras such as Pinus or Acer or many Fabaceae) where shape constancy is required for avoidance of stalling, and thus the exponent on mk is the isometric constant 0.67 (Greene and Johnson, 1993
). By contrast, with the Bombacaceae, as more kapok mass is added (more fibers or longer fibers) the already crowded surface of the placenta forces the fiber bundles upward. While this increases solidity, it also leads to a smaller increase in drag than would be provided by a simple isometric (constant shape) response. One could imagine a larger fruit with the same number and size of diaspores so that they were less crowded; then there would be no reason why kapok mass and disk area would not be isometrically related. For reasons that are not clear from our results, natural selection has not favored this relationship. The consequence of the foregoing argument was first noted by Augspurger (1986)
: the slope for a regression of terminal velocity on the square root of disk loading (or the equivalent—wing loading— for winged seeds) was much steeper for the Bombacaceae than for any of the aerodynamic classes represented by various kinds of winged seeds. We can now explain her result: because of isometry the terminal velocity of winged seeds is proportional to ms0.167 (Greene and Johnson, 1993
), and thus terminal velocity regressed on diaspore mass leads to a similar slope for all aerodynamic classes (although intercepts may differ by class). By contrast, for species with kapok, because of the packaging problem on the placenta, terminal velocity is proportional to, approximately, ms0.26 and thus increases more rapidly with mass than was the case with winged seeds.
Is the kapok allocation optimal for achieving the lowest possible terminal velocity given the seed mass? The eight species examined here showed a relationship between terminal velocity and seed mass that was not significantly different from our calculated optimum for kapok investment. While the mass investment in kapok by these species is hardly a draw from a random distribution, nonetheless, inspection of Table 1 reminds us that that the ratios mk/mT are most certainly not tightly clustered around the expected value of 0.52 (observed mean = 0.34; range = 0.17–0.60). All but one of these species could disperse farther if it invested more in the kapok. They are best regarded as "good enough" rather than optimal.
The foregoing interpretation has ignored other selection factors such as juvenile survivorship and the trade-off between allocation of photosynthate to individual fruits and seeds vs. total number of fruit and seeds. Also, one might follow Olivieri et al. (1995)
in arguing that very great dispersal distances might be selected against because they lead to poor subsequent survivorship of progeny in highly heterogeneous environments at ecological time scales. Finally, we have assumed that the only function of kapok is to produce drag; by contrast, Baker (1983)
speculated that perhaps the water-repellent kapok is also designed for water dispersal of the diaspores.
The fibers of the Bombacaceae are similar to those of Asclepidaceae and Asteraceae (Greene and Johnson, 1990
) in that they are hollow cells with a diameter of 15–50 µm and a density of about 200 kg/m3. These values are quite similar to plant cells generally. What makes the kapok fibers unusual is not their diameter but their length. The mean diameter may be very conservative within a species; our diameter value for C. pentandra (a herbarium specimen from a South American population) is almost identical to that reported from India (Kirby, 1963
) and Java (Goulding, 1917
).
The percentage mass allocation to the appendage (kapok in our case) is about twice as great on average for the Bombacaceae as for the Asteraceae (Greene and Johnson, 1990
). But this is because of the problem of dispersing such large seeds: only the smallest diaspore (O. pyramidale in Table 1) has a seed mass within the typical range for Asteraceae. Indeed, the normal Asteraceae pappus with a low solidity, planar array of short fibers (e.g., Erigonum; Aster) would certainly bend with a total mass greater than 50 mg. The much larger mass investment of Asclepius (mk/mT = 0.33) with the coma (appendage) no longer in a plane permits a maximum mass of about 150 mg (terminal velocity about 0.80 m/s) before it bends (Greene and Johnson, 1990
). As we have seen, the Bombacaceae perform better than this; unlike the Asclepiadaceae, the mutually supporting fibers permit a total mass of about 500 mg (terminal velocity around 1.8 m/s) before the kapok would bend. In short, among the wind-dispersed species that depend strictly on drag production to minimize terminal velocity, the Bombacaceae design seems to be the best one for supporting very large seeds (although of course they must invest more heavily, on a relative as well as absolute basis, in the appendage mass). It is possible to imagine a Ceiba, for example, that evolved to a seed size exceeding our maximum (and it simply fell very rapidly due to bending of the fibers), but terminal velocities much greater than about 2 m/s represent a waste of investment in the appendage; the realized dispersal distance would not be much greater than could be achieved without any appendage at all given the capacity of caching rodents (Greene and Calogeropoulos, 2002
).
Greene and Johnson (1992)
generalized that for populations of mid-latitude, wind-dispersed species, CVvf < CVms << CVma, where CV is the coefficient of variation (standard deviation divided by mean) and the subscripts vf, ms, and ma refer to terminal velocity, seed mass, and appendage mass, respectively. They argued that the terminal velocities of a population are expected to be less variable due to a statistical artifact: they are a function of the two other quantities (seed mass and appendage mass) that lie inside a square-root term (equation 1). For the tropical species reported here, the appendage mass CV certainly was greater than the terminal velocity CV for all 17 fruits that we examined. But unlike mid-latitude species, the CV of seed mass does not tend to be greater than the seed mass of terminal velocity. Although we did not quantify it, it seemed to us that most of the variation in kapok mass occurred along the fruit with smaller kapok masses associated with the diaspores at either end.
Nonetheless, the CVvf values (0.11 and 0.15) of the two Ceiba populations were very similar to those obtained in a mid-latitude survey in which the average coefficient of variation was 0.13 (Greene and Johnson, 1992
). In short, these two tropical species appear to be no more or less variable in their terminal velocities than extra-tropical species.
FOOTNOTES
1 We thank the following for assistance in the lab and in the field: Gumersindo Sanchez, Melanie McCavour, Cathy Calogeropoulos, Carolina Palacios-Guevara, Mariluz Yared Hernandez Flores, Miguel Angel Munguía-Rosas, Ethel Arias, Eva Cué, Karla Oceguera, Miguel Salinas, Roberto Sayago, Mike Hesketh, and Trent Gielau. We thank the Missouri Botanical Garden in St. Louis for permission to examine herbarium specimens of Bombacaceae species. Funding was provided by NSERC and Centro de Investigaciones en Ecosistemas, Universidad Nacional Autónoma de México.
Funding was provided by NSERC to DFG. For MQ funding was provided by Centro de Investigaciones en Ecosistemas, Universidad Nacional Autónoma de México and by Direccion General de Asuntos del Personal Academico at the Universidad Nacional Autonoma de Mexico (Proyecto Papiit IN221305). 
4 Author for correspondence (e-mail: greene{at}alcor.concordia.ca
)
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Goulding E. 1917 Cotton and other vegetable fibers: their production and utilization. John Murray, London, UK
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