• anemochory;
  • collision;
  • plumed seeds;
  • seed dispersal;
  • Stokes number;
  • terminal velocity;
  • winged seeds


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  • 1
    The role of collisions with vegetation elements in seed dispersal by wind has been examined only anecdotally. In particular, the idea that the effect of collisions in dispersal may depend on the aerodynamic class of the diaspore has not been broached.
  • 2
    We adapted a collision model for small particles to predict the probability of a winged or plumed seed colliding with a vegetation element as a function of the Stokes number (a dimensionless parameter which quantifies inertial tendency and includes diaspore terminal velocity, wind speed and diameter of the target element).
  • 3
    We performed experimental releases of seeds upwind of tree boles in two deciduous forest types (temperate and dry tropical) for 10 mid-latitude and tropical species to test the collision model. The model was a reasonable expression of collision efficiency. At higher Stokes numbers, collisions were far more likely for seeds than for water droplets or other small particles.
  • 4
    Experimental releases were used in both forests to determine the effect of collisions with boles on distance travelled for several species. Seeds of the three species with asymmetric wings had significantly reduced dispersal following collisions; the single species with plumed seeds did not.
  • 5
    In a leafless tropical forest, we experimentally determined the frequency distribution of collisions per metre of travel for seeds released from a canopy. Approximately one collision occurred for every 2 m of flight through the volume occupied by branches and lianas. Distance achieved by asymmetric samaras was relatively unaffected by collisions with small vegetation elements, because the samaras quickly readopted stable autorotation. Conversely, bilaterally symmetric samaras had their dispersal greatly reduced.
  • 6
    Synthesis. The effect of collisions on dispersal depends on aerodynamic type. Collisions with small vegetation elements in forests should be more common for samaras than for plumed seeds, because plumed seeds generally have lower terminal velocities. Among winged seeds, collisions with branches will not seriously reduce dispersal except for bilaterally symmetric diaspores, because they are unable to rapidly regain stable autorotation. Reduction in dispersal due to collisions with boles will be unimportant because bole collisions, unlike branch collisions, are rare.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Scientists studying the flight and deposition of spores and pollen have shown considerable interest in collisions because the results of the contact (bouncing off or sticking) are crucial in understanding the aerial concentration of allergens and the probability of a spore reaching a suitable substrate (Jackson & Lyford 1999). However, far less is known regarding the effect of collisions on wind-dispersed seeds.

Collisions have not been explicitly treated as a potential cause of distance reduction in any mechanistic model of seed dispersal by wind (Nuttle & Haefner 2005). Most such models assume that vegetation elements can affect nothing more than the wind speed at some broad scale. That is, an area with a high density of vegetation elements will slow the wind and modify the turbulence regime (e.g. Greene & Johnson 1996; Nathan et al. 2002; Nathan & Katul 2005). Empirical models can sometimes be context-dependent in this same way. For example, LePage et al. (2000) parameterized their dispersal functions separately for intact forests vs. a stand filled with small gaps vs. a clearcut.

What kind of direct effects might collisions have on wind-dispersed seeds? One obvious effect is a reduction in distance travelled, and this could happen in a number of ways. First, plumed seeds (with appendages such as kapok, coma, pappus, etc.) could be caught by twig tips or elements of low porosity (e.g. umbels). We know of no studies on this phenomenon. Second, a diaspore may simply collide with a wide vertical bole and be unable to move around it. A third possibility, for winged seeds only, is that the loss of autorotation following a serious collision could lead to an increase in downward speed before stable autorotation, and consequently terminal velocity, is re-attained. As shown by Norberg (1973), Guries & Nordheim (1984) and Greene (1990) for still air, a winged seed initially reaches a speed faster than its subsequent terminal velocity because of the slow lateral acceleration of the wing. The descent then slows, as the rotation rate of the wing increases and the coning angle (the angle between the wing and the horizontal plane) decreases. By contrast, in still air, a plumed seed smoothly accelerates to its terminal velocity, and does so over a very short distance. A fourth possibility is that the temporary loss of stable autorotation could also cause the loss of horizontal momentum. Given an abscission-induced bias toward wind speeds that are higher than average (Greene 2005; Soons & Bullock this issue), any event that causes the seed to lag behind the ambient wind speed will likely cause it to subsequently experience a lower horizontal speed than that which initiated abscission. Again, this should be far less important for plumed seeds simply because they are usually far less massive than samaras, and thus ought to accelerate very rapidly to the ambient horizontal wind speed (Burrows 1973; Greene & Johnson 1990).

This discussion of possible negative effects on dispersal begs the question: do we have any empirical evidence that collisions greatly reduce dispersal distances?

Bullock & Moy (2004) quantified the effect of seed trapping by two short (0.3 m) evergreen ericoid shrub species. They observed that more seeds were deposited to the windward side of the shrubs than to the leeward side; further, there were 19–33 times as many seeds found beneath allospecific shrubs as in the intervening grass. This dramatic effect of trapping by the shrubs on seed density was found to extend to a radius of < 0.1 m from the shrub drip-line. The authors were cautious in attributing a cause for this marked pattern, pointing out that it might be due to a reduction in the ambient wind speed around a shrub, an increase in turbulence, or collisions.

A number of other studies (Sheldon & Burrows 1973; Watkinson 1978; Fuentes et al. 1984; McEvoy & Cox 1987; Thiede & Augspurger 1996; Aguiar & Sala 1997; Russell & Schupp 1998; Jongejans & Telenius 2001) also demonstrated either clumping of seeds around non-source plants or a reduction in distance where plant densities were greater. Like Bullock & Moy (2004), all of these studies mentioned, speculatively, a possible role for collisions, but could not rule out merely a local reduction in wind speed. In summary then, to the best of our knowledge there is no direct evidence, even anecdotal, that collisions occur frequently, or can cause a significant reduction in dispersal distance.

For the present study, we conducted a series of experiments, within two forest types, to test several of the hypotheses mentioned above. First, we experimentally evaluated a collision model using boles as targets. We used a wide range of diaspore masses, and two different diaspore types: asymmetric samaras and plumed seeds. Species were chosen according to availability; both woody and herbaceous species were used indiscriminately as representatives of winged and plumed seed types (cf. Augspurger 1986 for a thorough introduction to the aerodynamic classes of wind-dispersed diaspores). Further, we asked: when collisions with boles do occur, is the dispersal distance greatly reduced? We then examined the effect of collisions with smaller-diameter elements (branches and lianas in a leafless tropical stand) using experimental mid-crown releases for two diaspore types: asymmetric and bilaterally symmetric samaras. We quantified the number of collisions and the mean reduction in distance travelled. Finally, we used photography within this same leafless tropical stand to estimate the woody area index (WAI) for comparison with other forest types.

modelling collisions with cylinders (branches and boles)

Intuitively, the probability of collision of a particle with a vegetation element will depend on the size and shape of the element, the air speed, and the mass and area of the particle. For both winged and plumed seeds, the latter two quantities are subsumed in the terminal velocity (Vt), a function of the square root of the total mass divided by the planform area of the lift- or drag-producing appendage (Augspurger 1986; Greene & Johnson 1990). The vegetation element (bole or branch) may be represented by a cylinder.

A regression model of spore dispersal advanced by Aylor et al. (1981), and further refined by Aylor & Flesch (2001), predicts the horizontal collision efficiency E (i.e. the colliding proportion of all particles that were initially on a trajectory intersecting the obstacle) as a function of the Stokes number, St. This dimensionless parameter is defined as.

  • image(eqn 1)

with U, the horizontal wind speed; g, the gravitational acceleration; and L, the diameter of the cylinder along the path of the trajectory. The Stokes number is, effectively, a measure of inertia (Davies 1966); as St increases, a particle carried by a fluid toward a stationary object is increasingly likely to maintain a straight trajectory and, therefore, collide. Based on data from the wind tunnel experiments of May & Clifford (1967), in which minute water droplets were carried toward a cylinder oriented perpendicular to the flow, Aylor & Flesch (2001) concluded:

  • image(eqn 2)

with the empirical coefficients in eqn 2 being a = 0.86, b = 0.442 and c = −1.967. Given that the exponent (c) on St is negative, it follows that the faster and more massive the diaspore, the more likely it will collide with the cylinder. Likewise, the wider the cylinder, the greater the speed of the diverging air flow, and the more likely this laterally-spreading air will carry the diaspore around it.

Certain predictions follow from eqn 2. First, within forests, collisions with branches should be far more likely than with boles, not merely because the former are more numerous, but also because they have smaller diameters and will tend to be found in the crowns, where greater wind speeds prevail. Second, winged seeds will risk more collisions than plumed seeds simply because, on average, they are more massive and have far higher terminal velocities (Augspurger 1986; Greene & Johnson 1993).

Note that eqn 2 was initially parameterized using droplets that were tiny relative to the cylinders they were approaching. By contrast, seeds (exceptions such as Orchidaceae notwithstanding) have much greater characteristic sizes, and indeed can be larger than the objects, such as higher-order shoots, with which they might collide. Thus, for any Stokes number, we expect a greater collision rate for seeds than for spores or pollen or the droplets of May & Clifford (1967).

We also expect that the probability of collision during a seed's descent will be affected by the density of element area per volume (units of m−1), which is a sum of the leaf area density and woody area density. The former is on the order of 2.0 in dense grassland, but much higher in closed canopy forests (Aylor & Flesch 2001; Scurlock et al. 2001). Meanwhile, maximal mean woody area densities are typically about 0.1 in forest canopies for mid-latitude hardwood forests (Bréda 2003). Thus, collisions should be more common in dense grasslands than in closed-crown forests with fully deployed leaves.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

data collected in canada

Study species and site

Four wind-dispersed species commonly found in eastern North America were used in the experiments: Acer negundo L., A. saccharinum L., A. rubrum L. and Tragopogon porrifolius L. The Acer species have asymmetric winged seeds; Tragopogon has plumed seeds. Diaspores were collected from several plants of each species, gathered from beneath Acer trees and directly from the capitula of Tragopogon. Seeds that had no endosperm (judging by mass) were discarded, as were seeds with damaged wings or plumes. Winged seeds were tested for normal autorotation; the few that would not autorotate reliably in still air were also discarded. From the remaining specimens, seeds were chosen randomly for release during collision trials. A random subsample of 20 seeds was used to estimate average mass, length, and terminal velocity for each species, following the method used by Greene & Johnson (1993).

For three of the four mid-latitude species (all but A. negundo), experiments took place during the summer in Mount Royal Park, in Montreal, Quebec, on level ground upwind of a group of A. saccharinum trees. The experiments with A. negundo occurred during the winter, in a Pinus strobus stand about 100 km east of Montreal. However, because wind speed was not recorded during collision trials for A. negundo, this species is included only in the analysis of the effect of collisions on distance travelled. For all four species, every seed was recovered and discarded after release; none was re-released.

Experiment 1: testing the collision efficiency model and the effect of collisions with boles on dispersal distance

Seeds of each species were released singly, by hand, about 2 m from a chosen tree. Release height, between 1.42 and 1.66 m, was kept constant for all releases for a species. We only included those trials in which the seed was initially on a trajectory toward the bole. (Because the diameter of the bole ranged from 0.29 to 0.66 m, the seed's complete trajectory windward of the bole was easily observed.) For this subset only, we then noted whether the seed did indeed collide with the bole or was suddenly pushed to the side by the diverging air-stream and therefore avoided collision. From here on, the phrase ‘averted collision’ will be used specifically to describe the divergence of a seed from its initial trajectory toward a bole. Distance from release to landing was also recorded.

Seeds were only released if the wind speed was > 2 m s−1. With the exception of A. negundo releases, an average wind speed (Ua) for each species was measured using a cup anemometer placed typically at around 1 m height (ha). The anemometer height was not perfectly consistent between sessions, due to slight differences in terrain. Long periods without wind, and therefore without releases, were deleted from the anemometer record.

Generally, given the wind speed and terminal velocity, seeds struck (or avoided) the bole at a height only slightly less than the release height (hrel). To calculate the wind speed at the release height (Urel), we used the one-seventh power-law model (Greene & Johnson 1996):

  • image(eqn 3)

The stand we used had little or no shrub cover; thus eqn 3 would give essentially the same values as, for example, a logarithmic model over these short height intervals.

data collected in mexico

Study species and site

Diaspores of five tropical species were collected for experiments: Cordia alliodora (Ruiz & Pavón) Oken, Cordia gerascanthus L., Matelea quirosii (Standl.) Woods., Swietenia humilis Zucc. and Entada polystachya (L.) DC. in DC. The two Cordia species have wings like fixed rotors; Swietenia has an asymmetric wing; Entada has a bilaterally symmetric wing; Matelea is plumed. Seeds were gathered from ripe fruits of these species, in the vicinity of Careyes (state of Jalisco, Mexico). Selection of seeds for release was done in the same manner as for those released in Canada. Terminal velocity estimates were also performed for the tropical seeds.

Seeds were only released when the wind speed exceeded a minimum of approximately 2 m s−1. All seeds were recovered and discarded after release; none was re-released. Again, we used eqn 3 to estimate the slight difference in wind speed between the anemometer height and the typical height at which seeds collided or passed by the bole.

Experiment 2: testing the collision efficiency model

In a repeat of the releases performed in Canada to test the collision efficiency model (eqn 2), we released seeds of the five tropical species at a Pacific Ocean beach at Careyes about 2 m from the target, a palm bole. All seeds were released one at a time in the early afternoon, when the speed of the afternoon sea breeze would typically be greatest Greene et al. 2008. Release height was approximately 2 m. To increase the range of the terminal velocities available to us, we glued a 1-cm cylinder of solder to the centre of a sample the Entada seeds; the solder did not prevent these seeds from maintaining stable autorotation. As in Canada, we recorded whether the seed collided, or was carried around the tree in the diverging air-stream.

Experiment 3: the effect of collisions with branches on dispersal distance

We released 100 Entada seeds from a ladder mid-crown in each of 21 trees in a leafless stand at Careyes. As is typical of drought-deciduous tropical forests, values of basal area per area (almost 10 m2 ha−1) and height (about 9 m) were low. The release height for each tree was 6.9 m (i.e. approximately 75% of the canopy height). Although a few dried, curled leaves still remained on branches, the stand, occupying a broad hilltop 2 km from the Pacific Ocean, was essentially leafless. Because the trees were leafless and the seeds were massive, collisions with branches were easily seen and clearly heard. Again, we simulated an abscission bias by only releasing these 2100 diaspores when the wind speed gusted to at least about 2 m s−1. In this experiment, we recorded whether a collision had occurred (not the total number of collisions) during a seed's descent, and the distance travelled. For this and the following experiments, Entada seeds were painted to facilitate retrieval; therefore, their terminal velocity (1.71 m s−1) was somewhat higher than that listed in Table 1.

Table 1.  The species used in this study, ordered by seed mass. m is the seed mass, x is the seed length, Vt and U are the terminal velocity and wind speed, d is the tree diameter, n is the number of seeds colliding, and E is the collision efficiency. Note that these Entada data are for unpainted seeds
Speciesm (g)x (m)Vt (m/s)U (m/s)d (m)nE
  • *

    With added weight from solder.

Cordia alliodora0.0040.0261.001.790.29350.38
Acer rubrum0.0180.0320.662.380.66310.41
Cordia gerascanthus0.0450.0141.462.880.29400.68
Acer saccharinum0.0830.0410.814.900.59140.37
Entada polystachya0.410.0591.411.700.29560.56
Swietenia humilis0.650.1070.861.880.29470.61
Entada polystachya*0.730.0592.052.630.29500.77
Tragopogon porrifolius0.0080.0290.592.500.55 90.21
Matelea quirosii0.0200.0310.431.000.29 50.10
Experiment 4: frequency distribution of collisions within the crown space for individual diaspores

To estimate the frequency distribution of collisions by a single seed, we released an additional 100 painted Entada seeds from the canopy of a single tree used in experiment 3, but now we recorded the number of collisions for each seed (not merely the presence or absence of collisions). The methodology was otherwise the same as in experiment 3.

Experiment 5: the effect of collisions with branches on dispersal distance and frequency distribution of collisions within the crown space for individual diaspores

We released 100 Swietenia seeds each from the canopies of five trees used in experiment 3. As in experiment 3, we recorded the distance travelled by each seed. As in experiment 4, we also recorded the number of collisions for each of these 499 seeds (the wing of one diaspore broke during a collision, and it was deleted from the analysis).

Forest branch density and collision efficiency

Clearly, the probability of collision is affected not just by the parameters encapsulated in the Stokes number but also by the density of vegetation elements. At the leafless stand on the Careyes hillside, we used photographs to estimate the WAI (a measure of woody element density). This approach permits extrapolation of our results regarding the branch-collision probability to other stands with different values of the WAI.

We took a series of photographs vertically from the ground into the canopy to calculate the WAI (analogous to a leaf area index) and compare this with woody area indices obtained in a similar manner by investigators elsewhere. All images were examined using SigmaScan (Systat Software Inc., San Jose, CA) to determine the proportion of the image covered by woody elements.


The Stokes number (St; eqn 1) for each species used in Canada and Mexico (experiments 1 and 2) was calculated from the mean values of terminal velocity, the tree diameter at release height, and the wind speed at the release height (Urel; eqn 3). For species involved in multiple release sessions (Canada only), weighted results were calculated for both tree diameter and mean wind speed. The number of seeds that could collide was used as a weight for each session.

We solved for new empirical parameters b and c through linear regression of eqn 2, following logarithmic transformation. Because the seeds used were so much larger than the water droplets used in the original May & Clifford (1967) study, and therefore a diaspore with a large St should have a near certainty of colliding with an element on its trajectory, the maximum collision efficiency (coefficient a) was fixed at 1.0.

Because a small fraction of seeds travelling very great distances in experiment 1 were simply recorded as having dispersed > 25 m, we used Mann–Whitney U tests to compare the distances travelled by seeds that collided with a bole to those of seeds that diverged around it, to normalize the distribution.

The right-skewed distances of the Entada in experiment 3 were log-transformed, and the distance distributions for seeds that collided vs. seeds that did not collide were compared using Student's t-test.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

testing the collision efficiency model (experiments 1 and 2)

Combining the Mexican and Canadian species, measurements of mean diaspore properties are presented in Table 1. The mass of the seeds (including the solder-augmented Entada seeds) ranged as 4–730 mg, while terminal velocities spanned the range of 0.4–2.0 m s−1. Experiments 1 and 2 resulted in collision efficiencies ranging from 0.1 (Matelea) to 0.77 (artificially weighted Entada).

Our regression recast eqn 2 as

  • image(eqn 4)

(r2 = 0.87; P < 0.0003; Fig. 1), and the 95% confidence intervals for the b and c parameters were 0.45 to 1.02 and –0.77 to –1.61, respectively.


Figure 1. Experimental data for the species in Table 1. Curves represent the best-fit equations for seeds (Present study; eqn 4) and droplets (Aylor and Flesch model; eqn 2).

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the effect of collisions with boles on dispersal distance (experiment 1)

For the three winged Acer species, collision with a bole caused dispersal distances to be significantly reduced (Mann–Whitney U tests; one-tailed P < 0.04 for all). The percentage reduction in median distance travelled ranged from 13% for A. saccharinum to 37% for A. rubrum. The effect of collisions with boles on distance travelled was not significant, however, for the plumed seeds of Tragopogon (Z = 0.47; one-tailed P = 0.31).

While the colliding diaspores of these asymmetric samaras (Acer) tended to travel shorter distances than conspecifics that did not collide, nonetheless we observed that many of these seeds were able to quickly regain autorotation and continue travelling around and beyond the bole. As for the subsequent distance travelled, those seeds which collided and fell within 1 m of a bole constituted between 33% (in Tragopogon) and 52% (in A. saccharinum) of all colliding seeds. Typically, deposition of these seeds at the foot of the bole would occur at the windward edge, but occasionally also at the sides.

the effect of collisions with branches on dispersal distance (experiments 3 and 5)

Of the tropical seeds, only Entada and Swietenia were used to examine the effect of collisions with branches and lianas on dispersal distance. Few seeds avoided collisions. For Entada, only 2.9% (N = 100; Fig. 2; experiment 4) and 0.9% (N = 2100; experiment 3) avoided collisions. For Swietenia (N = 499; Fig. 2; experiment 5), only 2.4% escaped collisions. For Swietenia, the mean distance (3.8 m) travelled by the 12 non-colliders was less than that travelled by the 487 seeds experiencing one or more collisions (4.8 m), but not significantly so (t-test with log-transformed values; P = 0.13). By contrast, for Entada (with N = 2100; experiment 3), the 19 non-colliders achieved a significantly greater distance than the 2081 colliding seeds: 7.2 vs. 4.9 m, respectively (t-test with log-transformed values; P = 0.00002).


Figure 2. Collisions with branches and lianas by Entada polystachya and Swietenia humilis seeds. These distributions are not significantly different from a Poisson expectation.

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frequency distribution of collisions within the crown space for individual diaspores (experiments 4 and 5)

Released over a few weeks, the seeds of Entada (N = 2100) and Swietenia (N = 499) did not travel far; the mean horizontal distances for both were about 5 m. Although the idealized mean trajectory length of the diaspores of both species averaged only about 8.5 m (i.e. the Pythagorean result, given an average release height 6.9 m and a final distance of about 5 m), nonetheless, collisions were quite common (Fig. 2). Swietenia averaged 60% more collisions per seed than Entada: 4.6 vs. 2.9. Roughly then, there was about one collision per 2 m of straight-line trajectory.

Neither of the two frequency distributions in Fig. 2 was significantly different from a Poisson expectation (Kolmogorov–Smirnov test; 0.31 < P < 0.34). Collisions with boles also occurred, but were quite rare because inter-tree distances were greater than the bulk of the dispersal distances.

forest branch density and collision efficiency

Analysis of the photographs taken looking straight up from the ground through the 9-m high canopy showed that 34% of the sky was obscured by vegetation elements. Because the probability of collision depends greatly on the density of vegetation elements, we wondered if our Careyes stand was unusual in this regard. We therefore calculated the dimensionless WAI, a function of woody element cover in photographs, for this stand so that we might compare it with other sites. Kalacska et al. (2005) examined dry season WAI using stands in the Careyes area. Employing their regression, we estimated WAI in this stand as 1.74.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

The diaspore properties we measured cover much of the range in size and terminal velocity that exists in mid-latitude and tropical forests for wind-dispersed species (cf. Augspurger 1986; Greene & Johnson 1993). We have shown (experiments 1 and 2; Fig. 1) that the Aylor & Flesch (2001) predictor (i.e. the Stokes number) for the collision efficiency of tiny droplets provided a reasonable characterization for our much larger diaspores approaching boles. However, at very high Stokes numbers, seeds were more likely to collide than were droplets (Fig. 1). More generally, neither of our confidence intervals included the values obtained by Aylor & Flesch (2001) for droplets.

Further, we have demonstrated that collisions with smaller vegetation elements (branches, lianas) occur quite frequently within a leafless tropical forest: about one collision for each 2 m of straight-line trajectory. The remaining question concerns the conditions under which these collisions can cumulatively have a significant effect on the final dispersal distance of a diaspore. We will argue that the answer depends greatly on the seed's aerodynamic type.

the effect of collisions with boles on dispersal distance

We showed experimentally that collisions with boles had a high probability as the Stokes number increased beyond about 1.0. How often should a diaspore be travelling towards a bole? According to the calculation of Greene et al. (2004), we might expect that for an idealized commercial mid-latitude deciduous forest (boles 0.3 m in diameter at breast height; basal area about 30 m2 ha−1), around 15% of the seeds would be on a flight trajectory intersecting a bole. With a wind speed of, say, 1.0 m s−1 in the trunk space (Greene & Johnson 1996), and, to take one extreme, a very high terminal velocity of 2.0 m s−1, we would have St = 0.68 (eqn 1), and therefore a collision efficiency of 0.48 (eqn 4). Thus, about 7.2% (i.e. 0.15 × 0.48) of a crop would collide with a bole. How seriously will the dispersal distance be reduced?

For colliding seeds there was, on average, a 25% reduction in dispersal distance for the winged seeds of the Acer species (experiment 1). The reduction was not significant for the plumed seeds of Tragopogon. As mentioned in the Introduction, this is to be expected: a collision (assuming the diaspore is not trapped by the contact) carries less severe consequences for a plumed (drag-producing) seed. Moreover, any seed travelling within the low wind speed regime of the trunk space is necessarily near the end of its flight. That is, we predict a 25% reduction in the final segment of the total dispersal journey for 7.2% of the crop. In consequence, we conclude that collisions with boles should cause little discernable change in the calculated mean dispersal distance of a crop or in the variance in dispersal distances.

the effect of collisions with branches and lianas on dispersal distance

Collisions for both types of diaspores were common in the leafless tropical forest. Interestingly, the frequency distribution of numbers of collisions for diaspores was not significantly different from a Poisson expectation. This implies that the branch elements were randomly distributed, at least within that part of the stand volume in which most seed trajectories occurred. Further, reliance on the one-parameter Poisson distribution for collision frequency not only simplifies any subsequent modelling of the collision process within a stand, it may permit estimation of that single parameter from knowledge of the characteristic size of the diaspore in flight and a calculation of the proportion of branch-filled space from a photograph.

For our experimental releases at Careyes (experiments 3 and 5), we expected that if these collisions, although numerous, had no effect on dispersal, then collision frequency and distance travelled should be positively correlated, simply because there would be more opportunity for collision given a longer flight. On average, Swietenia seeds that collided travelled a bit farther than those that experienced no collisions, but the difference was not significant. In the field, we qualitatively noted that this type of winged seed (the asymmetric samara) was unaffected by collision; the seeds seemed to recover their autorotation almost instantaneously, with no perceptible loss in height or in forward momentum.

By contrast, the fraction of the Entada seeds experiencing no collisions travelled significantly farther than those that had one or more collisions; this result is exactly the converse of what we might expect if collisions were unimportant. The diminished travel distance for colliding diaspores corresponded with our qualitative observations: typically, a collision was accompanied by a rapid loss in height as the seed very slowly recovered autorotation.

Why should there be this difference between two types of winged seeds? With photography of A. negundo specimens (the asymmetric type of winged diaspore, rotating in one plane only) in a wind tunnel, Greene (1990) noted that the time to reach terminal velocity was greatly decreased in moving air relative to still air because, at first, the drag due to the wind was much stronger than the drag due to the gravitational acceleration. In consequence, the wing began to autorotate around its mass centre much faster in moving air and, correspondingly, terminal velocity was reached much more quickly. We observed the same rapid recovery with Swietenia in the field. There is no equivalent photography of the bilaterally symmetric type of seed (these have a second, simultaneous, rotation – this time around the span-wise axis) such as Entada, but it seemed to us qualitatively that the recovery from a collision was often as sluggish as in still air: that is, the specimen might drop as much as 1 m after a collision before autorotation was re-attained. Because of the second type of autorotation, the woody wings of bilaterally symmetric seeds invariably have much thicker chord-wise sections than do asymmetric wings. This generalization is true only for similar-sized diaspores: the wing of a very large asymmetric diaspore, such as that of the New World Centrolobium, is not only woody but far thicker than the much smaller Fraxinus wing. We speculate that the enhanced wing mass of Entada makes it more difficult for the wind to accelerate the wing laterally following a collision.

the effect of forest density on collisions

Previously, there were only anecdotal accounts to suggest that collisions occurred during seed flight and might significantly reduce dispersal. Given our results with the Aylor & Flesch (2001) model, one expects that collisions with smaller-diameter elements would be quite common. To take an extreme for the crown space, let us posit a wind speed of only 2 m s−1, a terminal velocity of 0.3 m s−1 (e.g. Populus and Salix for trees; many herbaceous species with plumed seeds also have values this low) and a shoot diameter as great as 0.05 m. The probability of collision would be 0.65 (eqns 1 and 4). More typically, though, high-order shoots are narrower than this, and so the collision probability would also be much greater.

The probability of striking a woody vegetation element per unit of distance travelled should be as common in other leafless forests (e.g. mid-latitude hardwood forests in winter) as at Careyes. Our estimated WAI of 1.74 is similar to the reports reviewed by Bréda (2003) for deciduous mid-latitude stands in Europe: all were in the range 0.4 < WAI < 2.5. Kalacska et al. (2005) reported a similar range for three Central American drought-deciduous tropical forests.

One might also expect that the mean collision rate will be far higher when leaves are present than observed here. As pointed out by Nathan & Katul (2005) for mid-latitude North American wind-dispersed tree species, however, most abscission occurs either just before angiosperm leaf flushing (the diaspores of the angiosperm genera Salix, Populus, most Ulmus, and some Acer) or, more commonly, after autumnal leaf abscission has begun in earnest (seeds of all gymnosperms and most angiosperms). Note, however, that the overlap of these seed dispersal and leaf deployment schedules is considerable (cf. Fig. 1 in Nathan & Katul 2005). Further, as the evergreen component of a forest increases from 0% toward 100%, the density of elements that can cause collisions increases enormously. Lastly, in tropical forests lacking a prolonged dry season, the deciduous component of the tree flora is often minor. In short, collisions with small elements in most forests will be even more common than reported here because at least some leaves will also be present.

Nonetheless, there is an interesting complication: as the density of elements – branches and, especially, leaves – rises, the proportion of possible trajectories intercepting elements will also rise, but the probability of any one of those trajectories leading to collision will decrease. This will occur because the attendant 61% decline in wind speed (cf. Greene & Johnson 1996 for full-leaf vs. leafless conditions in mid-latitude hardwood forests) lowers the Stokes number and therefore the collision efficiency, E (eqn 4). Further, the decline in wind speed caused by an increase in leaf number will also lessen the total dispersal distance, such that collisions will be less numerous than we otherwise might have expected. Clearly, we cannot examine this issue fully until we have a tested argument relating the collision efficiency of leaves to the Stokes number.

conclusions for winged and plumed seeds

In summary, collisions with small vegetation elements such as branches, lianas, and leaves should be extremely common in all vegetation types, and this should be true especially for the larger diaspores because their size increases the likelihood of collision. Nonetheless, excluding extreme examples like the Neotropical Centrolobium, we conclude that the dispersal distance of asymmetric winged seeds will be essentially unaffected by collisions. Their (relatively) light wings are easily accelerated laterally by the drag of the wind following a collision. By contrast, the typically much heavier wings of bilaterally symmetric winged seeds are much more resistant to being pushed into autorotation by wind, and thus this group should have their dispersal distances significantly reduced by collisions. A third type of winged seed has multiple wings arrayed in a plane above the seed, and it autorotates in this plane only. Examples include our Cordia and the Dipterocarpaceae of Southeast Asia. Given that these species have thick, woody wings, one assumes that their dispersal capacity will be greatly reduced by collisions, but this remains to be verified.

The effect of collisions on plumed seeds is quite different. These diaspores accelerate vertically very little before terminal velocity is attained (Greene & Johnson 1990). Further, their low mass : area ratios (relative to winged seeds) mean that they would more rapidly accelerate horizontally to the ambient wind speed following a collision. In sum, although we have no dispersal experiments within crowns like those with Swietenia and Entada, we might expect little direct effect of collisions on the dispersal of plumed seeds. Certainly, the plumed Tragopogon was our only species that showed no significant reduction in dispersal distance due to collisions with boles. There is perhaps one exception for this conclusion regarding plumed seeds. We have frequently observed large numbers of plumed Populus balsamifera L. diaspores captured by the dense needle-studded shoots of conifers and the low-porosity umbels of herbs as they dispersed. As well, we have frequently seen the kapok of Ceiba diaspores caught by twig tips, the large black seed still inside the hemisphere of kapok fibres. Whether this sieving of plumed diaspores by vegetation elements is important for the dispersal of plumed seeds is not known, but it is clear that some elements (e.g. umbels or densely-needled conifer shoots) can trap seeds quite efficiently. Because our results with solid cylinders cannot be applied to this situation, a re-evaluation of the probability of impaction for plumed seeds, given interception by a porous element, would be enlightening.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Gumersindo Sánchez, Bonnie Hayden, Jennifer Roberts, Kevin Ryder, Victor Rosas, Lucero Rios, Nathalia Carrillo, Julia Astegiano and Paola Fernandez assisted in the field. Financial support was provided by an NSERC Discovery Grant, and by grants from the Secretaria de Educación Pública (SEP) and Consejo Nacional de Ciencia y Tecnología (CONACyT) (grants SEP-CONACYT 2005-CO1-51043 and 2005-CO1-50863) and the Dirección General de Asuntos del Personal Académico at the Universidad Nacional Autónoma de México (grant IN221305).


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
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