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).
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.
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.
- (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:
- (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.