998 American Journal of Botany 92(6): 998–1005. 2005. SEED SIZE, DISPERSAL, AND AERODYNAMIC CONSTRAINTS WITHIN THE BOMBACACEAE 1 DAVID F. GREENE 2,4 AND MAURICIO QUESADA 3 2 Department of Geography, Concordia University, 1455 de Maisonnueve Boulevard, Montreal, Quebec, H3G 1M8; and 3 Centro de Investigaciones en Ecosistemas, Universidad Nacional Auto ´noma de Me ´xico, Apartado Postal 27-3 (Xangari), 58089, Morelia, Michoacan, Mexico 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 no- tion contributes to the conventional idea of a trade-off in evo- lutionary 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 typ- ically animal-dispersed while wind dispersal is almost invari- ably 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 dis- tance is inversely related to terminal velocity (Kohlermann, 1950; Greene and Johnson, 1989; Nathan, 2001; Tackenberg, 2003), and terminal velocity (v f ), in turn, is related to seed mass (m s ) as: 0.5 v  ((m + m )/A) f s a where m a is the mass of the dispersal-promoting appendage, A is a characteristic area, and the term inside the square-root function is referred to variously as the wing loading (A w for lift-producing winged species as in Augspurger [1986]), plume loading (A p for the drag-producing pappus of Asteraceae as in 1 Manuscript received 23 July 2004; revision accepted 21 February 2005. We thank the following for assistance in the lab and in the field: Gumer- sindo Sanchez, Melanie McCavour, Cathy Calogeropoulos, Carolina Palacios- Guevara, Mariluz Yared Hernandez Flores, Miguel Angel Munguı ´a-Rosas, Ethel Arias, Eva Cue ´, 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 spe- cies. Funding was provided by NSERC and Centro de Investigaciones en Ecosistemas, Universidad Nacional Auto ´noma de Me ´xico. Funding was provided by NSERC to DFG. For MQ funding was provided by Centro de Investigaciones en Ecosistemas, Universidad Nacional Auto ´n- oma de Me ´xico 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@alcor.concordia.ca) Greene and Johnson [1990]), or disk loading (A D 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; Tack- enberg, 2003), the following questions arise: Why must ter- minal velocity increase with seed mass? Why do larger seeds not have a correspondingly larger investment in m a (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 lim- its, otherwise the wing would stall and stable autorotation would be lost as the diaspore plummeted. Thus with this im- posed isometry, v f  m s (1-b)/2 (where b is the allometric expo- nent relating appendage mass to area). Given isometry and simple mass/volume relations, necessarily b = 0.67 and v f  m 0.167 . 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 v f . 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 Bombaca- ceae 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 optimiza- tion, involves the characterization of the area (A) in the loading value for Bombacaceae. Augspurger (1986) measured A as A D