Ecology, 87(6), 2006, pp. 1489–1496 Ó 2006 by the Ecological Society of America THE EFFECTS OF PLANT DISTRIBUTION AND FRUGIVORE DENSITY ON THE SCALE AND SHAPE OF DISPERSAL KERNELS JUAN MANUEL MORALES 1,3 AND TOMA ´ S A. CARLO 2,4 1 Ecology and Evolutionary Biology, University of Connecticut, Storrs, Connecticut 06269 USA 2 Ecology and Evolutionary Biology, University of Colorado, Boulder, Colorado 80309-0334 USA Abstract. For many plant species, seed dispersal is one of the most important spatial demographic processes. We used a diffusion approximation and a spatially explicit simulation model to explore the mechanisms generating seed dispersal kernels for plants dispersed by frugivores. The simulation model combined simple movement and foraging rules with seed gut passage time, plant distribution, and fruit production. A simulation experiment using plant spatial aggregation and frugivore density as factors showed that seed dispersal scale was largely determined by the degree of plant aggregation, whereas kernel shape was mostly dominated by frugivore density. Kernel shapes ranged from fat tailed to thin tailed, but most shapes were between an exponential and that of the solution of a diffusion equation. The proportion of dispersal kernels with fat tails was highest for landscapes with clumped plant distributions and increased with increasing number of dispersers. The diffusion model provides a basis for models including more behavioral details but can also be used to approximate dispersal kernels once a diffusion rate is estimated from animal movement data. Our results suggest that important characteristics of dispersal kernels will depend on the spatial pattern of plant distribution and on disperser density when frugivores mediate seed dispersal. Key words: animal movement; diffusion model; frugivory; kernel shape; landscape; plant and frugivore distribution; seed dispersal; spatial ecology; spatially explicit simulation. INTRODUCTION For many plant species, seed dispersal is one of the most important spatial demographic processes, directly influencing the colonization of new habitats, population dynamics, genetic differentiation, and species interac- tions, as well as community structure and diversity (Nathan and Muller-Landau 2000, Levin et al. 2003, Levine and Murrell 2003). The probability of a seed being deposited at a particular distance from the parent plant can be described by functions called dispersal kernels (Nathan and Muller-Landau 2000). The char- acteristics of these kernels, in particular their scale and shape, can have significant ecological consequences. Mean dispersal distance and its variance set the spatial scale of dispersal, which, depending on the scale of individual interactions, can alter population dynamics, carrying capacity, and the coexistence of competitors (Bolker and Pacala 1999, Law et al. 2003, Snyder and Chesson 2003). Kernel shape can be summarized by its kurtosis, which indicates how the probability density is distributed among the peak and tails of the whole distribution. In nature, dispersal kernels often are leptokurtic, with a sharp peak near the point of origin and a long tail (Kot et al. 1996). Leptokurtosis can greatly increase the rate of spread of an invading organism or allele, and has been hypothesized to explain otherwise surprisingly fast rates of spread (Kot et al. 1996, Cain et al. 1998, Clark et al. 2001). Moreover, if the dispersal kernel is ‘‘fat’’ (i.e., its tail decays with distance at a slower rate than an exponential), invasion can progress with jumps, and with increasing rather than constant speed (Kot et al. 1996). What ecological mechanisms are behind the main attributes of dispersal kernels? Frugivorous (i.e., fruit- eating) animals are the dominant seed dispersers for woody plant species in many temperate and tropical communities (Herrera 2002; see Plate 1). For these plants, seed dispersal kernels are a function of frugivore movement and gut passage (or regurgitation) times for seeds (Murray 1988, Schupp 1993). Assuming that, after consuming fruit, animals perform a random walk, it is possible to approximate movement with a diffusion equation (Turchin 1998). The solution of the diffusion equation can then be combined with a probability density function for gut passage time for seeds in order to solve for the distances at which they would be deposited. However, diffusion may be a poor approx- imation for frugivore movements (Holbrook and Smith 2000, Westcott and Graham 2000, Wenny 2001), especially at the small temporal scales defined by gut passage times. Furthermore, animals may detect and Manuscript received 17 June 2005; revised 28 October 2005; accepted 6 December 2005. Corresponding Editor: E. Siemann. 3 Present address: The Statistical Laboratory, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB UK. E-mail: J.Morales@statslab.cam.ac.uk 4 Present address: University of Washington, 528 Kincaid Hall, Box 351800, Seattle, Washington 98115 USA. 1489