Juan Manuel Morales and Tomás A. Carlo. 2006. The effects of plant distribution and frugivore density on the scale and shape of dispersal kernels. Ecology 87:1489–1496.

Appendix A. A description of the simulation model.

We simulated bird behavior as a stochastic, event-driven process where birds moved from plant to plant, spending a variable length of time at each site. The amount of time spent perching was determined by drawing from a Gamma distribution (Evans et al. 2000), with shape parameter a_t = 4 and scale parameter b_t = 1.25. This function produces perching times similar to those reported by Wheelwright (1991), and Carlo and Aukema (2005), although some bird species typically show shorter visitation times (Carlo et al. 2003, Levey et al. 2005). Once perching time expired, individuals had to decide where to move. We assumed that individuals perceived the number of ripe fruits available at each plant in the landscape, and they could also assess the distance from their current location to each plant. This information was combined to assign the probability of choosing to move to each plant in the landscape. The number of ripe fruits (F) in a particular plant was translated to an attraction value (A_f) between 0 and 1

where a_f and b_f are parameters. The attractivity of a plant decreased with distance (R) as

where A_d is attractivity based on distance and a_d and b_d are parameters. The hyperbolic tangent, tanh(x) is a sigmoidal function between -1 and 1 with inflection at x = 0. Since F and R are always positive, A_f will be zero for small F and will go to one as F increases, and A_d will be close to one for small R and will go to zero as R increases. Note that A_d effectively limits the scale at which movement decisions are made; under our baseline parameter values (Table A1), attraction A_d drops to about 0.004 at 250 meters. These attractivities were multiplied and standardized to obtain, for each plant, a probability of being chosen as the next bird location. This distribution was then sampled to determine which plant the animal would visit next. Once a bird decided where to go, it flew at a speed of 6 meters per second (Marcum et al. 1998) following a straight line between current location and destination.

While perching at a plant, simulated birds could eat fruits. The number of fruits consumed (C) was given by a hyperbolic functional response but kept within the limits of gut size:

where  and  are parameters, F is the number of ripe fruits available at the current plant, and G is the fraction of the bird’s gut already filled. The maximum number of fruits that a bird could hold in its gut (N) was fixed at 15. The value of C from the above equation was rounded to the smallest nearest integer. Every time a frugivory event occurred, the fraction of gut filled and the number of available fruits at the focal plant were updated. This functional response match field observations from Carlo (2005a & 2005b) on frugivory that show  that frugivores remove similar amounts of fruit per visit, irrespectively of fruit crop size (as long as crop size is larger than gut capacity, see also Appendix on Carlo et al. 2003).

Each fruit was assumed to contain a single seed, and after ingestion, gut passage time was sampled from a Gamma distribution with a mean of 27 minutes and SD of 15 (Gamma (3, 9)). The scale and shape of this Gamma were chosen to broadly match seed gut-passage rates reported from several frugivorous bird species (Murray 1988, Wahaj et al. 1998). For simplicity, all seeds from a frugivory event had identical gut passage time. Birds defecated seeds at the time dictated by gut passage time, irrespective of whether the animals were perching or flying. The program recorded the spatial coordinates of each dispersed seed, as well as the identity of the mother plant.

Simulated birds kept moving, eating and defecating until they accumulated 6 hours of daily activity. At the end of each simulated day, every plant produced new ripe fruits according to a regrowth model (Turchin and Batzli 2001):

where  is regrowth rate and M is the maximum number of fruits that a plant can bear at any time. We assumed that plants produced fruits during 30 days.

We generated landscapes with four levels of spatial aggregation by simulating a Neyman-Scott process (Zollner and Lima 1999). To generate the landscapes our algorithm did the following. First, given a pre-defined number of clusters, “parent” plants were initially distributed over space as a Poisson process by sampling x and y coordinates from a uniform distribution. Second, one of the parent plants was chosen at random and a “daughter” plant was added at a random direction and at a distance sampled from a Weibull distribution with shape parameter equal to 2 and with a predefined scale parameter. The scale parameter of the Weibull determined the degree of aggregation of the cluster around parent plants. Finally, the process of choosing a “parent” plant and adding a “daughter” was repeated until the desired number of plants in the landscape was obtained. Aggregation of plants ranged from very low to highly clustered and was determined using Weibull scale parameters 0.01, 0.001, 0.0001, and 0.00001 (Fig. A1), which resulted in mean (SD) nearest neighbor distance, in meters, of 6.6 (12.1); 19.0 (15.4); 50 (32.7); 75.9 (44.2). Simulated landscapes where composed of 200 clusters and a total of 1000 plants distributed over a 5,000 × 5,000 meter space. We used a large landscape size to minimize edge effects and to better estimate seed dispersal over long distances.

TABLE A1. Baseline parameters for frugivore simulation model.

Parameter	Description	Value	Units
at	Shape of Gamma distribution for perching time	4
bt	Scale of Gamma distribution for perching time	1.25
ag	Shape of Gamma distribution for gut passage time	3
bg	Scale of Gamma distribution for gut passage time	9
af	Factor in attractivity due to number of fruits	0.001
bf	Exponent in attractivity due to number of fruits	2
ad	Factor in attractivity due to distance	0.00005
bd	Exponent in attractivity due to distance	2
	Maximum consumption rate in hyperbolic functional response	10	fruits/visit
	Half saturation in hyperbolic functional response	2	fruits
N	Maximum gut capacity	15	fruits
	Fruit regrowth rate	20	fruits/day
M	Maximum number of fruits per plant	100	fruits
v	Flying speed	6	m/sec

FIG. A1. Examples of plant distributions generated using a Neyman-Scott process. All cases have 200 clusters and a total of 1000 plants; (a) scale = 0.01; (b) scale = 0.001; (c) scale = 0.0001; (d) scale = 0.00001.

LITERATURE CITED

Carlo, T. A., and J. E. Aukema. 2005. Female directed dispersal and facilitation between a tropical mistletoe and its dioecious host. Ecology, in press.Carlo, T. A., J. A. Collazo, and M. J. Groom. 2003. Avian fruit preferences across a Puerto Rican forested landscape: pattern consistency and implications for seed removal. Oecologia 134:119–131.Evans, M.., N. A. J. Hastings, and J. B. Peacock. 2000. Statistical distributions, Third edition. Wiley, New York, New York, USA.

Levey, D. J., B. M. Bolker, J. J. Tewksbury, S. Sargent, and N. M. Haddad. 2005. Effects of landscape corridors on seed dispersal by birds. Science 309:146–148.

Marcum, H. A., W. E. Grant, and F. Chavez-Ramirez. 1998. Simulated behavioral energetics of nonbreeding American robins: the influence of foraging time, intake rate and flying time on weight dynamics. Ecological Modelling 106:161–175.

Murray, K. G. 1988. Avian seed dispersal of three neotropical gap-dependent plants. Ecological Monographs 58:271–298.

Turchin, P., and G. Batzli. 2001. Availability of food and the population dynamics of arvicoline rodents. Ecology 82:1521–1534.

Wahaj, S. A., D. J. Levey, A. K. Sanders, and M. L. Cipollini. 1998. Control of gut retention time by secondary metabolites in ripe Solanum fruits. Ecology 79:2309–2319.

Wheelwright, N. T. 1991. How long do fruit-eating birds stay in the plans where they feed? Biotropica 23:29–40.

Zollner, P. A., and S. L. Lima. 1999. Search strategies for landscape-level interpatch movements. Ecology 80:1019–1030.