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 B. Sensitivity analysis.

We calculated main and total Sobol’ sensitivity indices using the Winding Stairs method (Chan et al. 2000, Ellner and Fieberg 2003). The Winding Stairs method is based on sequential changes in model input values and allows to explore model performance while minimizing model runs (Chan et al. 2000). Main effects can be measured by the expected variance reduction in model output due to fixing a factor (parameter) while the others vary. Total sensitivity is defined as the sum of all the sensitivity indices (including all the interaction effects) involving the factor of interest. We varied the number of frugivores as well as the parameters that controlled the distributions of perching time and gut passage time as well as the parameters that control the scale of the attractivity functions, bird functional response, plant crop size, productivity and spatial aggregation. Note that we changed gut passage time from a Gamma to a Weibull distribution to allow for long waiting times in seed passage. The Gamma distribution can be conveniently combined with distance moved in the diffusion model but its tail is always exponentially bounded. Sensitivity was performed on a total of k = 13 parameters for which we defined a range of possible values from where uniformly distributed samples were taken sequentially using the Winding Stairs algorithm. We ran the model for a total of 6500 parameter combinations and recorded mean dispersal distance and kurtosis as model output.

TABLE B1. Main and Total sensitivity indices for the simulation model. MM_i and MT_i are main and total sensitivities for mean dispersal distance.

Param	Description	Range	MMi	MTi	KMi	KTi
at	Shape of Weibull for perching time	0.4 to 4	0.100	0.218	0.048	0.198
bt	Scale of Weibull for perching time (*)	0.001 to 2	0.259	0.417	0.073	0.253
ag	Shape of Weibull for gut passage time	0.4 to 4	0.090	0.190	0.214	0.329
bg	Scale of Weibull for gut passage time (*)	0.0001 to 2	0.164	0.249	0.145	0.339
af	Factor in attractivity due to number of fruits	1e-05 to 1	0.003	0.032	0.064	0.091
ad	Factor in attractivity due to distance	-1e-06 to -0.05	0.016	0.026	0.061	0.022
	Maximum fruit consumption rate	1 to 100	0.004	0.021	0.070	0.043
	Half saturation in fuctional response	1 to 50	0.000	0.039	0.065	0.025
N	Maximum gut capacity	5 to 200	0.057	0.155	0.040	0.140
	Fruit regrowth rate	1 to 500	0.001	0.007	0.062	0.010
M	Maximum number of fruits per plant	10 to 10000	0.002	0.012	0.087	0.030
	Scale of Weibull in Neyman-Scott process (*)	1e-07 to 1	0.191	0.265	0.065	0.013
U	Number of frugivores	1 to 50	0.090	0.102	0.118	0.306

   Notes: KM_i and KT_i and main and total sensitivities for kurtosis of dispersal distance. Large sensitivity values are in boldface. Note that for greater flexibility in model input we used Weibull distributions instead of Gammas for perching time and gut passage time (compare with Table A1).

(*) For these variables we first draw values from a uniform distribution of mean distances and then solved for the corresponding scale parameter given known shape parameters.

LITERATURE CITED

Chan, K., A. Saltelli, and S. Tarantola. 2000. Winding Stairs: A sampling tool to compute sensitivity indices. Statistics and Computing 10:187–196.

Ellner, S. P., and J. Fieberg. 2003. Using PVA for management despite uncertainty: Effects of habitat, hatcheries, and harvest on salmon. Ecology 84:1359–1369.