Models of forest ecosystems are needed to understand how climate and land-use change can impact biodiversity. In this paper we describe an ecological dispersal model developed for the specific case of predicting seed dispersal by trees on a landscape for use in a forest simulation model. We present efficient approximation algorithms for computing seed dispersal. These algorithms allow us to simulate large landscapes for long periods of time. We also present experimen- tal results that (1) quantify the inherent uncertainty in the dispersal model and (2) describe the variation of the approximation error as a function of the approxi- mation parameters. Based on these experiments, we provide guidelines for choosing the right approximation parameters, for a given model simulation.