The efficacy of dispersal in relation to safe site density

For plant species, the most immediate function of dispersal is the placement of propagules in safe sites where they can grow and survive. The efficacy of any mode of dispersal is measured by the number of propagules so placed, and depends on the distribution of distances traveled by propagules and by the density of safe sites. A graphical model is developed to describe the relationship between these two factors, and to provide a method for comparing the efficacy of dispersal in different species. When safe sites are rare, distributions of distances with long tails are most efficacious; when safe sites are more abundant, distributions with broader peaks are more suitable. This analysis is shown to apply in a qualitative fashion to a group of species inhabiting the eastern forests of North America.