Species-area curves, neutral models, and long-distance dispersal

We simulate species-area curves (SACs) using a spatially explicit neutral model. These display three distinct phases with the central phase being well approximated by a "power law" where species richness (S) is related to area (A) by S = cA(z). If seeds are normally distributed in space about their parent, the power law phase of the SAC is unrealistically narrow, and implausibly large speciation rates are required to fit empirical data. However, if dispersal follows a more realistic "fat-tailed" distribution (where long-distance dispersal events are more likely) the SACs fit the empirical data better, have a power law that holds for a much broader range of areas, and require a dramatically smaller speciation rate than when dispersal is normally distributed. Neutral models with biologically plausible dispersal parameters and speciation rates lead to empirically realistic SACs.