Dispersal is the process that binds the subpopulations of a metapopulation together. Previous models of the evolution of dispersal have tended to be deterministic and not spatially explicit. We develop an individual–based, spatially explicit lattice model to determine how subpopulation equilibrium density, reproductive rate and form of competition affect the rate of dispersal that is selected for. For comparison, a deterministic analogue of the individual–based model is also developed. Dispersal rate is a neutral character in the deterministic model. The individual–based model makes predictions which differ significantly from its deterministic counterpart, particularly when subpopulation equilibrium densities are low. Higher rates of dispersal evolve when reproductive rate is high and subpopulation equilibrium density is small. Our results demonstrate that the propensity to disperse is not a neutral character and that deterministic models of metapopulations should be interpreted with caution.