Many spatial models of ecological processes achieve analytical tractability by neglecting variability among individuals, in their patterns of movement, and among locations, in their favorability for colonization or persistence. We develop a series of simulations, based on standard metapopulation and partial differential equation models, that explicitly track variability among individuals or locations, and compare the results with what would be obtained by ignoring such variability. We find, first, that variability among patches can have a strong influence on the outcome of community dynamics, by promoting the coexistence of species that would otherwise exclude one or the other through competition. Second, variability among individuals in their rates of movement can markedly increase the rate of spread of a population. Construction and analysis of a modified PDE (partial differential equation) model for a population that consists of two classes of individuals, dispersed and nondispersers, confirms the second result, and also shows that the presence of even a few rapidly dispersing individuals can markedly increase the rate of spread of the population. Our simulations and analysis show that the incorporation of variability into ecological thinking is feasible and that it can strengthen our ability to investigate the effects of spatial processes.