To predict a fine-scale invasion of Argentine ants (Linepithema humile) into a natural area from the surrounding suburban matrix, we introduce a grid-based invasion model, similar to a cellular automaton model. Our model was based on observations of ant presence and absence but, unlike other models based on presence-absence data, it incorporated the process of invasion by spread from neighboring areas. Simulations were parameterized from a statistical analysis of a 17-year survey of ant distributions in the Jasper Ridge Biological Preserve in northern California. We simulated the effects of Argentine ant presence at neighboring grid squares, distance to development, presence of the native winter ant Prenolepis imparis, and other habitat and climate variables, and used these models to simulate invasion over many decades. The best predictions of the extent of Argentine ant invasion were based on the distance of each site to developed areas. Adding the effect of neighbors improved the predictions of the time at which sites would be invaded. Winter ants responded mainly to vegetation cover. Our results suggest that Argentine ants may reach their potential distribution in insular urban reserves rapidly, perhaps within 10 years, and that reserve size determines whether the reserve is likely to become fully invaded.