Current theories of plant invasion have been criticized for their limited heuristic and predictive value. We explore the heuristic and predictive potential of a model which explicitly simulates the mechanisms of plant invasion. The model, a spatially-explicit individual-based simulation, is applied to the invasion of pine trees (Pinus spp.; Pinaceae) in three vegetation types in the southern hemisphere. The model simulates factors which have been invoked as major determinants of invasive success: plant traits, environmental features and disturbance level. Results show that interactions between these determinants of invasive success are at least as important as the main effects. The complexity of invasions has promoted the belief that many factors must be invoked to explain invasions. This study shows that by incorporating interactions and mechanisms into our models we can potentially reduce the number of factors needed to predict plant invasions. The importance of interactions, however, means that predictions about invasions must be context-specific. The search for all-encompassing rules for invasions is therefore futile. The model presented here is of heuristic value since it improves our understanding of invasions, and of management value since it defines the data and models needed for predicting invasions.