Communities have been viewed as the end product of an assembly process that results in increasing stability through time as progressively better competitors eventually dominate the other species that can emigrate from a regional pool. Previous work has explained species assemblages based on the traits of the successful species. We suggest that the traits of unsuccessful species in the regional pool may also be important for understanding which species are successful in communities. We constructed a simulation model to study what distinguishes stable, uninvasible assemblages from other possible assemblages from a regional pool of species. Our model demonstrates that both the interactions among the successful species and the interactions between these species and unsuccessful species attempting to invade the community contribute significantly to determining success in the final stable community. Understanding the structure of natural communities may require some knowledge of the unobserved "ghost" species that fail to establish in that same community yet still have significant effects on structure.