Understanding the mechanisms that allow exotic species to have rapid population growth is an important step in the process of controlling existing invasions and preventing future invasions. Several hypotheses have been proposed to explain why some exotic species become invasive, the most prominent of which focus on the roles of habitat disturbance, competitors and consumers. The magnitude and direction of each of these mechanisms on population dynamics observed in previous studies is quite variable. It is possible that some of this variation results from interactions between mechanisms. We examined all of these mechanisms and their interactions on the population dynamics of the Asian exotic tree Ailanthus altissima (Simaroubaceae) in fire-suppressed oak-hickory forests in Missouri, USA. We experimentally reduced herbivory (using insecticide), reduced interspecific competition (plant removals), and manipulated disturbance with prescribed fire. We projected the effects of these treatments and their interactions on population dynamics by parameterizing an integral projection model. The lowest population growth rate is found where fire is absent and biotic interactions are present. Fire increased population growth rate, likely through the suppression of interspecific competitors, since competitor removal treatments increased population growth rate in the absence but not presence of fire. These results indicate that biotic resistance from interspecific competitors, more so than consumers, is important for slowing the invasion of A. altissima. Furthermore, disturbances that weaken biotic interactions, such as fire, should be used with caution when restoring habitats invaded by A. altissima. Synthesis and applications. Examining the main and interactive effects of disturbance, competition and herbivory on the population dynamics of exotic species provides a comprehensive understanding of the role of these factors in the invasion process and provides guidance for exotic species management.