Since the 1950s, the tree of heaven (Ailanthus altissima) has progressively invaded forests in southern Switzerland and is becoming a growing concern also north of the Alps. Recent studies have increased the understanding of the species’ ecology, but its role in long-term stand dynamics remains uncertain. Therefore, we simulated the long-term dynamics of unmanaged and managed forest stands in southern and northern Switzerland under current and future climate conditions (RCP8.5) using the forest gap model ForClim. Our results indicate that A. altissima will increase its presence in the short term (< 100 yrs), but does not gain dominance in the long term (> 200 yrs), confirming its pioneer character. Timber harvesting led to an increasing share of A. altissima compared to unmanaged stands. Overall, our findings suggest that in the long run, a competitive displacement of native dominant species by A. altissima appears unlikely, with the exception of drought-prone sites under strong climate change. Furthermore, our findings underline the importance of the frequency and intensity of forest management for the long-term abundance of A. altissima in forest stands.