Fighting tree of heaven in the northern Italian coppice forest shows that repeatedly cutting down the tree of heaven reduces its share in the canopy.
At the same time, it becomes clear that doing nothing will eventually lead to the almost complete disappearance of the tree of heaven from these forests. This pioneer tree species is losing out to native successor species. A nice Italian application of the ecosystem resilience approach (ERA) as we develop it in LIFE Resilias:

Tree of heaven, a pioneer tree species in Italian coppice forest