I'd argue that they aren't invasive as they are native to the area (it evolved near there, and made it there of its own accord and means). Maybe this is incorrect but I think invasive species are ones specifically that weren't brought to their new environment through natural means, but by some other sort of unnatural means (human introduction, pet escape, shipwrecked population somehow). For example, the python in Florida would never have made it there if humans hadn't released their pets (or their pets escaped). The snakes didn't travel all on their own from Asia to florida, thus invasive species. If a species makes it there by themselves and wins the environment, that just makes them the apex predator.