I have seen Caribbean Islands like Cuba, for instance, totally invaded by thorny African acacias. Other acacias may be invasive, even some of the ones from Australia.The story goes that a particularly rich lady who liked the look of the plants (so striking and dramatic) while travelling in Africa decided to import a couple of them for her garden...These plants are now found everywhere in the fields in Cuba because they propagate so easily. They have taken over rich agricultural lands and form thickets one can not penetrate except by using a bulldozer. Even if you bulldoze through them you can not eliminate them, can't clear them out. But fortunately, when the plants recover with a new set of leaves, the cattle can feed on them. I say that if a plant can be said to be even potentially invasive, please don't plant them in your garden. And, be well informed before you get to the purchase stage.