I do believe rats and mice come from overseas, and was brought to America. Correct me if I'm wrong, and it's the other way around.
I do not agree with bringing new species into the mix. The St Lawrence River is threatened by a new type of crab that will kill other species, by eating all the food.
As well, we humans farm fish that are native to the Atlantic Ocean on the coasts of the Pacific. These fish escape their pens, and infect the wild fish with their diseases, as well as breeding with other fish, creating a new, dangerous species. The Altantic Salmon is the most aggressive salmon in America, and if they don't breed with the other salmon, they will kill them.