@Lioba, I totally understand your thinking. I've been confused by the term, "invasive," and so have done a bit of research on it to try to understand better. Evidently, plants that simply send out seeds and multiply a LOT are considered to be "aggressive." While "invasive" plants are not only aggressive, but also block out the growth of indigenous plants so that eventually, there are no more and only the invasive species remains. Some definitions also apply invasive to plants that aren't that aggressive.
I believe the term is applied in the same way to birds, frogs and other creatures. A very important definition.
