Dizzlen, here is an example of how big of an impact a non-native species can have on our ecology.
Believe it or not....earthworms are not native to America. They came from Europe and Asia. Well, here in Minnesota without worms, fallen leaves decompose slowly, creating a spongy layer of organic "duff." This duff layer is the natural growing environment for native woodland wildflowers. It also provides habitat for ground-dwelling animals and helps prevent soil erosion.
Invading earthworms eat the leaves that create the duff layer and are capable of eliminating it completely. Big trees survive, but many young seedlings perish, along with many ferns and wildflowers. Some species return after the initial invasion, but others disappear. In areas heavily infested by earthworms, soil erosion and leaching of nutrients may reduce the productivity of forests and ultimately degrade fish habitat. [mndnr]
So...you can see the impact a tiny earthworm can have on an entire forrest and it's ecology, effect even fish.
Now imagine what is happening to the florida ecology with the Burms and Iguanas roaming freely?