I would think the pythons can just stick to eating baby alligators and eventually wipe out the population. Or at least make alligators much more scarce as a predator-prey equilibrium is achieved. Of course, alligators are not the only possible meal for pythons. As long as there is something they can eat, their population will grow. But for that matter, about 6-7% of baby alligators are eaten by big alligators, so the life of a baby alligator has never been carefree.

Boy, we really have gotten off topic!