Now that I think about it, overpopulation is really a temporary problem.
Creature <x> has no natural predators and/or has such a high rate of reproduction that the birth rate exceeds the death rate, so the population can grow unchecked. Eventually the population reaches a point where there just aint enough resources to go around. At that point, they start dying off due to lack of resources (food and shelter) and due to fighting over the few resources there are. Until eventually the population drops back down to a sustainable level, and the cycle repeats itself.
This would make for an interesting campaign actually. Elves that never die of old age are reaching the breaking point, so they start invading the other races territories. At that point all the other races join forces to BECOME the "natural predators" of the elves and keep their population under control, or the elves win and eventually run out of resources anyway, though only after wiping out most other beings