No overpopulation can happen under Nature's watch.

Nature is nothing if it is not a mechanism to control populations. This is the mere essence of Evolution.
Therefore, altough man is not 100% subject to Nature’s command,  we somehow disrespect Nature when we believe that humans are able to overpopulate. After all, one of our most animal instinct -fear- emerged in the 20th century to put the breaks on human population growth.
So, relax: Mom knows best