Balance of nature: As it should be

How come predators never hunt their prey to extinction? Is this balance of species in an ecosystem a natural law or more of a superstition?

Already the ancient Greeks seemed to have believed in a balance of nature and nowadays this terminology is still sometimes used. But what exactly is this balance and can it be defined in a scientific way?

This question was raised in the 18th century when the discovery of fossils of unknown species radically changed our view on ecology. While some scientists still tried to make sense of it, today the world “balance” is no longer seen as useful when describing ecosystems.