The Second Law of Thermodynamics

Maintaining order requires effort. The Eiffel Tower in Paris, a steel structure that was supposed to be temporary when it was built in 1889 for the universal exhibition cost over $14 million annually to maintain. Strictly speaking, extinction is what happens after a species fails to maintain a higher proportion of births to death. It's a numbers game and so the real competition between Neanderthals and early modern humans wasn't localized quarrels for food or territory but a quiet millennium long demographic marathon. Each species repopulating itself until one fell so far behind that it vanished.