A reconstructed Neanderthal skeleton, right, and a modern human skeleton, left, on display at the Museum of Natural History in New York. (Frank Franklin II/Associated Press)

By the standards of the Paleolithic age, members of Homo neanderthalensis were the height of sophistication. These ancient hominins ranged across Europe and parts of Asia for more than 300,000 years, producing tools, jewelry and impressive cave creations. They cared for their sick and elderly. They perhaps even performed a primitive kind of dentistry.

But then Homo sapiens showed up, and the Neanderthals disappeared. So what happened?

For decades, modern human scientists assumed there must have been something wrong with the Neanderthals — or something right with us — that led to their extinction. Maybe H. neanderthalensis had bad genes that made the species more vulnerable to disease. Maybe…