Interview with Charles Koch on Nautilus:
[Q:] We also know Neanderthals had bigger brains than the Homo sapiens who lived near them in Europe. Yet we survived and they didn’t.
[A:] Their brain was maybe 10 percent larger than our brain. We don’t know why we survived. Did we just outbreed them? Were we more aggressive? There’s some research showing that dogs play a role here. At the same time when Homo neanderthalensis became extinct—around 35,000 years ago--Homo sapiens domesticated the wolf and they became the two apex hunters. Homo sapiens and wolves/dogs started to collaborate. We became this ultra-efficient hunting cooperative because we now had the ability to be much more efficient at hunting down prey over long distances and exhausting them. So the creature with the larger brain didn’t survive and the one with the smaller brain did.