Neanderthal disappearance

At www.smithsonianmag.com/science-nature/did-neanderthals-die-out-because-p… …. Neanderthals had bigger brains than we have and a similar tool repertoire to early modern humans so why did they die out? This obviously intrigues a lot of people and some odd theories have been touted to account for their sudden disappearance and the equally sudden appearance of modern humans in their place. The latest and also odd explanation being put forward is that they died out as a result of their diet – assumed to be high in meat (but lacking enough fat). There is a paradox there somewhere as animal flesh has a high fat content – and it is an assumption they hunted mammoths to feed on and avoided smaller game. Another assumption is that they lived on the edge of the ice sheets where supplementary plant food was in short supply. I expect this one will be shot down in flames fairly rapidly. Eventually they might get around to looking at the idea of catastrophism.