Anthropology

We know that there was interbreeding. What is no so obvious is what happened with hybrids. As is the case in other close species hybrids, the likeliest scenario was that the males shot blanks. I wonder if he's considered this particular effect in his models. My guess is not.

We didn't outcompete them, they were ideally suited to Ice Age Europe and Asia. We weren't any smarter, their tools might look big and clumsy to the untrained eye, but they were a lot more ergonomic than modern human tools of the same period. What we were is a lot more mobile, extending our own range far beyond their semi fixed settlements, and if we'd left enough infertile male offspring with those foxy Neanderthal ladies, that could explain both the signs of inbreeding geneticists have seen in later remains and a drop in population that likely finished them off.

This field, like the planet itself, is continuing to evolve. I tend to mistrust computer modeling at this stage because we really don't know anywhere near the whole story yet. It's like looking through a keyhole and thinking you can see the entire interior of Versailles.

Likely different populations faced different pressures. We don't know what some of them were, likely we'd brought new diseases with us along with everything else. The effects of hybridization were likely another. Climate did vary widely during the last Ice Age, and for settled people, it was likely feast of famine.