It is being assumed by some scientists, that Neanderthal y-DNA not present in modern humans would indicate that there were fertility issues in Neanderthal men. Or an incompatibility. This replacing an ancient theory that Neanderthals were killed by modern humans screams for middle-ground. It is much more likely that homo sapiens would have killed Neanderthal men and took the women. It would be the most common way history has taken place. And not that much has changed if you look at the Bosnian war where the men were killed off and the women raped… but left alive.
Who were the Neanderthals and why should we care?
Why did the Neanderthals go extinct?