Canvasback, I am not an expert, but have read on the genetics side and talked with a friend who is a PHD in that area. The theory involved the RH Negative [think Rhesus Monkey] being held by the Neanderthal. Cross breeding with RH positive HS developed Neanderthal mothers who would then form antibodies preventing future births. The lack of fertile mothers then led to the depletion of the Species. This phenomena is present today with RH negative females mated to RH positive males, but modern medicine helps curb this possibility. After the first birth, the mother develops antibodies , affecting the future births from a RH positive father. The RH positive is the dominant gene. Tens or hundreds of thousands years later, the Neanderthal just lost out.
Now, don't criticize my explanation of this theory, because I have told you all I know or remember. I'm sure Google has some better , more clear explanations.
