A recent study indicates that Neanderthals had relatively little diversity in their gene pool suggesting that they were few in number at least for some period. Per the article:
Neanderthals were remarkably less genetically diverse than modern humans, with Neanderthal populations typically smaller and more isolated, researchers say...."The amount of genetic diversity in the Neanderthals was about a quarter of that in Africans today, and about a third of that in Europeans or Asians."....This suggests that Neanderthal populations across Eurasia were likely small and isolated. "Neanderthals seem to have been few in numbers either over a long time or for some periods," Pääbo said. "There is also an indication that they have been subdivided in populations that had little contact with each other."....The scientists detailed their findings online today (April 21) in the journal Proceedings of the National Academy of Sciences.
John, I wonder if that lack of diversity is a partial explanation for their demise, or for being subsumed into the modern human genome. Lack of genetic diversity has been used to explain why Native Americans' populations were decimated by diseases that spread faster than the colonizers themselves. It is also why some agricultural crops are more susceptible to disease.
Maybe as soon as modern humans encountered Neanderthals, diseases spread into the relatively uniform Neanderthal population, wiping out most of them. They were too immunologically homogeneous to adapt.
Or, modern humans just killed them off.
You don't need low genetic diversity to explain the rapid spread of diseases in Native American populations from European visitors. Europeans had been coevolving with those diseases for tens of thousands of years. Continental American populations had never been exposed to them.
But I would like to see your source, consider their evidence.
Certainly agricultural crops have low genetic diversity and consequent vulnerability.
It seems reasonable that lack of genetic diversity left them vulnerable to some extent to diseases carried by modern humans and that modern humans killed some of them off. However, there is evidence that they were struggling to hang on in Eurasia even before modern humans got there. http://www.livescience.com/5570-neanderthals-poised-extinction.html As such, most of them could have just been absorbed into the modern human population. I had my DNA analyzed by National Geographic and it is 2.9% Neanderthal.