It's a very interesting subject that has become popular around the world as it is showing everyone how well we are all from the same tribe - long, long ago. Heidelbergensis.
Sure, there were x3 'off-shoot' tribes that struck it out alone for awhile.
Neanderthals in Europe/Middle-East
Denisovians in Asia
'mystery X' in Africa
...then some mixed up Sapien lot emerged to breed with all of them.
The Neanderthal were mostly 'cave dwellers' and never ventured far for their resources - they were not as Nomadic as the Sapiens who 'followed the food' and its this lack of diversity was probably their downfall ...until there was so few of them left, they were probably hunted as 'Evil Ogres or Trolls' in Caves in their twilight.
I personally think that when Sapiens spread out into the world - there were many different species of modern Homo and ancient Hominids still roaming around - giving rise to legends and myths along the way. Eventually though, they either faded into the Sapien tree or died out in isolation.
San Bushmen have the most number of 'ancient genetic' combinations - their gene pool is the most varied, which is ironic, considering as a 'people' they are the most ...few.
In the end though - all males will be 'Dominant Gene' and females will be 'Regressive Gene'.
Black Groom - White Bride
How do you know Neanderthal were cave dwellers? Most humans used caves and rock shelters. Were Aboriginals cave dwellers? They certainly used caves and rock shelters as their paintings will attest. Then we have the replacers of Neanderthal using caves and rock shelters as paintings in Lascaux and Altamira will attest.
Do you have some sort of genetic memory going on? I don't fear the genetic future of man, just as his genetic past allowed me to be. Nothing stays constant.