The way in which this seems to have happened in Europe is rather interesting: first you have the old Mesolithic hunters. They are then largely replaced by farmers from the Levant, some settling the southern coast of Europe and others moving up along the Danube - genetically  similar to modern Sardinians.   

A new wave [Indo-Europeans, surely] mostly replaces those farmers, and this new wave has a fair amount of ancestry from a group very similar to those original Mesolithic hunters.  So the amount of Mesolithic hunter ancestry among Europeans first goes way down and then goes up again. 

The return of the native strikes back. 

Those Mesolithic hunter-gatherers aren’t exactly a lost race, since they had plenty of descendants, but it seems that there are no longer any unmixed examples – although we really need to check out the Lapps. 

The problem is, they need a name.  “Ancestral North Eurasians” just doesn’t sing.  Neither does “Ancient Siberians”.  Personally, I like “Hyperboreans.”