When we look at ancient DNA and see some sharing with the modern populations living in the same region, we tend to think we’re seeing population continuity – people in that region today are to some extent descended from the people who lived there a long time ago. And sometimes that is the case. But it ain’t necessarily so.
Imagine a land (let us call it East Dakota) that was once entirely populated by Amerindians. Later, Norwegians show up and entirely replaced the Amerindians, all of whom were killed or displaced. Later still, a conquering horde of Guatemalans entirely replaces the Norskis: all of the European-descended types are killed or displaced.
People from the far future, looking at this through the lens of ancient DNA, might at first conclude that the last population was the product of a fusion between the first and second, at least if they didn’t have good enough sampling to notice how completely disjoint the first and second populations were. Or they might know about the kind-of European Ancient North Eurasian component in Amerindians, and confuse themselves with that. Or they might conclude that the the third population’s European component was derived from the second population – plausible but wrong.
Eventually, if they looked at the fine details, they might notice that even when mtDNA and Y-chromosome haplotypes are shared, the sub-haplotypes aren’t. So some people from population I have Q-haplotype Y-chromosomes, as do some of the people in population III, but nobody in population III is a direct male descendant of anyone in population I – which ought to make you wonder. If nobody in Pop III is a direct female descendant of Pop I, you should wonder even more.
I don’t know if this, or something like it, is what happened in European prehistory. But hunter-gatherer autosomal DNA first becomes quite rare, and then makes a comeback a couple of thousand years later. Unless they were sleeping inside the hill of Alderley, it’s hard to see how the people executing the reconquista can be direct descendants