The thesis of European migration to the American continent appears to be sound. However, the problem with DNA testing is that the subsequent history of those European colonists is unknown. Did they leave descendants whose DNA can be found in present-day Americans? Or did they colonize and then die out?

There's modern research from special air-to-ground observations in North America that Vikings (for example) reached further south than previously suspected. But what happened to them - did they leave DNA traces in local inhabitants, or did they leave, die out, etc.?

It's a fascinating topic. There's a whole set of modern research papers, based on group DNA testing, which challenges the history of Celtic/Roman/Saxon history as set out by Bede - i.e. the Celts were driven out of the body of England by the Romans and, when the Romans left, the Saxons poured in. However, DNA group tests suggest that the pre-Roman inhabitants of England were related more to the Germanic tribes of Europe, that the Celts were more in evidence in Cornwall, Wales, etc., and that there is very little evidence in archaeology, of Celts in the main body of England.

All interesting stuff, and ripe for good, heated arguments!