thats a really cool project. I would love to see how different dimensionality in that data (time, geographic, plus genetics) was related to big historical events maybe even events we didn't know about

Yeah I was thinking about how one could explore this information to look at spcefic events but they might not have enough data to show them. For example I would expect the enclaves of Occitan speakers in far southern Italy would show up.

love it how most Balkan countries are not even Europe in (this particular author's) medieval times...

You're limited by dataset and sample size. Even in much of Western Europe, the sampling is limited.

That said, this is a point of contention that even the authors of the paper allude to:

"The most principled approach is thus to build ancestry models in which source and ‘outgroup/reference’ populations are older than, or at least contemporary with, the target genome or group that we are trying to model. However, this has been challenging, due to the limited statistical power offered by the thousands-fold lower sample sizes and reduced sequence quality of ancient genomes"

Do I get this right: genes were flowing from Scandinavia down to mainland Europe in the first half of the first century (i.e. before the Vikings, are they talking about the ancestors of the Goths and Vandals, for example?) and it reversed direction during the Viking period?? Isn't that quite the opposite of what was expected?

Iron age British ancestry being found in Ukraine with Viking graves also sounds really fascinating.

No that is indeed what is expected. You see gene flow towards scandinavia and other viking held areas because they would capture and take women back with them when raiding.

So they didn't settle in most regions then? I had imagined they did not only settle in England and Iceland, but also in the other regions that they went towards the East, but that was just not as obvious today because those regions already had larger populations.

Well, Curonian settlemen on Gotland and Uralic male gene flow into Scandinavia via Alands during Viking age can't be explained by just capture of females. Not to mention that some of the English male ancestry that landed there during Viking times is shared with Estonians and not Scandinavians.

But frankly, this paper is not about captured females(which btw are more uniformly spread across whole Europe, so their capture even in Southern Europe would not radically add anything new to a Scandinavian female gene pool), when it specifically mentions whole populations coming to Scandinavia from Central Europe. It is differences in males that really make distinctive population groups.

Look up New England when early Rus ruler married Anglo-Saxon, that were part fo refugees from Norman ivasion.

Low-resolution images used in article on High-resolution genomic history of early medieval Europe.

Somewhat related, Dwarkesh Patel has an excellent talk with David Reich about the broader history of genetics:

https://www.dwarkeshpatel.com/p/david-reich