I completely agree that there's something wrong with the modeling.
The Imperial Tuscan samples, as Pax has pointed out, are few, and from areas of southern Tuscany more adjacent to Rome. They may not be representative.
The same may be true of the "Early Medieval Samples".
As Ihype2 has pointed out, a better model for the Imperial Tuscan samples we do have so far might be admixture with the Imperial Romans, and certainly doesn't seem to be 50% Levantine. The authors themselves make a blanket statement that the admixture could be Anatolian or Levantine, and then proceeded to only show it as Levantine. I don't get what that's about at all.
As I've pointed out in a prior post, the yDna of Toscana does not support a 20% Germanic admixture, so modeling Early Medieval Tuscans in that way makes no sense to me.
Then there's the fact that the Early Medieval Tuscans, despite what the authors claim about "continuity", don't plot on top of most modern Tuscans if I'm looking at the PCA correctly.
Instead, there's a distinct shift even further away from the Imperial Tuscan samples and toward the Northern Italians AFTER the Early Middle Ages which can be seen in the PCA provided by the authors. All this while the Iran Neo actually increased. If I'm missing something here, please tell me.
There's no attempt whatsoever by the authors to explain that, although the PCA is two dimensions, and the chart is based on qpAdm.
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The Germanics wouldn't explain that, given their arrival was hundreds of years before, nor do I think it likely that whole masses of Northern Italians moved south. There's certainly nothing in the history which would imply that.
When I was majoring in European history at university, before all the revisionism where archaeologists and historians wanted to believe that there were no "invasions" by Germanic tribes, only a "Wandering", and the fall of Rome was only coincidental to their arrival, that nothing was destroyed or lost, the 5th-10th centuries (starting in 476) were called the "Dark Ages". The Middle Ages proper started around 1000 CE. (Thank goodness for Ward-Perkins, who, because he approached the period from an archaeological point of view, stemmed the time of revisionism.)
I would really love to know what actual medieval and Renaissance Tuscans looked like genetically. Perhaps the continuity was from 1000 CE, not from the "Early Middle Ages" at all, even if those samples are indeed representative. It shouldn't be hard; we have the remains. It's just no one is opening up the coffins testing them, although they did test the remains of a sample thought to be Petracco for yDna. Whoever he was, he was J2a, btw.