Early admixture involving source groups most similar to contemporary populations from in and around the Levant (which we define as the World Region containing individuals from Syria, Palestine, Lebanon, Jordan, Saudi, Yemen and Egypt) is seen at high proportions in several clusters from Italy dating to the first half of the first millennium CE, from Southern Italy (itali8: 295CE (72BCE-604CE); α = 0.34), Tuscany (tsi23: 400CE(30BCE-686); α = 0.29), and Sardinia, as well as in a large cluster from Armenia at an early date (armen27: 363BCE(1085BCE-383CE)). [. . .] these events loosely coincide with the formation of the pan-Mediterranean Roman Empire [S?], which may also have allowed increased gene flow from east to west Mediterranean
I've written about this in my review of Robert Graves's I, Claudius. Years ago I came upon an article whose author used grave inscription statistics to claim that the early-Roman-era population of Italy was partially replaced in imperial times by Middle Eastern slaves.
I've read lots of contradictory historical claims in my life. Why did I believe that one? Because it fit other data. Rome experienced a gradual shift from a typically-European political setup (popular assemblies, elections, debates, term limits) to a typically-Middle Eastern one (the worship of the absolute monarch as a God). At the same time its native religion was to a large extent replaced with Middle Eastern ones (Mithraism, Christianity, the Cybele cult, Egyptian Gods), which then fought it out against each other for supremacy with well-known results.
The quote above states that the study measured the admixture from a region that includes "Syria, Palestine, Lebanon, Jordan, Saudi, Yemen and Egypt". Why didn't they include Turkey? Anatolia was an enormously important part of the ancient Med world and a large source of slaves for the Romans. I'm guessing that the admixture result would have been higher if Turkey was included. And, now that I think of it, where are Libya, Algeria and Tunisia (the ancient Africa and Numidia)? Also, the amount of Middle Eastern ancestry in Italy must have been decreased somewhat by the Germanic invasions of the 400 AD - 800 AD period.
I'm interested in this partly because I'm a product of this mixture myself and partly because it can shed light on the history of civilization. Greece also gradually went from a typically-European political setup to a typically-Middle Eastern one. It also imported Middle Eastern slaves, starting after Alexander's conquest. And a couple of centuries after that conquest Greece's mathematical and proto-scientific progress stopped. Which is the same thing as saying that the quality of its intellectual life gradually merged with that of the Near East.
Based on all of that I feel confident in predicting that genetic studies will show (maybe they've already shown it and I just don't know it) that modern Greeks have even less to do with classic-era Greeks than modern Italians have to do with the Italians of the time of the Roman Republic.