All the academic papers show how close southern Italians, mainland Greeks, and island Greeks are to one another.
The discrepancy in 23andme is because of where they place their clusters. It's because they have an Italian cluster which is heavily based on Southern Italians and to an extent on central Italians, and then a cluster on the Balkans including mainland Greece. That leaves the island Greeks out in the cold, so the algorithm chooses the "closest" clusters and makes them sort of a mix.
If they had a cluster based on northern Italy and one based on mainland Greece, but no southern Italian cluster, then southern Italians would come out with a big chunk of Greek, and a chunk of "Italian", or Northern Italian.
Some companies, like Ancestry, I think, just combine Southern Italy and Greece. I assume that people like Romanians get a chunk of that component?
The ancestry doesn't change: just the labels.
You can't think so linearly, people.
FYI, the Lombards and Goths moved north to south.
Also fyi, my husband's beta map shows a bit of movement north to south, but although widespread, it's not very significant. Colonia as well? Or perhaps in his case it's northerners going into Napoli. It does a great job of showing that he has mixed Calabrian and Campanian ancestry. The Sicily signal makes sense as well: the province of Reggio Calabria isn't all that different from eastern Sicily.
He has 12% "West Asian" i.e. Caucasus, and .7% North African and Arabian. It doesn't seem as if much traveled up into the mainland. Also, Balkan shows up: 2.2%.
I wonder what Sicilians show.