Sardinia_Punic is not North Africa, its MENA ancestry is mostly levantine, I would use Sardinia_C_O, Mozabite, Iberia_Central_CA_Afr
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Sardinia_Punic has North African shifted samples:
https://i.imgur.com/GPNO1Vu.png
Those 4 categories:
North Levant Iron Age
North Levant Bronze Age
South Levant Iron Age
South Levant Bronze Age
BTW I imagine by north we mean Syria+Lebanon and south Israel+Palestine+Jordania, also maybe it would be nice to add any Turkish samples that is within the region, if there are any, I need to check.
Where do you think the Mittani came from? They're Indo-Iranians and Indo-Iranians originated in Central Asia. Based on the fact this Central Asian was almost entirely BMAC with minor Steppe, it was probably either some BMAC concubine that the Mittanis brought with them or one of the Mittanis that didn't have much Steppe admix.
Edit: Never mind. You were referring to the minor SC Asian admixture that came during the combined Persian and Greek rule.