My understanding is that Ancestry.com goes back roughly 8 generations, whereas Geno 2.0 determines your "deep ancestry" from 500 years ago to 10,000 years ago, which is an awfully long window of time.
I remain intrigued by the finding that I am 2% Eastern African. Unless there was a significant admixture event involving Saracen incursions along the coast of Calabria circa 1000 AD, affecting the entire countryside of the area (and this seems unlikely), I suspect that this might have something to do with the fundamental population structure of the Southeastern Mediterranean, dating back to the original Neolithic settlements. Perhaps there was a significant Natufian or Basal Eurasian component among the first farmers fanning across the sea?
See this article from 3 years ago,
https://egyptsearchdetoxed.blogspot.com/2015/01/lets-face-it-basal-eurasian-is-heavily.html
I would strongly advise you not to believe the things said on that site. It's very biased and highly suspect.
The fact is that some Southern Europeans, particularly Iberians and Italians, but even in parts of southern France, will sometimes, in a good analysis, throw up a percent or two of SSA, most of which arrived during the periods of Saracen rule (although not all, as the discovery of an SSA admixed sample in Copper Age Iberia. People travel, trade, some genetic admixture occurs.), or, in the case of Iberia, which had colonies around the world where people admixed, some of those people might have returned and injected those alleles in the genetics of the population. There's some controversy about it, but some people believe that happened in some parts of Portugal. I don't have a strong position on that.
I can say that I've seen hundreds of Italian samples, and only very few throw up 1 or 2% SSA, and they are mostly Sicilians, which makes sense since they were ruled by the Saracens for 250 years or so. That's not the case for mainland southern Italy, so it would be difficult to explain, except perhaps through an unknown Sicilian ancestor? My husband's whole family has tested, practically (3/4 Calabrian and 1/4 Neapolitan), and he's the only one who gets any, .4% to be precise. So, it's hit and miss which little bits someone will get.
Bottom line, yes, there was obviously some movement even in the Copper Age from North Africa to Iberia, and probably some from the Middle East or North Africa might have landed near your ancestors in Italy. Or it might be Saracen in origin, which the consensus seems to be suggesting is when the majority of it arrived in both Iberia and Italy. We settled for exiling the ones unwilling to convert. We didn't exterminate anyone with "tainted" ancestry, at least not all of the time, although there were horrible incidents such as the ones by the Emperor Frederick against Saracen soldiers he sent to Bari.
So, by chance, some SSA might have been passed down, but except for one strange result where a Neapolitan got 1%, I've really only seen it in Sicilians, and not all Sicilians by a long shot.
I really do think some companies are better at doing this than others.
Ed. Just saw you were really talking about East African. Sorry for the misunderstanding. It's quite possible someone from the Middle East with "East African" in them might have landed near your ancestors, and it survived recombination because it was perhaps an isolated community. However, the thing to remember about East Africans is that they are half West Eurasian like. Some people think that West Eurasian signal comes from Levantines, or even from further back from early farmers from the Levant. Just lately someone is saying the alleles are from Sea Peoples, i.e. Greek like. That seems bizarre to me. The paper is on my list; when I've read it I'll post about it.
Anyway, point is, what are you matching? Are you matching the SSA or the Middle East/Sea Peoples portion or both? This isn't an exact science yet.