You guys have already said what I was willing to say: results should not be taken too literally, and they must be discussed and interpreted (which we've been doing here). Taken together, and compared to others, they may provide good clues on ancient movements, as we all know.
@Jovialis
As a general rule, professionals should be taken more seriously, of course.
I found the time to revisit those p-values. I missed something, indeed.
In this case, the higher the p-value the better. Ok then. What I don't understand now is why they used a threshold of 0.01 rather than 0.05, as for example Lazaridis et al. did
here and
here. Well, details...
At the end they must have used Barcin (predominant in EEF) rather than Tepecik (possibly predominant in ABA). So it'd be supposedly the opposite: Tepecik could have resulted in even better fits for Calabrians (?).
@Pax
Yes, I know. IIRC, we discussed it in a thread regarding Caucasus. Even Barcin itself would have a bit of Natufian, and Tepecik would have more, while PPNB would have something about 40% of ANF, if I'm not mistaken. Adding Natufian and eliminating PPNB could result in part of the former going to Anatolian, indeed; however, as Natufian is so old, this extra Natufian should correspond to some actual Levant Neo-like ancestry in that context, I believe, and Levant Neo (as well as Levant BA) did have Anatolian Neo after all. That's why I preferred PPNB, expecting that the tool would accommodate the extra Natufian into the correspondent pop of Levant in the timeframe chosen.
Of course, there would be different ways of estimating "Levantine(-like)" ancestry, from more recent pops to more ancient ones. As you know, shared ancestry is frequently an issue, especially when we use more recent pops as sources.
Apparently one way to estimate/isolate Natufian-like ancestry would be using it with AHG, CHG/Iran Meso etc., but this is another story.