For more details on the f3 statistic, you should really read the linked paper. Briefly, you should remember the following:
- Significant negative f3 statistics indicate that the target population and the two parentals do not form a simple tree, but are related in a complex way
- Positive f3 statistics are consistent with either a simple tree or a history of admixture followed by genetic drift
- It is not necessary for the parental populations to be themselves unadmixed
Below you can see the 30 most negative f3 statistics.
The first thing that immediately jumps out is that Sardinians participate in most of these comparisons. And, given the mounting evidence for a Sardinian-like population in prehistoric Europe, including the Balkans, it does appear likely that a Sardinian-like element in the ancestry of Greeks is quite possible.
A different element that is paired up with Sardinians in the most negative f3 statistics consists of a variety of South Asian populations; these comparisons appear stronger than the Sardinian+East Asian ones. This dataset does not include Amerindian populations, for which the effect was strongest in the Patterson et al. paper. I suspect that South Asian populations give out stronger f3 statistics than East Asian ones, because South Asians are composed of a West Asian-like element and an Ancestral South Indian element which is related to East Eurasians. So, South Asians appear as a parental population on account of both the East Eurasian-shift effect observed by Patterson et al., as well as the West Asian-shift effect I've described in a few posts such as this.
A third set of significant comparisons involve Northern Europeans vs. Near Eastern populations, with extrema in the Baltic area and Arabia, which seems to correspond quite well with what I've called the "West Eurasian cline", with populations of northeastern Europe likely possessing a higher degree of continuity with the Mesolithic hunter-gatherers.
Overall, this exercise has convinced me that 2-way admixture models do not capture the complexity of Eurasian prehistory. The Greek population appears intermediate on a number of different clines, the two most important ones being between Sardinia and far Asia and between the Baltic and the Near East.
I will probably repeat this experiment with other populations from this set. I will also probably try to get some admixture dates using as many SNPs as possible, although rolloff appears to have fairly long running times, so I am not sure how practical that will be.