As far as I can tell, the hypothesis of "several mixtures" comes from looking at many pairs of populations and seeing that different types of pairs seem like they mixed to make Armenians. Possibility (1) is that Armenians have multiple mixtures, and possibility (2) is that none of the sources work very well.
Hellenthal et al. did not find mixture in Armenians, but they worked with a different methodology and smaller sample size. Either, the N=173 sample size enabled detection of this admixture, or differences in methodology account for differences in conclusions. If true, the admixture dates in this paper would be some of the earliest discovered by looking at modern populations (without the help of ancient DNA).
The TreeMix analysis (Figure 4) is inconclusive about admixture from a population best represented by Neolithic Europeans. There is no plot of residuals in this figure, so this model with one migration event may not be adequate. Prior knowledge suggests that it isn't, as Pakistani and European populations have no admixture in Figure 4.
It's great that the authors will share their data!
As of this writing, the data is not "live"; it might appear when the paper is published.
bioRxiv doi: http://dx.doi.org/10.1101/015396
Genetic evidence for an origin of the Armenians from Bronze Age mixing of multiple populations
Marc Haber et al.
The Armenians are a culturally isolated population who historically inhabited a region in the Near East bounded by the Mediterranean and Black seas and the Caucasus, but remain underrepresented in genetic studies and have a complex history including a major geographic displacement during World War One. Here, we analyse genome-wide variation in 173 Armenians and compare them to 78 other worldwide populations. We find that Armenians form a distinctive cluster linking the Near East, Europe, and the Caucasus. We show that Armenian diversity can be explained by several mixtures of Eurasian populations that occurred between ~3,000 and ~2,000 BCE, a period characterized by major population migrations after the domestication of the horse, appearance of chariots, and the rise of advanced civilizations in the Near East. However, genetic signals of population mixture cease after ~1,200 BCE when Bronze Age civilizations in the Eastern Mediterranean world suddenly and violently collapsed. Armenians have since remained isolated and genetic structure within the population developed ~500 years ago when Armenia was divided between the Ottomans and the Safavid Empire in Iran. Finally, we show that Armenians have higher genetic affinity to Neolithic Europeans than other present-day Near Easterners, and that 29% of the Armenian ancestry may originate from an ancestral population best represented by Neolithic Europeans.