Well, this new study does have some new information/data on the whole idea of "Basal Eurasian" posed in Lazaridis et al. 2013-2014.
For one, we have this helpful figure and what they seem to be posing with it is that more Basal Eurasian ancestry correlates with a depletion in Neanderthal ancestry:
"We report genome-wide ancient DNA from 44 ancient Near Easterners ranging in time between ~12,000-1,400 BCE, from Natufian hunter-gatherers to Bronze Age farmers. We show that the earliest populations of the Near East derived around half their ancestry from a ‘Basal Eurasian’ lineage that had little if any Neanderthal admixture and that separated from other non-African lineages prior to their separation from each other. The first farmers of the southern Levant (Israel and Jordan) and Zagros Mountains (Iran) were strongly genetically differentiated, and each descended from local hunter-gatherers."
Though, it does seem like the Basal Eurasian Vs. Neanderthal allele sharing relationship doesn't entirely perfectly correlate. I.e. CHGs and Chalcolithic Iranians are more or less equally Basal Eurasian but one shares alleles with Altai Neanderthals much more.
"West Eurasians harbour significantly less Neanderthal ancestry than East Asians, which could be explained if West Eurasians (but not East Asians) have partial ancestry from a source diluting their Neandertal inheritance. Supporting this theory, we observe a negative correlation between Basal Eurasian ancestry and the rate of shared alleles with Neanderthals (Supplementary Information, section 5; Fig. 2). By extrapolation, we infer that the Basal Eurasian population had lower Neanderthal ancestry than non-Basal Eurasian populations and possibly none (ninety-five percent confidence interval truncated at zero of 0-60%; Fig. 2; Methods). The finding of little if any Neanderthal ancestry in Basal Eurasians could be explained if the Neanderthal admixture into modern humans 50,000-60,000 years ago largely occurred after the splitting of the Basal Eurasians from other non-Africans."
But if they're right about Basal Eurasian having a negative effect on Neanderthal ancestry; I did initially think this could led some credence to those, including myself, who used to argue that Basal Eurasian may in fact be some pre-historic crypto-North/East African admixture into pre-historic West Asians but the location of the supposedly single most Basal Eurasian individual does make that possibility rather puzzling:
|Hotu cave is apparently 5 km from there
We'll need more samples and data in the future but, for now, it seems like Basal Eurasian has more of a pull toward Iran than the Levant (the latter area being adjacent to Africa) and it doesn't, so far, seem like it's any sort of "African" admixture. Perhaps some at Anthrogenica might be right about the Gulf Oasis or perhaps they might be wrong.
Time will tell...