Hoisted from the comments: The Genomic Formation of South and Central Asia

A pre-print on bioarxiv: The Genomic Formation of South and Central Asia

Some excerpts follow.

4) the first ever ancient DNA from South Asia from Iron Age and historical settlements in the Swat Valley of Pakistan (1200 BCE– 1 CE) from 7 sites.........

Finally, we examined our Swat Valley time transect from 1200 BCE to 1 CE. While the earliest group of samples (SPGT) is genetically very similar to the Indus_Periphery samples from the sites of Gonur and Shahr-i-Sokhta, they also differ significantly in harboring Steppe_MLBA ancestry (~22%). This provides direct evidence for Steppe_MLBA ancestry being integrated into South Asian groups in the 2nd millennium BCE, and is also consistent with the evidence of southward expansions of Steppe_MLBA groups through Turan at this time via outliers from the main BMAC cluster from 2000-1500 BCE. Later samples from the Swat time transect from the1st millennium BCE had higher proportions of Steppe and AASI derived ancestry more similar to that found on the Indian Cline, showing that there was an increasing percolation of Steppe derived ancestry into the region and additional admixture with the ASI through time. 

Comment: See below for all the acronymns and terms.  This is way after the Indus Valley Civilization, and the potential Rakhigarhi aDNA and after the hypothetical arrival of Aryans around 1500 BC.  More on the above later.

The absence in the BMAC cluster of the Steppe_EMBA ancestry that is ubiquitous in South Asia today — along with qpAdm analyses that rule out BMAC as a substantial source of ancestry in South Asia — suggests that while the BMAC was affected by the same demographic forces that later impacted South Asia (the southward movement of Middle to Late Bronze Age Steppe pastoralists described in the next section), it was also bypassed by members of these groups who hardly mixed with BMAC people and instead mixed with peoples further south.  In fact, the data suggest that instead of the main BMAC population having a demographic impact on South Asia, there was a larger effect of gene flow in the reverse direction, as the main BMAC genetic cluster is slightly different from the preceding Turan populations in harboring ~5% of their ancestry from the AASI.

qpAdm: See here.
BMAC = Bactria–Margiana Archaeological Complex
Steppe_EMBA = Steppe Early-Middle Bronze Age
AASI =

Ancient Ancestral South Indian (AASI) - related” : a hypothesized South Asian Hunter - Gatherer lineage related deeply to present-day indigenous Andaman Islanders

This image from Wikipedia puts this in context.

CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=868992

On Steppe_EMBA

Lazaridis et al. show that Early to Middle Bronze Age steppe groups, including Yamnaya, tagged by them as Steppe EMBA, are best modeled with formal statistics as a mixture of Eastern European Hunter-Gatherers (EHG) and Chalcolithic farmers from western Iran. The mixture ratios are 56.8/43.2, respectively.

However, they add that a model of Steppe EMBA as a three-way mixture between EHG, the Chalcolithic farmers and Caucasus Hunter-Gatherers (CHG) is also a good fit and plausible.

If the purportedly "ubiquitous" in South Asia Steppe_EMBA arrived without going through BMAC, it seems to me that an explanation that the same ancestral hunter-gatherers diffused through Iran into India as into the Steppes before the BMAC was populated is simpler than this ancestry diffused into the Steppes and then into India through the BMAC without affecting BMAC.  But we shall see.

...we estimate that the time of admixture between Iranian agriculturalist-related ancestry and AASI ancestry in the three Indus_Periphery samples was 53 ± 15 generations ago on average , corresponding to a 95% confidence interval of about 4700-3000 BCE assuming 28 years per generation.  This places a minimum date on the first contact between these two types of ancestries.

Indus_Periphery samples: three "outlier" aDNA samples:

...between 3100-2200 BCE we observe an outlier at the BMAC site of Gonur, as well as two outliers from the eastern Iranian site of Shahr-i-Sokhta

 Continuing:

Previous work has shown that the Indian Cline — a gradient of different proportions of West Eurasian related ancestry in South Asia — can be well modeled as having arisen from a mixture of two statistically reconstructed ancestral populations (the ANI and the ASI), which mixed mostly after 2000 BCE.  Ancient DNA analysis has furthermore revealed that the populations along the Indian Cline actually descend more deeply in time from at least three ancestral populations, with ancestry from groups related to early Iranian agriculturalists, Steppe_EMBA, and Onge. 

To shed light on the mixture events that transformed this minimum of three ancestral populations into two (the ANI and ASI), we used qpAdm to search for triples of source populations — the AASI, all sampled ancient Iran/Turan-related groups, and all sampled ancient Steppe groups — that could fit as sources for South Asians.  As South Asian test populations we used an Indian Cline group with high ANI ancestry (Punjabi.DG), one with high ASI ancestry (Mala.DG), early Iron Age Swat Valley samples (Swat Protohistoric Grave Type - SPGT), and Early Historic Swat Valley samples (Butkara_IA).  Fig. 3A shows that the only models that fit all four test South Asians groups are combinations that involve the AASI, Indus_Periphery and Steppe_MLBA (in the analyses that follow, we therefore pooled the Steppe_MLBA).  The evidence that the Steppe_ MLBA cluster is a plausible source for the Steppe ancestry in South Asia is also supported by Y chromosome evidence, as haplogroup R1a which is of the Z93 subtype common in South Asia today was of high frequency in Steppe_MLBA, but rare in Steppe_EMBA  absent in our data).

Steppe_MLBA = Steppe Mid-to-Late Bronze Age.  This is a pre-print, but the ubiquitous in India Steppe_EMBA is now really Steppe_MLBA - that is a bit disconcerting.

One of the problems I have with all of this is - India was almost certainly more densely populated than the surrounding areas, it was one of the refuges of humanity during the glacial periods; but because there is no aDNA from India, Indian populations are always modeled as having arrived from outside.

To obtain a richer understanding of the ancestry of the entire Indian Cline, we took advantage of previously published genome-wide data from 246 ethnographically diverse groups from South Asia, from which we sub-selected 140 groups that fall on a clear gradient in PCA to represent the Indian Cline (the other groups either fall off the cline due to additional African or East Asian-related ancestry or had small sample size or heterogeneous ancestry).

The per-group qpAdm estimates for the proportions of ancestry from these three source sare statistically noisy.  We therefore developed new methodology that allows us to jointly fit the data from all Indian Cline groups within a hierarchical model.
The analysis confirms that the great majority of all groups on the Indian Cline can be jointly modeled as a mixture of two populations, and the analysis also produces an estimate of the functional relationship between the ancestry components.  Setting Steppe_ MLBA to its smallest possible proportion of zero to estimate the minimum fraction of Indus_Periphery ancestry that could have existed in the ASI, we obtain ~39%.  Setting AASI to its smallest possible proportion of zero to estimate the maximal fraction of Indus_Periphery ancestry that could have existed in the ANI, we obtain ~72%.

Notice one thing - out of modern 246 groups, 106 were discarded as noise; but aDNA from one population in Swat and three Indus Periphery outliers is taken to be typical.  This is a constraint introduced by the paucity of aDNA data, not because it necessarily reflects reality.

In fact, this paper puts ANI and ASI to be Bronze Age.

These results suggest that the ASI and ANI were both largely unformed at the beginning of the 2nd millennium BCE, and imply that the ASI may have formed in the course of the spread of West Asian domesticates into peninsular India beginning around 3000 BCE (where they were combined with local domesticates to form the basis of the early agriculturalist economy of South India, or alternatively in association with eastward spread of material culture from the Indus Valley after the IVC declined.

 So the largely unformed by the beginning of the 2nd millenium BCE the ANI and ASI ancestries formed and started mixing immediately ("can be well modeled as having arisen from a mixture of two statistically reconstructed ancestral populations (the ANI and the ASI), which mixed mostly after 2000 BCE.").

Here's what is confusing to me:

The three Indus Periphery samples date to 3100-2200 BCE.  They are taken to be emigrants from India ("we hypothesize that these outliers were recent migrants from the IVC"). But they are taken to be ancestors of ANI rather than descendants.  The general prejudice that Iran and the Steppes were more densely populated and/or had more population than the IVC continues. All to save the Indo-European languages' hypothesis.

PS:--- some observations

If aDNA population X in geography x has characteristics that modern population A in geography a does not have, then X is unlikely to be ancestral to A  (those characteristics could have gone extinct, so unlikely, not impossible).  But then, some of the ancestors of population A who were located in geography a could be ancestors of the aDNA population X in geography x.  What precludes that hypothesis is the lack of aDNA from geography a plus a liberal application of Occam's Razor.

PPS: the geographic isolation of Swat, e.g., Wiki: "Swat was home to the last isolated pockets of Gandharan Buddhism, which lasted until the 11th century, well after most of the area had converted to Islam." 

PPPS:

bennedose‏ @bennedose

I cannot dispute "Steppe ancestry" for Indians if genetics shows it. My main contention is that geneticists try to "match" their findings to existing fake theories made up by linguists using fake languages. The logic used to link Steppe grave with India language is garbage.