The authors caution about this evidence of admixture:
It is also important to emphasize what our study has not shown. Although we have documented evidence for mixture in India between about 1,900 and 4,200 years BP, this does not imply migration from West Eurasia into India during this time. On the contrary, a recent study that searched for West Eurasian groups most closely related to the ANI ancestors of Indians failed to find any evidence for shared ancestry between the ANI and groups in West Eurasia within the past 12,500 years3 (although it is possible that with further sampling and new methods such relatedness might be detected). An alternative possibility that is also consistent with our data is that the ANI and ASI were both living in or near South Asia for a substantial period prior to their mixture. Such a pattern has been documented elsewhere; for example, ancient DNA studies of northern Europeans have shown that Neolithic farmers originating in Western Asia migrated to Europe about 7,500 years BP but did not mix with local hunter gatherers until thousands of years later to form the present-day populations of northern Europe.15, 16, 44 and 45This is of course true, because admixture postdates migration and it is conceivable that the West Eurasian groups might not have admixed with ASI populations immediately after their arrival into South Asia. On the other hand, a long period of co-existence without admixture would be against much of human history (e.g., the reverse movement of the Roma into Europe, who picked up European admixture despite strong social pressure against it by both European and Roma communities, or the absorption of most Native Americans by incoming European, and later African, populations in post-Columbian times). It is difficult to imagine really long reproductive isolation between neighboring peoples.
Such reproductive isolation would require a cultural shift from a long period of endogamy (ANI migration, followed by ANI/ASI co-existence without admixture) to exogamy ~4.2-1.9kya (to explain the thoroughness of blending that left no group untouched), and then back to fairly strict exogamy (within the modern caste system). It might be simpler to postulate only one cultural shift (migration with admixture soon thereafter, with later introduction of endogamy which greatly diminished the admixture.
The authors cite the evidence from neolithic Sweden which does, indeed, suggest that the neolithic farmers this far north were "southern European" genetically and had not (yet) mixed with contemporary hunter-gatherers, as they must have done eventually. But, perhaps farmers and hunters could avoid each other during first contact, when Europe was sparsely populated. It is not clear whether the same could be said for India ~4 thousand years ago with the Indus Valley Civilization providing evidence for a large indigenous population that any intrusive group would have encountered. In any case, the problem of when the West Eurasian element arrived in India will probably be solved by relating it to events elsewhere in Eurasia, and, in particular, to the ultimate source of the "Ancestral North Indians".
It is also possible that some of the ANI-ASI admixture might actually pre-date migration. At present it's anyone's guess where the original limes between the west Eurasian and ASI worlds were. There is some mtDNA haplogroup M in Iran and Central Asia, which is otherwise rare in west Eurasia, so it is not inconceivable that ASI may have once extended outside the Indian subcontinent: the fact that it is concentrated today in southern India (hence its name) may indicate only the area of this element's maximum survival, rather than the extent of its original distribution. In any case, all mixture must have taken place somewhere in the vicinity of India.
My own analysis of Dodecad Project South Indian Brahmins arrived at a date of 4.1ky, and of North Indian Brahmins, a date of 2.3ky, which seems to be in good agreement with these results.
The authors also report that "we find that Georgians along with other Caucasus groups are consistent with sharing the most genetic drift with ANI". I had made a post on the differential relationship of ANI to Caucasus populations which seems to agree with this, and, of course, in various ADMIXTURE analyses, the component which I've labeled "West Asian" tends to be the major west Eurasian element in south Asia.
Here are the estimated admixture proportions/times from the paper:
Sadly, the warm and moist climate of India, and the adoption of cremation have probably destroyed any hope of studying much of its recent history with ancient DNA. On the other hand, the caste system has probably "fossilized" old socio-linguistic groups, allowing us to tell much by studying their differences and correlating them with groups outside India.
Coverage elsewhere: Gene Expression, HarappaDNA
Related podcast on BBC.
Genetic Evidence for Recent Population Mixture in India
Priya Moorjani et al.
Most Indian groups descend from a mixture of two genetically divergent populations: Ancestral North Indians (ANI) related to Central Asians, Middle Easterners, Caucasians, and Europeans; and Ancestral South Indians (ASI) not closely related to groups outside the subcontinent. The date of mixture is unknown but has implications for understanding Indian history. We report genome-wide data from 73 groups from the Indian subcontinent and analyze linkage disequilibrium to estimate ANI-ASI mixture dates ranging from about 1,900 to 4,200 years ago. In a subset of groups, 100% of the mixture is consistent with having occurred during this period. These results show that India experienced a demographic transformation several thousand years ago, from a region in which major population mixture was common to one in which mixture even between closely related groups became rare because of a shift to endogamy.