Several important conclusions of the discovery that Oase1 had a Neandertal ancestor 4-6 generations before his time (37-42 thousand years ago):
  • This is a smoking gun that modern humans interbred with Neandertals, following up on the publication of the Ust'Ishim and Kostenki-14 genomes; these two had longer Neandertal chunks than modern humans, from which it was estimated that their Neandertal admixture happened more than 50,000 years ago, roughly what one gets when looking at Neandertal chunks in modern humans alone. The Oase1 has even longer Neandertal chunks, and Neandertal admixture happened in its very recent past. 
  • So, it seems that Neandertal admixture was not a one-off event but is bracketed at least by the period 50-40 thousand years ago and happened in at least two places: Europe and the Near East.
  • The fact that the earliest European sample (N=1) has a recent Neandertal ancestor indicates that Neandertal admixture in the earliest Europeans cannot have been extremely rare or non-existent; if it were, the chances of finding one with the first try would be extremely low.
  • It is unlikely that Neandertals were killed off by modern humans immediately after the arrival of the latter in Europe, as the Oase1 is dated well after the arrival of modern humans to Europe.
  • Modern Europeans don't seem to be particularly related to the population of Oase1. After one substracts contamination and Neandertal admixture, what is left over is actually closer to East Asians than modern Europeans. But, it's equally close to East Asians and European hunter-gatherers. This can be explained if modern Europeans have ancestry from the mysterious "Basal Eurasians" via the Neolithic farmers.
Why did the Neandertals (and the significantly-Neandertal admixed AMH like Oase1) disappear? My bet is on the Campanian Ignibrite eruption.

Nature (2015) doi:10.1038/nature14558

An early modern human from Romania with a recent Neanderthal ancestor

Qiaomei Fu, Mateja Hajdinjak, Oana Teodora Moldovan, Silviu Constantin, Swapan Mallick, Pontus Skoglund, Nick Patterson, Nadin Rohland, Iosif Lazaridis, Birgit Nickel, Bence Viola, Kay Prüfer, Matthias Meyer, Janet Kelso, David Reich & Svante Pääbo

Neanderthals are thought to have disappeared in Europe approximately 39,000–41,000 years ago but they have contributed 1–3% of the DNA of present-day people in Eurasia1. Here we analyse DNA from a 37,000–42,000-year-old2 modern human from Peştera cu Oase, Romania. Although the specimen contains small amounts of human DNA, we use an enrichment strategy to isolate sites that are informative about its relationship to Neanderthals and present-day humans. We find that on the order of 6–9% of the genome of the Oase individual is derived from Neanderthals, more than any other modern human sequenced to date. Three chromosomal segments of Neanderthal ancestry are over 50 centimorgans in size, indicating that this individual had a Neanderthal ancestor as recently as four to six generations back. However, the Oase individual does not share more alleles with later Europeans than with East Asians, suggesting that the Oase population did not contribute substantially to later humans in Europe.

Link