A deluge of new data from Upper Paleolithic Europe will give us all a lot to think about. It is incredible that Neandertal ancestry seems to have decreased over time in Europe (Oase1 is off-cline with lots of extra Neandertal ancestry from a recent genealogical Neandertal in the family tree). The functional form of the decrease seems pretty well approximated as linear.

The authors write:
Using one statistic, we estimate a decline from 4.3–5.7% from a time shortly after introgression to 1.1–2.2% in Eurasians today (Fig. 2).
This is remarkable because it shows  that most of the Neandertal ancestry of the earliest AMH in Europe was gone by the Mesolithic. It really seems that Neandertal genes were bred out of the gene pool over time. Will this trend continue into the future? Perhaps only minute traces of Neandertal DNA will remain in humans in 10,000 more years. Some of Neandertal DNA may yet prove to be neutral or beneficial, so at the limit the percentage may be more than zero. Nonetheless, the historical trend does suggest that modern humans inherited mostly genetic garbage from Neandertals and evolution is more than halfway through the process of getting rid of it.

As a corollary, there may have been other episodes of archaic admixture that are no longer detectable. Perhaps our modern human lineage has repeatedly admixed with other species, but traces of those admixtures are long gone by the action of natural selection. The reason for our relative homogeneity as a species may not be that we avoided intermixing with others, but that, sadly, most others had not much that was beneficial to offer to our ancestors.

Nature (2016) doi:10.1038/nature17993

The genetic history of Ice Age Europe

Qiaomei Fu et al.

Modern humans arrived in Europe ~45,000 years ago, but little is known about their genetic composition before the start of farming ~8,500 years ago. Here we analyse genome-wide data from 51 Eurasians from ~45,000–7,000 years ago. Over this time, the proportion of Neanderthal DNA decreased from 3–6% to around 2%, consistent with natural selection against Neanderthal variants in modern humans. Whereas there is no evidence of the earliest modern humans in Europe contributing to the genetic composition of present-day Europeans, all individuals between ~37,000 and ~14,000 years ago descended from a single founder population which forms part of the ancestry of present-day Europeans. An ~35,000-year-old individual from northwest Europe represents an early branch of this founder population which was then displaced across a broad region, before reappearing in southwest Europe at the height of the last Ice Age ~19,000 years ago. During the major warming period after ~14,000 years ago, a genetic component related to present-day Near Easterners became widespread in Europe. These results document how population turnover and migration have been recurring themes of European prehistory.

Link