Comparisons of DNA sequences between Neandertals and present-day humans have shown that Neandertals share more genetic variants with non-Africans than with Africans. This could be due to interbreeding between Neandertals and modern humans when the two groups met subsequent to the emergence of modern humans outside Africa. However, it could also be due to population structure that antedates the origin of Neandertal ancestors in Africa. We measure the extent of linkage disequilibrium (LD) in the genomes of present-day Europeans and find that the last gene flow from Neandertals (or their relatives) into Europeans likely occurred 37,000-86,000 years before the present (BP), and most likely 47,000-65,000 years ago. This supports the recent interbreeding hypothesis, and suggests that interbreeding may have occurred when modern humans carrying Upper Paleolithic technologies encountered Neandertals as they expanded out of Africa.This corresponds to the range of dates of the classic Neandertals from La Chapelle, La Ferrassie, Feldhofer Cave and La Quina, and may in fact partly explain the morphology of the earliest modern humans from Europe that people like Dave Frayer have been arguing for years have Neanderthal-reminiscent traits. It certainly refocuses interest on sites like Mladeč (34 ky BP), where the faces are modern but the vaults for some of the individuals are long and low, with small buns.
I think the demographic picture in central and western Europe is a whole lot more complex than we currently understand. I look forward to reading this paper when it comes out.