To summarize my own take: the paper proves that recent gene flow between Neandertals (or a Neandertal-like population) and modern humans did occur. But, because of inherent limitations of LD-based methods (due to the exponential decay of LD), such methods can only work on relatively recent signals of admixture. One of the contributions of this paper is its treatment of recombination maps which had not hitherto been used to date such old admixture events.
Both the inherent limitations of LD-based methods and the choice of using SNPs with less than 10% minor allele frequency in Europeans leave open the possibility that the genomewide signal from D-statistics of the form D(African, Eurasian, Neandertal, Outgroup) is driven in part by African population structure. In particular, if one looks at SNPs that have either been ascertained in African individuals or are polymorphic in Africans and monomorphic in Eurasians, the D-statistic signal persists.
In any case, the authors are well aware of this possibility:
Combining these various strategies, we are able to obtain accurate estimates of the date of last exchange of genes between Neandertals and modern humans (also see Discussion). This date shows that recent gene flow between Neandertals and modern humans occurred but does not exclude that ancient substructure in Africa also contributes to the LD observed.
One of the problems hindering our ability to infer the presence of archaic African admixture is the absence of an ancient DNA sequence from archaic Africans, due to poor conditions for DNA preservation in high temperature regions. But, Pickrell et al. (2012) developed techniques for showing that a population is admixed (in their case all Khoe-San) groups even in the absence of a reference unadmixed individual. That admixture occurred in the last few thousand years, so it is not obvious how well that method would work on potential old signals of admixture. However, both Hammer et al. and Lachance et al. discovered signals of archaic admixture in Africans in targeted regions that date to a similar timeframe as the Neandertal admixture in Eurasians, so I am hopeful that such a signal might be extractable even in the absence of a reference archaic African genome.
PLoS Genet 8(10): e1002947. doi:10.1371/journal.pgen.1002947
The Date of Interbreeding between Neandertals and Modern Humans
Sriram Sankararaman et al.
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.