This is quite the paradox, because even though Neandertals are now known to have existed all the way to the Altai, they were still overall a West Eurasian-distributed species. As far as I can tell, three explanations have been proposed: (1) East Asians have at least one extra Neandertal admixture event on top of what all Eurasians share, (2) West Eurasians have at least one admixture event that reduces their Neandertal ancestry relative to what all Eurasians share, (3) Neither of them have any such events, but natural selection has acted to reduce Neandertal alleles more in Europeans than East Asians.
I don't really have an opinion on this highly technical subject, but a couple of papers in AJHG make the case for (1 or 2) and 2, and against (3).
Complex History of Admixture between Modern Humans and Neandertals
Benjamin Vernot, Joshua M. Akey
Recent analyses have found that a substantial amount of the Neandertal genome persists in the genomes of contemporary non-African individuals. East Asians have, on average, higher levels of Neandertal ancestry than do Europeans, which might be due to differences in the efficiency of purifying selection, an additional pulse of introgression into East Asians, or other unexplored scenarios. To better define the scope of plausible models of archaic admixture between Neandertals and anatomically modern humans, we analyzed patterns of introgressed sequence in whole-genome data of 379 Europeans and 286 East Asians. We found that inferences of demographic history restricted to neutrally evolving genomic regions allowed a simple one-pulse model to be robustly rejected, suggesting that differences in selection cannot explain the differences in Neandertal ancestry. We show that two additional demographic models, involving either a second pulse of Neandertal gene flow into the ancestors of East Asians or a dilution of Neandertal lineages in Europeans by admixture with an unknown ancestral population, are consistent with the data. Thus, the history of admixture between modern humans and Neandertals is most likely more complex than previously thought.
Selection and Reduced Population Size Cannot Explain Higher Amounts of Neandertal Ancestry in East Asian than in European Human Populations
Bernard Y. Kim, Kirk E. Lohmueller
It has been hypothesized that the greater proportion of Neandertal ancestry in East Asians than in Europeans is due to the fact that purifying selection is less effective at removing weakly deleterious Neandertal alleles from East Asian populations. Using simulations of a broad range of models of selection and demography, we have shown that this hypothesis cannot account for the higher proportion of Neandertal ancestry in East Asians than in Europeans. Instead, more complex demographic scenarios, most likely involving multiple pulses of Neandertal admixture, are required to explain the data.