I’m still digesting the papers on the Neandertals which just came out. You can find them here. If you have questions, please read the papers first. They’re open access, so free to all. There’s a lot to mull over, and I don’t know what I can add right now, but I will note:
1) There’s a lot of stuff that doesn’t have to do with admixture, but focuses on genes where Neandertals and modern humans differ. There is for example an enrichment of differences in genes which relate to skin morphology. But my friends who think that modern human uniqueness can’t be pinned down to changes in SNPs will probably feel even more validated by this paper.
2) The fact that non-Africans as a whole, including Papuans, have Neandertal admixture, presumably from interactions in the Middle East, seem close to falsifying the “two-wave” model of expansion “Out of Africa” which came to prominence in the early aughts. That is, one group of Africans went north through the Middle East, and another swept along the Indian ocean fringe and onto southeast Asia. If there were two waves then they interacted a lot because they both received the same proportion of Neandertal alleles, which makes the idea of two genetically distinct waves a bit useless.