The availability of many genome sequences coupled with our sophisticated understanding of population genetics allows workers to estimate how much Neanderthal DNA entered the modern European and Asian populations. It won't be long before similar studies are done with the Densovan genome.
There's lots of discussion about whether the strict "Out-of-Africa" scenario is still valid [Out of who knows where] [The scientists behind Mitochondrial Eve tell us about the "lucky mother" who changed human evolution forever]. There's little doubt that some version of the multiregional hypothesis is correct although it may not be as thorough as the original proponents argued.
John Hawks is an expert on this sort of thing and he's just posted some of his work on his blog [Which population in the 1000 Genomes Project samples has the most Neandertal similarity?]. He doesn't allow comments so you can ask questions here—he's been known to read Sandwalk when he gets bored doing real science.
I'll ask the first questions. John, what percentage of the genomes of Africans, Europeans, and Chinese are derived from the Neanderthal population? Your figure shows the amount of Neanderthal (Vi33.16) intrusion as something called "shared derived variants" but how much of the total genome does that represent? Is any of it in parts of the genome where there are genes?
[Image Credit: I don't know where this picture came from. I got it on Just Another Brooklyn Blog.]