https://en.wikipedia.org/wiki/Archaic_human_admixture_with_m...
When we say that chimpanzees and humans share 99% of their genome, we're looking at base pairs, but when we say that modern Eurasians have 1-4% of their genome from Neanderthals we're looking at genes.
[1]: http://www.telegraph.co.uk/news/worldnews/northamerica/usa/1...
And then there's the Denisovans... I gotta get my DNA done...
3.3% Neanderthal. That's 99th percentile.
Not sure if that means anything.
You can read the abstract here: "The Combined Landscape of Denisovan and Neanderthal Ancestry in Present-Day Humans" https://www.ncbi.nlm.nih.gov/pubmed/27032491
And here is the global map of Neanderthal and Denisovan DNA it contains: https://i.imgur.com/SjrzV93.jpg
The figure legend reads: Figure 2.
Variation in Denisovan Ancestry Proportion
(A) Proportion of the genome inferred to be Denisovan in ancestry in diverse non-Africans. The color scale is not linear to allow saturation of the high Denisova proportions in Oceania (bright red) and better visualization of the peak of Denisova proportion in South Asia.
(B) Proportion of the genome confidently inferred to be Denisovan in ancestry in mainland Eurasians plotted against the rate of allele sharing of each sample with non-West Eurasians as measured by an f4 statistic. Error bars (1 SE) were obtained from a block jackknife. The Denisovan ancestry estimates in South Asians are systematically above expectation (fitted trend line) (p = 0.0013).
Then, most genes not related to the immune system were removed through natural selection creating the modern mix.
There is not enough evidence about the immune system of the neanderthals. When the Out-of-Africa migration(s) happened, there is no evidence that the neanderthals had encountered significant diseases and epidemics in the past -- up to that point. This does not rule out the possibility that they neanderthals were spreading some unique parasites amongst themselves. Disease is all about congestion [1].
What the neanderthals had that was most beneficial to humans was geographic adaptation. And the are genes for that can jump-start (by many generations) the evolution of features like longer and more straight hair.
Also, during Natural Selection genes that become useless will stay in the gene pool. Natural Selection selects for advantageous genes [2], that does not mean that it selects against neutral (useless) genes. DNA has no size cap and the gene pool of organisms continues to hold onto the genes long after they offered a survival edge [3].
[1] It is also congestion that increases the likelyhood that a disease jumps species.
[2] And by compliment, against disadvantageous genes
[3] This is a virtue of DNA, it likes to keep a memory bank of all solutions that have been useful in the past. It is a hoarder.
That is absolutely true, but useless genes have a much higher probability of getting corrupt by accumulating errors, because the lack of useless genes is not selected against.