One thing that many don't realise is Neanderthals aren't gone, because many of us are part Neanderthal. The distinction between what is Neanderthal and what isn't has just been blurred. It would be kind of like saying your mother's lineage went extinct because she had a child with your father.
If 1-4% of the Eurasian genome comes from Neanderthals, but sub-Saharan Africans have no Neanderthal genes, does that mean that the EA genome differs from the SSA one by 1-4%? And even more so the Melanesian genome, which has 4-6% Denisovan DNA. But at the same time, chimpanzees and humans supposedly share over 99% of their genome. How is that possible? Are these all percentages of the same whole, or is there something else going on?
That's measuring different things. We can tell whether a particular copy of a gene came from the Neanderthal gene pool or the main SSA gene pool by looking at its sequence (esp. at SNPs), but the overall base pair sequence of that gene will still be 99.9% the same.
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.
Because we were already 99.x percent the same as Neanderthal, so if you take 4% of a Neanderthal genome and replace those sections in a human genome, not very much actually changes.
Of normal human genetic variation, 1-4% is sourced from Neanderthal DNA, which sub-Saharan African peoples do not share. They still may share up to 96-99% DNA variations. In absolute terms they share in excess of 99.9%[1]. The variations inside ethnic groups are almost 16 times larger than the variations between ethnic groups.
What I found interesting is that, while any given modern human has no more than about 4% Neanderthal DNA, it isn't the same 4% in everyone. About 20% of the Neanderthal genome is found in humans. I'm not sure what this says about interbreeding.
And then there's the Denisovans... I gotta get my DNA done...
(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).
I've seen work suggesting that some of the surviving Neaderthal characteristics are pale skin, freckles, straight hair, brown, blonde and ginger hair. That might not be a high proportion of the genome but it sure is noticeable.
When anatomically modern humans migrated from Africa to Europe, their immune systems were not as adapted as neanderthals. So the humans that crossbred had increased chances of surviving, were healthier and more fertile.
Then, most genes not related to the immune system were removed through natural selection creating the modern mix.
I think you have a few errors in your explanations.
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.
Just to elaborate, because eukaryotic genomes are so huge the marginal cost of copying excess genes is negligible so the selective pressure against them is as well. But prokaryotes have very small genomes and reproducing useless genes would be relatively disadvantageous for them so there is noticeable selective pressure to eliminate useless genes for them. So you will see the frequency of unused genes in bacteria tend to decrease over time.
> Also, during Natural Selection genes that become useless will stay in the gene pool.
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.