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Rapid progress in the field since 2010 has resulted in a pile-up of disconnected and poorly understood sources.
The divergence time between the Neanderthal and modern human lineages is estimated at between 750,000 and 400,000 years ago. The more recent time depth has been suggested by Endicott et al. (2010) and Rieux et al. (2014) A significantly deeper time of separation, combined with repeated early admixture events, was calculated by Rogers et al. (2017).
In July 2006, the Max Planck Institute for Evolutionary Anthropology and 454 Life Sciences announced that they would sequence the Neanderthal genome over the next two years. It was hoped the comparison would expand understanding of Neanderthals, as well as the evolution of humans and human brains.
In 2008 Richard E. Green et al. from Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany, published the full sequence of Neanderthal mitochondrial DNA (mtDNA) and suggested "Neanderthals had a long-term effective population size smaller than that of modern humans." In the same publication, it was disclosed by Svante Pääbo that in the previous work at the Max Planck Institute, "Contamination was indeed an issue," and they eventually realised that 11% of their sample was modern human DNA. Since then, more of the preparation work has been done in clean areas and 4-base pair 'tags' have been added to the DNA as soon as it is extracted so the Neanderthal DNA can be identified.
A visualisation map of the reference modern-human containing the genome regions with high degree of similarity or with novelty according to a Neanderthal of 50 ka has been built by Pratas et al.
Interbreeding with modern humans
The question of possible interbreeding between Neanderthals and anatomically modern humans (AMH) had been looked into since the early archaeogenetic studies of the 1990s. No evidence for interbreeding had been found as of 2006. As of 2009, analysis of about one third of the full genome of the Altai individual was still reported as showing "no sign of admixture". The variant of microcephalin common outside Africa, which was suggested to be of Neanderthal origin and responsible for rapid brain growth in humans, was not found in Neanderthals. Nor was the MAPT variant, a very old variant found primarily in Europeans.
Positive evidence for admixture was first published in May 2010. "Those of us who live outside Africa carry a little Neanderthal DNA in us," said Pääbo, who led the study. "The proportion of Neanderthal-inherited genetic material is about 1 to 4 percent [later refined to 1.5 to 2.1 percent].
It is suggested that 20 percent of Neanderthal DNA survived in modern humans, notably expressed in the skin, hair and diseases of modern people. Modern human genes involved in making keratin—the protein found in skin, hair, and nails—have especially high levels of introgression. For example, around 66% of East Asians contain a POUF23L variant introgressed from Neanderthals,[clarification needed] while 70% of Europeans possess an introgressed allele on BNC2. Neanderthal variants affect the risk of several diseases, including lupus, biliary cirrhosis, Crohn's disease, and type 2 diabetes. The genetic variant of the MC1R gene which was originally linked to red hair in Neanderthals is not found in Europeans but in Taiwanese Aborigines at 70% frequency and at somewhat high frequencies in East Asians; hence, there is actually no evidence that Neanderthals had red hair. While interbreeding was viewed as the most parsimonious interpretation of the genetic discoveries, the 2010 study still could not conclusively rule out an alternative scenario, in which the source population of non-African modern humans was already more closely related to Neanderthals than other Africans were, because of ancient genetic divisions within Africa. 
Research since 2010 has refined the picture of interbreeding between Neanderthals, Denisovans and anatomically modern humans. Interbreeding appears to have occurred asymmetrically among the ancestors of modern-day humans, and that this is a possible rationale for differing frequencies of Neanderthal-specific DNA in the genomes of modern humans. In Vernot and Akey (2015) concluded that the relatively greater quantity of Neanderthal-specific DNA in the genomes of individuals of East Asian descent (than those of European descent) cannot be explained by differences in selection. They further suggest 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 parsimonious with their data. Similar conclusions were reached by Kim and Lohmueller (2015): "Using simulations of a broad range of models of selection and demography, we have shown that this hypothesis [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] 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."
Khrameeva et al. (2014), a German-Russian-Chinese collaboration, compiled a consensus Neanderthal genome based on the genome of the Altai individual and of three Vindjia individuals. This was compared to a consensus chimpanzee genome as the outgroup and to the genome of eleven modern populations (three African, three East Asian, three European). Beyond confirming the significantly higher similarity to the Neanderthal genome in non-Africans than in Africans, the study also found a difference in distribution of Neanderthal-derived sites between Europeans and East Asians, suggesting recent evolutionary pressures. Asian populations showed clustering in functional groups related to immune and haematopoietic pathways, while Europeans showed clustering in functional groups related to the lipid catabolic process.
Evidence for AMH admixture to Neanderthals at roughly 100,000 years ago was presented by Kuhlwilm et al. (2016).
There have been at least three episodes of interbreeding. The first would have occurred soon after some modern humans left Africa. The second would have occurred after the ancestral Melanesians had branched off—these people seem to have thereafter bred with Denisovans. The third would have involved Neanderthals and the ancestors of East Asians only.
A 2016 study presented evidence that Neanderthal males might not have had viable male offspring with AMH females. This could explain why no modern man to date has been found with a Neanderthal Y chromosome.
A 2018 study concluded that interbreeding between Neanderthals and modern humans led initially to the exposure of each species to unfamiliar viruses. Later on, the exchange of genes granted resistance to those viruses, too.
A 2014 study on epigenetics of the Neanderthal published the full DNA methylation of the Neanderthal and the Denisovan. The reconstructed DNA methylation map allowed researchers to assess gene activity levels throughout the Neanderthal genome and compare them to modern humans. One of the major findings focused on the limb morphology of Neanderthals. Gokhman et al. found that changes in the activity levels of the HOX cluster of genes were behind many of the morphological differences between Neanderthals and modern humans, including shorter limbs, curved bones and more.
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