A recent paper by Emilia Huerta-Sánchez (2014)  has shown that Tibetans' adaptation to high altitude is due to a gene that they inherited due to admixture with our distant ancestors, the mysterious Siberian Denisovans.
This is of real interest because there are three particular areas located at high altitude (+3,600 m - 11,800 ft.) around the World, which are inhabited by people well adapted to the problems caused by high-altitude hypoxia: the Tibet, the Andean Plateau in Peru, Bolivia and Argentina, and the Ethioipian highlands.
It is also interesting because this variant of the EPAS1 gene (which encodes a protein, Endothelial PAS domain-containing protein 1) is not found in any other population around the world. This may either mean: few samples were used in the comparison or Denisovans did not interbreed much with H. sapiens (or they did and this gene disappeared in later bottlenecks, surviving only among Tibetans).
Since New Guinea people have a high proportion of Denisovan alleles ( 4 to 6%) , it is surprising that they do not carry it in their genes. Perhaps they do and the sampling overlooked them. If they don't then an answer should be provided as to why PNG populations don't carry the gene and the Tibetans do. It will be an interesting explanation. How did Denisovans mix with Tibetans and Proto-PNG people and each take their own set of genes? Were the Tibetans on the north of the Himalaya close to Altai? were the future New Guinea populations on the South? What was the range of the Denisovans? There is a lot to learn here!
Actually it seems that the Tibetans come from an area north of Myanmar, close to Yunnan, the Hengduan Mountains, and from there entered Tibet (close to what I termed the homeland of the C haplogroup dispersal in Asia, so it may make sense that these people were in close contact with those heading for New Guinea and Melanesia evolving the C2 haplogroup.
The altitude factor
Altitude provoked hypoxia (lack of oxygen) is an ailment due to the drop in atmospheric pressure as height increases. Air contains 21% oxygen at a normal pressure of 1 atmosphere (atm) at sea level, but as you gain altitude, the quantity of air above you decreases and so does the pressure it exerts. At a height of 3,600 m (11,800 ft.) the pressure is only 0.63 atm, and there are therefore 40% less oxygen molecules in the same volume of air, the partial pressure of oxygen gas drops and absorption is impaired. So each breath you take contains less oxygen than at sea level.
This has serious biochemical consequences and may cause death.
To worsen matters, the reduced pressure may cause body fluids to cross the alveolar membrane from the pulmonary capillaries into the lungs, causing edema and making it harder to breathe. Altitude sickness known as "Soroche" in my country's Andean Plateau (Puna Region of northern Argentina) is a nasty experience, your breath is short, any effort is exhausting, you get a headache and may feel nauseous. I have been at +4000 meters at three sites (Laguna Brava, La Rioja, Argentina: 4,320 m; Pikes Peak, Colorado, US: 4,303 m; and Shanzidou, Yunnan, China: 4,680) and it is ghastly, the only remedy is to go down to a lower altitude, fast.
The Denisovan legacy in Tibetans
The paper indicates that Tibetans carry a variant of the EPAS1 gene, and the only exact sequence match for this gene among extant and extinct populations (including Neanderthals) was found in the Denisovans.
What they discovered regarding a Hypoxia pathway gene (EPAS1), was that it had a "highly unusual haplotype structure that can only be convincingly explained by introgression of DNA from Denisovan or Denisovan-related individuals into humans" .
They searched for this haplotype among other populations (I must comment, not many and, none of them belonging to the Andean or Ethiopian highland communities - see below). They detected that this haplotype was very common among Tibetans, Denisovans and "at very low frequency among Han Chinese" .
Sample comprised: 1000 genomes: African American from the south western United States; Utah Residents with Northern and Western European ancestry; Han Chinese from Beijing; Southern Han Chinese; Colombian; Finnish; British; HAN, Han Chinese from Beijing; Iberian; Japanese; Mexican; Puerto Rican; Luhya; Tuscan; Tibetan; Yoruban, and also: Papuan, San, more Yoruba, Mandeka, Mbuti, French, Sardinian, Han Dai, Dinka, Karitiana, more Utah residents plus the extinct Denisovan and Croatian Neanderthal.
No Quechuas from Bolivia, Perú or Kolla from Argentina. No Ethiopians. The Papuans from New Guinea or other Melanesians would have deserved extra analysis since they do carry between 4 to 6% Denisovan genes. 
But other studies also failed to find a signal associated with EPAS1 in different populations.  It may mean that nobody but the Tibetans and a few Han carry the mutation.
The usual reaction found in lowland people at high altitudes is for their body's to adapt by producing more oxygen-carrying hemoglobin (Hb) via an increase in red blood cells (erythrocytosis). This is a partial solution because even though it allows for a better oxygen intake, the excessive production of red blood cells, makes the blood more viscous (thicker) and this in turn raises blood pressure increasing the risk of stroke or problems in pregnant women (stillbirth, preterm birth, or small for gestational age at births).
EPAS1 is involved in the production of haemoglobin (Hb). Apparently the EPAS1 variant found among Tibetans activates other genes when it is exposed to low oxygen levels (for instance, at high altitudes) and the response is optimal since it does not trigger the production of extra blood cells: "individuals carrying the derived allele have lower haemoglobin levels than individuals homozygous for the ancestral allele" , in fact, Tibetans carry about 10-20% lower Hb content in their blood than do their South American "Andean counterparts or acclimatized lowlanders". This means that they have adapted a mechanism to avoid erythrocytosis: the hypoxia-inducible factor (HIF). 
The EPAS1 gene match in Denisovans implies that it introgressed into modern humans via direct contact with Denisovans. It remained in the genetic pool of the Tibetan's ancestors and when they moved up to a higher altitude some 30 kya, this gave them a selective advantage which in turn spread it among their descent. Today most Tibetans carry this variant of the EPAS1 gene.
This does not mean that Denisovans were people living at high altitudes. Though the Denisova Cave where their remains were found is only at 750 m (2,460 ft.) to the south of it are the Altai Mountains over 3,000 m high (9,840 ft.), they may have evolved this variant of EPAS1 by chance and selected it positively because it conferred some advantage. What, I cannot say, I did not manage to glean it from the papers I read which are more focused on the advantages gained from it by populations living at high altitudes and not the other way round.
The other regions with populations adapted to high altitudes employ different strategies and genes:
There are two populations living at high altitudes (above 2,500 m - 8,200 ft.), the Oromo since c. 1500 CE and the Amhara far longer (5 ky or even 70 ky), it is likely that the latter have evolved adaptations to altitude hypoxia. 
However, the studies (Alkorta-Aranburu et al., 2012)  conducted among high altitude Ethiopians explored EPAS1 (well known to be associated with Hb levels in Tibetans) but found that "None of these SNPs were significantly associated with Hb levels in Ethiopians... we infer that the SNPs associated with variation in Hb levels in the Tibetans do not make a contribution in Ethiopians." .
This makes sense now after the new paper , since Denisovans and Tibetans are Asian, it is unlikely that later back-migrations from Eurasia into Africa carried this particular variant of the EPAS1 gene. This means that it never reached the Ethiopians. It also means that Denisovans evolved it separately in Asia and it is not found among Africans.
Andean Plateau, South America
The Andean plateau, is a vast region of Peru, Bolivia and Argentina peopled at least 11,000 years ago. The Andean people are different to the Tibetans: they have a vigorous erythropoietic response (they produce a lot of red blood cells). Studies have not detected the action of selective pressure at the EPAS1 locus, but this may be due to a bias in the methods employed in these studies and not necessarily mean that it is absent. 
It may also mean that Tibetans and the Andean people have evolved different genetic adaptations to cope with hyperbaric hypoxia.  and that the Denisovan introgression is not found among the Andean natives.
The bias mentioned above is due to the fact that the scanners use pre-ascertained SNPs so low-frequency alleles may be skipped and common ones over-represented, "this bias is more likely to miss candidate natural selection genes". This could be overcome by an overall comparison between genes of Tibetan and Andean populations. 
It is also very likely that any Denisovan genes that may have reached America are not likely to be found among the Andean Plateau populations. But we can leave this as an open question until deeper full sequencing is done and spans a wider range of populations.
In case you wonder why is hypoxia so important to Chinese researchers, look at it this way: China has a large population and is keen in implanting ethinic Han to balance local indigenous groups and stem any potential regional secession. Clear examples of this policy were Inner Mongolia, Manchuria and now Tibet and Xingjiang. The obstacle in Tibet is altitude and adaptation to it. Countless papers have been written by Chinese and Sino-Western teams, some with the belief that altitude sicknes can be overcome (Responses of Han migrants compared to Tibetans at high altitude., Weitz et al., 2013), others voicing the opposite point of view (Political Mobilization in Tibet, Christopher Paik).
Please don't get me wrong, China is a great place. I have been there may times over the years (Yes, that is me in the photo at the Jade Dragon Mountain), but the delicate balance with local ethnic groups has to be well managed and is something that concerns me.
An interesting paper on Tibetans and their adaptation to high altitude involving this gene is Petousi et al., 2014.
 Emilia Huerta-Sánchez, et al., (2014), Altitude adaptation in Tibetans caused by introgression of Denisovan-like DNA. Nature (2014) doi:10.1038/nature13408. Published online 02 July 2014
 Alkorta-Aranburu G, Beall CM, Witonsky DB, Gebremedhin A, Pritchard JK, et al., (2012). The Genetic Architecture of Adaptations to High Altitude in Ethiopia. PLoS Genet 8(12): e1003110. doi:10.1371/journal.pgen.1003110
 Cynthia M. Beall, et al., (2010). Natural selection on EPAS1 (HIF2a) associated with low hemoglobin concentration in Tibetan highlanders. vol. 107 no. 25 11459–11464, doi: 10.1073/pnas.1002443107
 Bigham AW, et al., (2009). Identifying positive selection candidate loci for high-altitude adaptation in Andean populations. Hum Genomics 4:79–90.
 Reich, D.; Green, R.E.; Kircher, M.; Krause, J.; Patterson, N.; Durand, E.Y.; et al., (2010). Genetic history of an archaic hominin group from Denisova Cave in Siberia. Nature 468 (7327): 1053–1060. doi:10.1038/nature09710
 Wang B, Zhang Y-B, Zhang F, Lin H, Wang X, et al., (2011) On the Origin of Tibetans and Their Genetic Basis in Adapting High-Altitude Environments. PLoS ONE 6(2): e17002. doi:10.1371/journal.pone.0017002
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