The bottom line is that the evidence is consistent with the possibility that a very small number of individuals in the founding population of the Americas had some Paleo-Asian admixture that did not penetrate into the larger founding population during the period in Beringia, either due to population structure in the founding population, or due to a late arrival to Beringia shortly before the commencement of migration from there to the Americas, or both. The percentages are tiny enough that a few other sources of this genetic ancestry that did penetrate beyond the band that founded the Amazonian population where these genes are found today could have been lost to genetic drift in the meantime. The longer that these individuals were part of an unstructured Beringian population with a reasonably high and stable effective population, the less statistically plausible this scenario becomes.
I see the most likely explanation involving the integration of one or two individuals (maybe three or four tops) from the same Asian community with some Paleo-Asian ancestry, into a single tribe within the Beriginian population that had been germinating there for thousands of years during the glacial period, who arrive not long before migration to the Americas begins and are integrated into a tribe that happens to be one of the first to migrate along the Pacific Coast, with a vanguard status and cohesive tribe structure that isolates them genetically from populations that follow them at a slower pace.
This isn't the only way to explain the data, but it is adequate to do so without making any terribly implausible assumptions. Few other narratives that explain the data can rival this hypothesis in plausibility.
Some key observations:
* The Paleo-Asian ancestry is limited to about 2% of the ancestry of some small Amazonian populations near the source of the Amazon. Even the populations in question have 98% of their ancestry from Native American founding populations.
* The Amazonian populations in question are currently quite small. The Suuri people, for example, number about 1,200 all told in ten villages, although in fairness, this is in part due to the death of about 90% of their population in the years immediately following first contact in 1969. The death rate on first contact also rules out pretty much any conceivable contact with Europeans in the post-Columbian era, as they would have had the same diseases and the population would probably harbor more immunity to those diseases in 1969.
The populations with this 2% Paleo-Asian admixture may have made up less than 0.1% of the Pre-Columbian population of the Americas, and definitely make up less than 1% of the Pre-Columbian population of the Americas. So, we are talking about Paleo-Asian genes that collectively account for 0.02% to 0.002% of the Native American gene pool (i.e. 1 part per 5,000 to 1 part per 50,000) that has disappeared in every population except the descendants of one band out of the founding population of South America. Many genetic studies of American indigenous population genetics support a founding population of the Americas with an effective population of fewer than 5,000 people.
If Paleo-Asian admixture was that rare in the founding population, even an occasional introgression of a population with this admixture into one that lacked it would be diluted to almost nothing within a few generations and the Paleo-Asian component would be very susceptible to genetic drift out of the population over the next many thousands of years.
No Y-DNA or mtDNA not derived from founding Native American population clades is found in either, which is unsurprising for a low frequency contribution to the gene pool of the Native America founding population, due to genetic drift, but which would be more surprising if found following a much more recent admixture event in which the introgressing population with Paleo-Asian ancestry had some important cultural or genetic fitness enhancing impact on these Amazonian tribes.
This phenomena could all be attributable to a single mixed ancestry individual in the founding population who arrived late to Beringia (perhaps a fisherman in a canoe of the coast of mainland Asia cast adrift by a storm that disorients him causing him to think that the way home is east rather than southwest until he meets these new people) and was at the vanguard of migratory advance as the founding population. It makes sense that any population that made it all of the way to the Amazon was in the vanguard of migratory advance.
If the Paleo-Asian ancestry level in this proto-Amazonian band of people had not reached fixation until after leaving Beringia, the likelihood that this person's Paleo-Asian genes did not spread to other populations would be even greater. And, any low frequency genetic component in a population is prone to leaving the gene pool through random genetic drift, particularly prior to the full on expansions into the Americas (because low frequency genetic components are preserved much better in expanding populations than in stable ones).
* We know that the Beringians integrated some individuals whose mtDNA haplogroups (e.g. X2) had a different source population than the rest of the mtDNA haplogroups found in the Americas (A, B, C and D), which may have been there for all or most of the eight thousand or so years of their isolation, and that the proportions of the mtDNA haplogroups varied greatly from one population to the next for populations for which we have Pre-Columbian ancient DNA data, for example, in the American Southwest. We also know that there were several other low frequency uniparental haplogroups in addition to the dominant ones in the Native American founding population. So it is not unprecedented for a stray bit of ancestry unrelated to the bulk of the Native American founding population's population genetic makeup to introgress into the founding population, or for there to be structure in population genetics despite many thousands of years during which populations could have equalized their gene pools through admixture. There are also a number of "gaps" between Asian genetics and Native American genetics that probably reflect ancestry lost during the Beringian period.
* There seems to be some significant structure in the frequency with which mtDNA X2 and a few less common mtDNA clades are seen in Native American populations (mostly in parts of North America), compared to others in South America that have a smaller subset of North American genetic diversity. This suggests that the hypothesis that the founding population of the Americas in Beringia had reached complete fixation and homogenization while "germinating" in Beringia is probably false. The more genetically varied the Beringian tribes were before migrating to the Americas, the more plausible it is that Paleo-Asian ancestry found in one such tribe would not spread widely to other tribes.
If mtDNA X2 had enough structure to exclude it from South America, it isn't so surprising that Paleo-Asian ancestry could have been isolated by population structure enough to keep it out of North America.
* The upper boundary of the time period of migratory advance from Beringia to South America is on the order of 1,000 years, but the possibility that some migrating populations made the trip more quickly, particularly if they had a thin preservable material culture, is not precluded. The shorter the trip, the more likely it would be to see the anomaly that we see in the Amazon. Also, it is entirely possible that there were waves of migration then that are impossible to discern as separate from what we know now 14 millenia removed.
A scenario in which a few bands take the Pacific route (not knowing that anyone was following them), followed a few years or decades later by a few more bands, until it becomes a wholesale mass migration once climate based push factors are added to the pull of a virgin frontier, could have left early migrating peoples in the vanguard of the migration quite isolated as a genetic population starting the moment the left Berginia.
One doesn't have to be in all that much of a rush to make the 5,600 mile or so trip by foot in a mere seven generations (210 years), which is an average migration of less than 3 miles a month (about 500 feet a day) for a group of nomadic hunter-gatherers who could have subsisted on a similar coastal shallow water flora and fauna diet for much of the trip. But, if everyone else who follows them is making the trip even slightly more slowly (e.g. 1.5 to 2 miles per month), the vanguard population becomes isolated genetically from the rest of the founding population within a few years of leaving in the very first generation. An intentional "go South along the coast" strategy may have been a successful one since it consistently led people who followed it to virgin territory in a warmer climate for most of the trip while staying close to food and water resources, until the principle had become almost sacred in the group.
* On the other hand, any other time in the last 12,000 years, you would need a very small group of travelers with at least partial Paleo-Asian ancestry (effective population size 1-3ish) to make a 7,000+ mile trip all of the way from the Amazon to Asia (on the order of 200 miles a month for 35 straight years), across a well populated couple of continents, in a few decades, to have children at the end of the trip in late middle age (by modern standards), and to decide not to stop anywhere else before reaching their destination. We can be quite certain that the trip was made made across the South Pacific Ocean (something the Austronesians managed only in the last couple of thousand years with their greatest consquests in the last thousand years). This is highly implausible.
* We don't know how much of the Paleo-Asian ancestry is functional, and how much is merely ancestry informative. If it was functional, we would expect genetic drift to remove low frequency components until someone bearing the genes arrived in the Amazon where their functionality (which was obscured in Beringia) emerged and elevated what may have been an even lower percentage of this band's gene pool because these genes were fitness enhancing in this environment.
In other words, if the Paleo-Asian ancestry was functional in the Amazon, but not in Beringia, it could have had a fixation level in the migrating band that was well below the 2% level seen now (which might represent near fixation levels of all functional Paleo-Asian genes, with almost all other Paleo-Asian genes that arrive in the Amazon lost in the meantime).
* One of the studies estimates that the date range of admixture with this component is 4,000 to 40,000 years old. To the extent that this is not an underestimate, that date is too old to be due to any known human contacts between the Americas and Asia after the founding period ca. 13,000 years ago. It is not inconsistent with admixture occurring during a Beriginian sojourn prior to the founding population entering the Americas or simultaneously with the founding population's migration into North and South America. Given the infrequency with which this component is seen and the estimated size of the Native American founding population, this ancestry component could be entirely attributable to a single individual in the founding population who was not himself or herself a full blooded Paleo-Asian.
It is hard to imagine a significant separate wave of migration of members of relict population containing Paleo-Asian ancestry not found now in any human population, in the time period from 13,000 to 4,000 years ago, that would not have left traces in any intermediate populations, that would have left no archaeological mark, and that would have left such a thin trace in the modern populations of uncontacted persons in the Amazon.
* The Surui people, and most Amazonian Native Americans who speak languages in the same language family, have origins legends that accentuate the necessity of marrying and having children with close relatives which is consistent with modern practice (e.g. a marriage between a maternal uncle and a niece is exemplified as an ideal, and the marriage between "cross-cousins" who have two independent cousin relationships to each other is considered second best). Some other tribes in that linguistic family have legendary histories support mother-son child bearing in the tradition of "Jaguar Woman", as a one time necessity. Other Surui legends, such as the origin of the moon, allude to later instances of incest involving people who are even more closely related.
If this population were in the vanguard of the race to populate the Americas, admixture on the journey from Beringia and the Amazon, it is reasonable to think that they may have been strongly endogamous simply because all of the other human (in this context there is no need to qualify that with "modern human") populations were far behind them in their migration.
This long tradition of tolerance for marriages between closely related people also suggests that these populations have never had very large effective populations relative to their geographic range.
The hybrid fitness advantages of a single individual with partial Paleo-Asian ancestry might give his (or her) descendants an edge in an otherwise highly inbred population until those genes reached fixation in the Amazonian population where these genes are found today.
* The distinctiveness of the populations including the Amazonians who have this Paleo-Asian ancestry, as a genetic cluster distinct from other South American populations (as shown in previous studies comparing language groups and genetic clusters) argues for the fact that they have probably been endogamous for a long time; so does the relatively forbidding environment in which they live (jungles have historically been strong barriers to population movement in modern humans).
The inference that there was genetic diversity in the founding population of the Americas that reflects the phenotypic diversity of Paleo-Americans has been fairly definitively rebutted, once again.
* The Paleo-Asian ancestry observed does not appear to involve any of the populations that are likely descendants of a "lost civilization" of the Amazon that built structures in the Amazon when that was possible in another climate era.
* The likely route of migration for all of the Amazonian peoples affected is along the northern coast of South America, up a river basin, and a short distance over a "continental divide" between river basins in South America into the river basin of a tributary of the Amazon River, not over the mountains on the Pacific Coast of Peru (this is illustrated by earlier population genetic studies of current Native Americans).
* While this 2% Paleo-Asian component has similarity to that found in Australian Aborigines, indigenous Papuans, Negrito Philippinos, and Oceanian populations derived from Papuans, all of whom have elevated Denisovan ancestry, this population does not have elevated Denisovan ancestry, is not more Papuan than Australian Aborigine in origin, and also shows affinity to Andaman Island populations. In short, this is a trace of a generic Paleo-Asian modern human population that did not experience Denisovan admixture in an measurable amount.
The fact that the Paleo-Asian component does not correspond to any known living population, and certainly not to any living population that could have admixed with the Amazonians in the last 4,000 years tends to corroborate the inference that this ancestry component had its origins in the founding population of the Americas, rather than in Bronze Age or more recent contacts between the Amazon and known somewhat similar populations in Asia.
For example, the available genetic information rules out contact with Polynesians, Papuans and Australian Aborigines, and Negrito Philippinos. It is not an exact match for Andaman Islanders, who have been non-contacted people from ca. 20,000 years ago until probably the last 1,000 years.
There is also no indication that the Paleo-Asian component reflects any archaic hominin admixture.
* The populations with Paleo-Asian ancestry are not populations that had been singled out as having distinct phenotypes relative to other early Native Americans that might reflect a separate wave of migration in addition to that of the founding population. Where DNA tests have been done of individuals with distinct phenotypes that has corresponded with pure founding population ancestry.
* The comments at a West Hunter post on the subject (also here) note legendary histories of Polynesians and Native Americans and mainland Asians that seem to reference a darker colored, physically small population of people, many of which assign the population similar names that could have a common origin that could be legendary descriptions of a relict Paleo-Asian population, Such legends seem to imply that such relict populations may have persisted into the Holocene or later in many places in East Eurasia.
* The existence of Paleo-Asians in mainland Asia who could have, in theory, contributed to the founding population of the Americans but no longer exist as distinct populations is highly plausible.
We know to a certainty that the recent population history of East Eurasia has seen the expansion of some populations, like the Han Chinese, at the expense of other populations (such as pre-food producing populations of regions that came under the rule of food producing populations), in a pattern that has been repeated again and again worldwide.
It is reasonable to hypothesize that Jomon-like populations (rich in distinctively Japanese clades of Y-DNA D) existed somewhere outside Japan before they arrived in Japan, ca. 30,000 to 15,000 years ago, a time frame appropriate for some member of that population to join the Beringian founding population. The genetic affinity of the Onge of the Andaman Islands (who all have Y-DNA D) to the Ancestral South Indian (ASI) component of South Asian populations (which have low frequencies of Y-DNA D), strongly suggests that there was a Paleo-Asian population in mainland South Asia which was genetically similar to the Onge, and no longer exists in unadmixed form. This is also suggested by the existence of people with related Y-DNA D in a path more or less straight to Tibet (which has significant amounts of Y-DNA D) from the Andaman Islands and then in a dispersed mix in Siberia to the North of Tibet (where Y-DNA D is found at low levels). It is worth noting that in Japan and Tibet, it seems likely that Y-DNA D male populations had overwhelmingly mtDNA M female counterparts. Thus, this population would be distinct from the putative Northern route mtDNA N bearing population that purportedly gave rise to the Australian Aborigines and original modern human Papuans in . The generic Paleo-Asian ancestry seen in the Amazonian tribes in these studies may draw from a population with origins in both the Y-DNA D/mtDNA M wave (Andamanese-like), and from the mtDNA N wave of Asian migration (Melanesian-like) of Paleolithic era migration by modern humans to Asia.
It is likely that many pre-Last Glacial Maximum populations of northern Asia went extinct or were rendered moribund with surviving members assimilated piecemeal into other populations by this climate event.
The existence of several relict Negrito populations in Southeast Asia, are presumably the descendants of Paleo-Asian populations and unlike the Negrito people of the Philippine Islands, Melanesia and Australia, they lack significant Denisovan ancestry (although recent studies show that some mainland Asian populations do have slight, but measurable levels of Denisovan ancestry).
Prior papers looking at the uniparental genetic makeup of Asia have proposed a multi-wave model with often more than one pre-Holocene wave of migration. Towards that end the comments at the previous post rightly call attention to  and .
* The argument that there was no new migration to the Americas with the Na-Dene people despite some private mtDNA clades and Reich's estimate of about 10% new migration wave architecture, and consistent with linguistic and archaeological evidence for a separate wave of migration, is not convincingly rebutted by the new study making that claim.
* The argument that the Paleo-Asian ancestry could be of recent (i.e. Bronze Age or later) origins in one study is contradicted pretty decisively by the evidence in the other study.
* To what extent is the Paleo-Asian ancestry in these populations fitness enhancing as opposed to selectively neutral?
* What other relict traces and low frequency admixture traces of Paleo-Asian populations are found in modern Asia?
* Highly inbred populations without unknown population histories that are isolated for long periods of time can distort ancestry analysis. It is plausible that the tools used to analyze the highly inbred populations of the Amazon were tuned to global assumptions about population dynamics and not inbred and isolated assumptions ones. It could be that what looks like Paleo-Asian ancestry is really just a case of distinctive locally evolved Amazonian genetic patterns being clearly Eurasian, but gravitating towards the Eurasian outgroup populations that are least like extant modern populations simply because the Australian, Papuan and Andamanese outgroups including this one are collectively dissimilar to other Eurasians, with Eurasian similarities at these loci haven arisen with a time depth of less than 25,000 years. Thus, is it possible that this is a case of mis-identification due to a methodological flaw of the software used that is particularly vulnerable to confusion in a highly inbred population that has been isolated for many thousands of years?
* Is it possible to use other genetic data to model a range of substructure models for the founding population of the Americas and then to see how difficult in those models it would be for Paleo-Asian ancestry that is not lost to drift to end up in just one tribe after a prolonged period of germination in Beringia (possibly 8,000 years)?
One needs quite strong substructure relative to what one would expect from an even slightly exogamous group of tribes, each of small population, to persist over 8,000 years, although low effective population size and multiple potential bottlenecks in that 8,000 years could counteract the tendency towards homogeneity in that population. Over 300 or so generations or so of even slight admixture between populations (one pairing every two or three generations even) there is enough time to really blend everyone's gene pools pretty completely and to push any gene that is functional in that environment to fixation. But, a low effective population size throughout that time period and multiple bottlenecks could insert enough founder effect randomness and genetic drift to produce what is observed. The shorter the "germination" period, the lower the average effective population size, and the more bottlenecks were experienced, the easier it would be to reproduce the observed level of population structure.
* There is pretty decisive evidence from population genetics that later Paleolithic wave of migration to Asia by modern humans came quite close to totally replacing earlier Paleolithic waves of migration to Asia by modern humans in huge swaths of territory that include almost any place that can be reached without crossing substantial bodies of water and that are not isolated in pockets of mountainous environments. Indeed, I'd say that there is pretty good evidence that there were at least two significant waves of pre-modern migration to Asia.
What process brought about this replacement of one "race" of hunter-gatherers with another? Could it be that admixture with archaic hominins by first contact wave hunter-gatherers while providing some fitness enhancing traits like immune system genes, also came with disadvantages of some kind compared to their unadmixed modern human peers in later waves?
Or, did the Neolithic revolution in Asia deal a final blow to Paleo-Asian communities that had survived as relict populations up until then, maybe as late as the Bronze Age, possibly giving rise to the persistent legendary histories of dark, small people given similar sounding names in many East Eurasian civilizations.
* Did populations that made first contact with archaic humans in mainland Asia have similar levels of Denisovan ancestry to that of existing Melanesian populations at first contact, only to see that ancestry wiped out as later Asian hunter-gatherers mostly replaced earlier Asian hunter-gatherers, and then Asian first and subsequent farmers replaced Asian hunter-gatherers? Or, did Denisovan admixture simply not take place at first contact in mainland Asia the way that it did in or around the Wallace Line and Flores? For example, perhaps the Denisovans and the Hobbits are one and the same, and admixture achieved by the Hobbits was made possible only because they were dwarf types of their mainland kin.
* What kind of hominins lived in Asia (beyond South Asia) in the time period from roughly 200,000 years ago to the Toba eruption around 75,000 years ago, during which the hominin archaeological record in this part of Asia is almost nil. The oldest evidence of Homo floresiensis on the island of Flores is about 94,000 years old. This predates the arrival of modern humans by tens of thousands of years, but is still 100,000 years after the oldest really definitive examples of Homo Erectus from either bones or archaeological tools kits associated with them.
Did the same climate factors that caused Neanderthals to become distinctive and eventually dominant in West Eurasia lead to the gradual (or not so gradual) near extinction of Homo Erectus in Asia at about the same time? Jungles and mountains could have impeded Neanderthal advancement on Homo Erectus territory via a Southern route. Perhaps other biogeographic barriers preventing Neanderthals from reaching Homo Erectus territory via a Northern route. So, Homo Erectus could have had 125,000 years or more to gradually decline pre-Toba, protected from replacement by biogeographic barriers until Toba temporarily destroyed Southeast Asian jungles that had prevented other hominin species from moving into its territories in numbers large enough that the Homo Erectus tribes in the borderlands could not repel them.
Could it be that fitness testing challenges of life in West Eurasia which was quite unlike Africa, placed greater pressure on archaic hominins in West Eurasia to evolve in ways that produced generalized fitness enhancements rather than merely locally adaptive ones, while Homo Erectus in tropical Asia could continue to manage perfectly well with behaviors established in Africa at the time of that species' migration to Eurasia, and that Asian Homo Erectus then reached stasis in its own evolution?
Were Homo Erectus replaced by Denisovans who for some reason left a much lighter archaeological footprint? Alternately, was Homo Erectus so incapable of responding the climate change in the wake of the Toba eruption, that this species collapsed of its own accord leaving a near vacuum in Asia until modern humans filled that void?
When did Denisovans arrive in Asia? Certainly in time to admix with proto-Melanesians ca. 50,000 years ago, but could they have entered Asia around the same time as modern humans, although perhaps by a different route?
Were the Denisovan an offshoot of Homo Erectus or did they have only modest admixture, at most, with Homo Erectus? If they weren't were Denisovans capable of producing hybrid offspring, while Homo Erectus, which may have remained dominant on the mainland, was not? Could Denisovans have been some clade of hominin more closely related to West Eurasian archaic hominins than to Asian Homo Erectus that made a more tentative and less effective invasion of Asia than subsequent modern humans that left them confined to territory that Homo Erectus couldn't handle, just as land across the Wallace Line, high altitudes in Tibet, and remote cave in Siberia? A single Denisovan skeleton that also produced ancient DNA could connect so many dots while ruling out so many other possible theories.
Was the only technological advance experienced by West Eurasian Homo Erectus but not by Asian Homo Erectus due to admixture with a more recent archaic hominin type in the West but not the East, of a species that had far less plastic intellectual hardware than we do?
We know that Neanderthals and modern humans were different enough that Haldane's rule that hybrids tend to be female (when female is XX and male is XY), held true. But, the time depth of the separation of Homo Erectus and modern humans was several times greater.
 Fregel, et al., "Carriers of Mitochondrial DNA Macrohaplogroup N Lineages Reached Australia around 50,000 Years Ago following a Northern Asian Route", PLoS One (June 8, 2015).
 Morten Rasmussen, et al. "Dispersals into Asia An Aboriginal Australian Genome Reveals Separate Human Dispersals Into Asia", 334 Science 94 (2011). The abstract of this paper, which is based on modern autosomal population genetics and some 100 year old hair from an unadmixed Aboriginal Australian states that:
We show that Aboriginal Australians are descendants of an early human dispersal into eastern Asia, possibly 62,000 to 75,000 years ago. This dispersal is separate from the one that gave rise to modern Asians 25,000 to 38,000 years ago. We also find evidence of gene flow between populations of the two dispersal waves prior to the divergence of Native Americans from modern Asian ancestors. Our findings support the hypothesis that present-day Aboriginal Australians descend from the earliest humans to occupy Australia, likely representing one of the oldest continuous populations outside Africa.