One, two and three admixture event scenarios are all plausible (and, of course, more complex scenarios are also possible).
The simplest model assumes that admixture took place ca. 100 kya to 75 kya at a time when the archaeology shows the two species overlapping in the Levant and the effective population size would have been smallest, and not thereafter. But, this would mean that a schism into West Eurasian and East Eurasian populations would have had to happen very early on to prevent the admixed Neanderthal genes from coming closer to fixation between the proto-West Eurasians and proto-East Eurasians than differences in which Neanderthal genes are found in each population reflect.
Another one admixture model puts the date closer to 50-75 kya when the modern human population is at a post-Toba low point after an initial Out of Africa surge, perhaps in an Arbian or Persian Gulf refugium. This reduced effective population size, and allows for a sustained period of declining population during which genetic drift can loose some of the Neanderthal inheritance and give rise to Founder effects not likely to be seen in a rapidly expanding population that has reached fixation.
In a simple two event model, West Eurasians and East Eurasians split before admixture takes place and Neanderthal admixture takes place in parallel processes that produce similar overall levels of admixture in each clade of Eurasians in different places - perhaps one in Anatolia, and another in Arabia, Persia or South Asia. This also has the virtue of driving down effective population sizes in each source population.
A three event model combines these two models, which some admixture taking place early on and pre-schism and some taking place later in parallel.
An example of a more complex model would be one with a common admixture event, additional East Eurasian admixture, and then additional West Eurasian admixture that is diluted in the Upper Paleolithic to Neolithic transition by West Asian populations that did not experience the additional West Eurasian admixture experienced by Europeans with prolonged co-existence with Neanderthals.
2. Were there cases of archaic admixture in Africa?
Preliminary population genetic analysis and possibly one Y-DNA haplogroup A00 that looks older than the species make this look plausible and may have happened in two or three separate cases there quite recently.
The case for Neanderthal and Denisovan admixture where observed is in my opinion rock solid and not adequately explained by any other mechanism (such as deep population structure in Africa within modern humans).
The window of time in which additional non-African, non-Neanderthal, non-Denisovan admixture could be discovered in modern humans alive today hasn't completely closed but is well on its way to doing so. It is quite clear that this isn't present outside modern relict populations of Eurasia and the Americas.
3. It is clear that there was a major modern human population genetic transition in Europe between the Upper Paleolithic and the early Iron Age. How much of this transition in any given part of Europe took place:
* during the Mesolithic era on the eve of the Neolithic revolution;
* when the first farmers arrived with the Neolithic revolution;
* in the mid- to late Neolithic (i.e. the Copper Age and early Bronze Age);
* in the early Iron Age.
Two subquestions here are particularly unclear.
First, were Y-DNA Haplogroup R1b and mtDNA haplogroup H, respectrively which expanded from Iberia during the Neolithic era and Bronze Age indigeneous haplogroups in continuity with the Paloelithic era, or did they arrive with folk migrations in the Mesolithic, the early Neolithic, or the Bell Beaker people?
Tenatively, I favor an arrival of R1b predominantly with the Bell Beaker people, and an arrival of mtDNA haplogroup H in Iberia mostly in the Mesolithic or with the Bell Beaker people. But, there is no ancient Y-DNA evidence old enough to definitively resolve the question, mutation rate based dates are too uncertain to resolve the issue, and the ancient mtDNA evidence is thin. Publically available data from France on this point is particularly thin.
Second, what were the relative contributions to the expansion of Y-DNA Haplogroup R1b and mtDNA haplogroup H, respectrively which expanded from Iberia during the Neolithic era and Bronze Age of the first farmer early Neolithic megalithism culture and the Bell Beaker expansion?
I suspect that R1b and H expansions in Western Europe are predominantly Bell Beaker rather than Megalithic, but the eivdence is not yet secure enough to be sure.
This goes hand in hand with the question of whether the Bell Beaker expansion gave rise to language shift from previous languages of the first farmers of that region. I suspect that it did, but resolution of this prehistoric genetic question would go a long way towards shoring up or undermining that assumption.
On the other hand, many points are fairly settled.
In my mind, there is increasingly little reason to doubt that linguistically Indo-European didn't arrive in Western Europe until at least the Urnfield culture, and that prior to that point almost the entire maximal range of Bell Beaker influence had at some point been linguistically Vasconic.
In my mind, it is all but settled that the Indo-European Iron Age tweaks to the gene pool of Western Europe were quite modest.
It is also likely all but settled in my mind that mtDNA H was at the very least confined to far Southern regions in Europe until the Neolithic at the earliest, and that mtDNA H bearers did not participate materially in the repopulation of Europe immediately after the retreat of the glaciers after the Last Glacial Maximum. This in turn implies that this was probably not an important mtDNA component of refugia populations that participated in this repopulation and were probably rare in, or absent from Southern Europe until at least the Mesolithic (e.g. as a pilot wave from the Fertile Crescent and vicinity in advance of the first farmers on the eve the Neolithic revolution).
4. What were the geographic and archaeological culture sources for the first wave Neolithic populations of Europe and the Bell Beaker peoples?
Modern Europe is to a crude approximation a composite of a West Asian, Mediterrean and Northeast Asian signal. New ancient DNA data from Central Europe makes it an unlikely Bell Beaker source population. A region roughly stretching from the Balkans to Anatolia to the Caucasus to the Zargos Mountains and Western Persia to the remainder of the Fertile Crescent are the most plausible candidates. But, some of these areas are blanks in the ancient DNA map, we don't have a perfectly solid sense of how the ancient populations of these regions differed from the modern ones other than to be forewarned that there has been a lot of historic and late prehistoric era population. It is also possible that at least one signal from a first wave Neolithic population (most likely the LBK) has been so obscured that it can no longer be distinguished from noise in modern populations.
The emerging notion of LBK as "the Neolithic revolution wave that failed" is looking more plausible.
Data from the Ukraine, Central Asia and Iran are particular thin.
5. Are the outlier dates for modern humans in the New World from 20,000 years ago and older valid or not?
There is good reason to scrutinize this data as explained in a previous post, but the evidence is what it is and if there is really no methodological flaw then we have to explain it. The possibility that outlier sites could represent archaic hominin populations that made the trip before modern humans but left a very modest footprint because their lithic technology was less advanced and they were less ecology distrupting top predators is particularly intriguing if the evidence becomes strong enough to force us to fit the theory to it.
6. What archaic hominin species is Denisovan DNA associated with?
Denisovan DNA was found in a Siberian cave. Denisovan admixture is found from roughly the Wallace line and beyond. At least two know archaic hominin species were present in between: Homo Erectus, in most of that region, and Homo Florensis on Flores and perhaps a couple of neighboring islands only. Theories about the existence as a separate species and range of Homo Heidlebergus is also sketchy.
There is no solid indication of Neanderthals beyond South Asia, but they aren't entirely ruled out, particular via a Northern route to the Denisovan cave. Some clade analysis of the Denisovan DNA suggests a clade shared with Neanderthals apart from Homo Erectus.
7. When did modern humans make it from South Asia to Southeast Asia?
The window admitted by archaeology is approximately 100,000 years ago to 45,000 years ago, with a time frame of 65,000 to 75,000 most strongly favored by the evidence, but not very conclusively established.
8. How many waves of mass migration were there to Asia in the Upper Paleolithic and when did they take place?
There is little evidence of prehistoric mass population genetic transfer between East Eurasia and West Eurasia (with a couple of notable exceptions, e.g., for Uralic populations and in the case of mtDNA haplogroup X) prior to the historic era after this initial first order split of Eurasians after leaving Africa.
The data is probably a better fit to several waves of pre-Neolithic migration, rather than just one (although the major Neolithic waves need to be understood to parse the earlier waves from the genetic data). But, the timing and paths of these waves is subject to reasonable dispute.
9. How did Homo Erectus go extinct?
While the evidence is very thin indeed on this point, extinction due to warfare and/or inability to complete for food and territory with modern humans upon first contact, outside of Flores where a cooperative mode emerged, possibly boosted by the Toba erruption or a climate shift seems most plausible.
10. When, if ever, did Homo Florensis go extinct?
The earliest possible date for the extinction is about 10,000 years ago, which is the date of the oldest skeletal evidence, but there is good reason to think that they persisted even after first contact with Europeans and that there may even be a tiny population of this species extant on one known part of one Indonensian island.
11. Is the Inuit language linguistically related to the Uralic languages as part of a transpolar language family?
There is some scholarly evidence to suggest that this might be the case, but it is not widely accepted at this point.
12. Was the Na-Dene a separate migration wave to the New World separate from the Paleo-Eskimo Dorsett, or do they represent admixture of Dorsett and first wave indigeneous American populations?
Historically, these have been treated as two separate post-first wave indigeneous population events, but some suggestive ancient DNA analysis points to collapsing them into one wave. This population is the only one strongly linked to an old world Paleo-Siberian population lingustically to date.
13. To what extent can known historical cultures of the New World in the last several thousand be properly said to be derived from each other? What is the sequence of historical cultures in North America?
There is accumulating evidence that a lot of separate archaeological cultures in the New World can all be traced back to an early one near Monroe, Louisiana.
14. What are the linguistic origins of Japanese?
The Yayoi people came from Korea and the evidence strongly favors one of the languages of Korea at about that time as a source, but there is not agreement on which one. There is likewise dispute over whether Korean and Japanese languages are related to the Altaic languages with some evidence, particularly statistical analysis of lexemes, favoring that position.
15. Is the Dravidian language family indigeneous or did it have an outside source, and if so which one?
Multiple theories exist. I tend to favor an Afro-Dravidian hypothesis with a source language not that different from early Swahili, although distinct from it. This is because the South Asian Neolithic involved a heavy component of Sahel African crops. Some archaeological evidence suggests that it could be that these crops were brought to South Asia, domesticated by the Harappans or related populations, and then returned to Africa.
16. How did Y-DNA haplogroup T end up in the
This distribution is suggestively similar to the expansion of the Dravidian language and South Asian Neolithic. But, the resolution of the Y-DNA haplogroup T data collected so far is not high enough to discern its source (and possibly with it a source for Dravidian crop transfer).