As many of you know when you have two adjacent demes, breeding populations, they often rapidly equilibrate in gene frequencies if they were originally distinct. There are plenty of good concrete examples of this. The Hui of China are Muslims who speak local Chinese dialects. The most probable root of this community goes back to the enormous population of Central Asia Muslims brought by the Mongol Yuan dynasty that ruled ruled China for over a century from the late 1200s to 1300s. Genetic studies of this group that I've seen indicate that a high bound estimate for West Eurasian ancestry is ~10%. The other ~90% is interchangeable with the Han Chinese. So let's assume that the Hui are ~10% West Asian. If you assume that in the year 1400 the Hui were "pure," you have 24 generations (25 years per generation). The original population of "Central Asian Muslims" were heterogeneous, including Iranians and Turks. But let's take it granted that they were 50% East Eurasian and 50% West Eurasian in ancestry at the time of their arrival. What would the intermarriage rate per generation have to be so that the Hui are ~10% West Eurasian at t = 24 (24 generations after the beginning of intermarriage assuming 50/50 West vs. East Eurasian splits)? Turns out all you need is a constant 7% intermarriage rate per generation (the Han Chinese population is so large in relation to the Hui that you can model it as infinite in size). The situation gets even simpler when you have one population which divides into two. For example, imagine that the Serbs and Croats fissioned from a set of unstructured South Slavic tribes which filtered into ancient Illyria ~600 A.D. Soon enough there was a cultural division between the two in terms of religion (Western vs. Eastern Christian) which threw up a population genetic barrier. If you assume that genetically the two groups were totally similar at t = 0, and you separated them perfectly, over time they would diverge due to drift in their allele frequencies. But the reality is that barriers between geographically close groups do not prevent all intermarriage. Even extremely insular groups in a cultural sense such as the Roma of Eastern Europe are clearly heavily admixed with their surrounding populations, as they seem to be no more than ~50% South Asian in total genome content. Going back to the South Slavs, who start out very similar in our putative scenario, how much intermarriage will be necessary for them to not diverge? The issue is not the rate of intermarriage,
rather, one migrant per generation across the two demes will be sufficient to equilibrate allele frequencies.
On the face of it this seems implausible, but recall that divergence is driven mostly by drifting of genes as well as new variation (whether through other exogenous migratory sources or mutation). Very small populations are subject to a lot of drift, and so diverge rapidly, but only very few migrants are needed to bring it back into alignment, because they are proportionally significant. In contrast, the frequencies of large populations are less buffeted by generation-to-generation sample variance (e.g., 10 tosses of a coin will deviate more from 50/50 proportionally than 100 tosses), requiring less gene flow proportionally to maintain parity.
These models of how genes flow between populations and how they diverge are analytically very useful. They allow us to conceptualize how gene flow and population substructure could work to generate allele frequency clines on a large geographical scale. Aggregating and averaging allele frequencies in deme-by-deme bins you can perceive the changes as a function of space as smooth continuities. This is certainly the take away from the synthetic maps derived from PCA results in L. L. Cavalli-Sforza's History and Geography of Human Genes. This gradualistic space of variation can be well accounted for by a few rapid expansion events and bottlenecks as well as geographic isolation building up variation, which eventually "smooths" over through gene flow (with a few exceptions such as Oceania and the New World). Imagine for example the New World. From what I have read the shortest time frame for the push of modern humans from north to the very far south is on the order of ~1,000 years. That's 40 generations. Depending on how you look at it, that's very short, or very long. If our understanding of pre-agricultural populations is correct, this would have occurred via a demic fission where tribes would rapidly expand demographically to fill the "empty space," and move the frontier forward due to classic Malthusian pressures which would manifest in tribal fissioning. To a great extent this model of small-scale demic diffusion can be projected into the future, and down to the recent past. From what I can gather L. L. Cavalli-Sforza and Albert Ammerman seem to be positing a shift in terms of quantity and not quality when it came to agriculture and demographics. Because agriculturalists could extract more per unit calories out of the same amount of land their population would surpass that of hunter-gatherers, and they would expand into a relatively "empty" land of hunter-gatherers through the bottom-up force of numbers, admixing with the indigenes as the wave of advance pushed on. As an American this aligns with some of the narrative of the recent history of our own nation, with the myth of pioneer families moving to the frontier drawn by the fruit which could be won by mixing of their labor with their land. But the reality is that such a narrative is mythic in that it focuses too exclusively on individuals. The settling of the frontier was not simply a matter of mass action and demographic pressure, as individuals or families expanded into new territory. It was rather a complex of individual, subcultural, cultural, and governmental dynamics which operated in concert to expand the frontier of settlement! The national, and to a lesser extent in the earlier years state, government set the institutional parameters by which Amerindian populations were cleared off the land and white settlers were allowed to start up their frontier homesteads with relative security. Additionally, there were pulses of settlement which followed broader cyclical dynamics in American and European society. Not only is reducing the expansion to purely individual level natural increase writ large probably not accurate, but it has little inferential power to explain the true arc of the phenomenon of how the West was won.
I believe this institutional parameter in the prehistoric past is far too often ignored. We we can not see, we can not imagine. In particular, I suspect that complex institutions between the level of the tribe and the state came to the fore with the rise of agriculture. The map at the beginning of the post shows the migrations of several historically attested people. You see where they start, and where they end, and you see how long they took. And importantly, these were folk wanderings, not just small bands of mobile males. Because all of these were nomadic populations heavily dependent on the horse it would be easy to fall into technological determinism. That is, we attribute the mobility to the horse (or camel) which these groups had access to. But the difference between the time taken by the Banu Hilal and the Alans was not the speed of their mount, but historical contingency. Rapid population movements of whole people require technologically necessary preconditions, but these are not sufficient. The 200 years that it took the Alans to sweep from the plains of Eurasian heartland to the North African Maghreb occurred in starts and stops. In Spain the Alans were decimated by Roman armies in the 5th century, and were absorbed into the confederacy of the Vandals, who eventually conquered North Africa. All this was possible due to institutional collapse on the part of the Romans. Similarly, the rapidity of the Banu Hilal transfer from Arabia to North Africa had to do with the facilitation on the part of the Fatimids of Egypt. The historical details of this folk wandering need not concern us, suffice it to say that without knowing the specifics one would be at a loss to understand this mass translocation of a whole society. And it is the issue of translocation which I think is critical. A mass-action and bottom-up model usually entails some synthesis across the source population expanding, and the target population being absorbed. But the Banu Hilal were simply Bedouin who had relocated, pure and simple. They had not had a long sojourn in Egypt, or been influenced by the cities of Cyrenaica. It is as if they had taken a worm-hole from point A to point E without encountering B, C, and D. They were a literal "culture shock" to the Maghreb, as well as a genetic shock. The Banu Hilal, and nomadic peoples in general, are perfectly suited to "leapfrog" in nearly an instant from position A to position D. But not just the Banu Hilal. The expansion of Europeans during the Age of Discovery to all suitable points across the globe is viewed to a great extent as sui generis. I do not think it we should see it as so exceptional in quality. Rather, it is an extension of an ancient pattern. Water transport is cheap, and one can shift matériel in bulk. In antiquity Egypt fed both Rome and Constantinople in turn because its surplus was easily accessible via river and sea. It seems entirely possible that the expansion of farming across the Mediterranean also occurred to a large extent through jumps from fertile locale to locale, facilitated by the ease of water transport. Instead of a demic diffusion one can model this as a series demic of pulses, which eventually filled in. Our perception of diffusion has to do with the coarseness of our measurements. This sort of translocation process en masse could not have occurred simply through the ingenuity of groups of a few families. Ancient hunter-gatherers were resident on far more fertile territory than modern ones, and so they were likely more well organized and numerous than we might think. Just as the Russian Empire had to pacify the black lands of Ukraine before peasants could farm without being molested by Cossack or Turk, perhaps military expeditions of some sort cleared out the way for the ancient farmers? But the power of institutions is not just military. One of the peculiar aspects of agriculture is that the regions which we perceive as rich and fertile today were often settled later than more marginal territories in terms of peak production. To give an example, farming began in the marginal uplands of the Fertile Crescent, only later to expand to the lowland territories of Mesopotamia. A more recent case is Thailand, where the uplands were the center of gravity before the shift began to the modern rice-basket of the lower Chao Phraya. Why? Because small-scale farming is far easier in drylands with easily tillable soil. The more potentially productive territory is often more intensive in capital and requires greater coordination of resources and population. In other words, without institutional scaffolding the frontiers of the production possibility are not exploited. One family or set of families can only do so much. One requires more elaborated structure to leverage the technology to its full range of possibilities. What does all this have to do with genetics? I believe that a relatively simple isolation-by-distance model re-equilibrating after a few major human population genetic fissions (e.g., "Out-of-Africa") is a very good first approximation to the patterns of variation we see around us. There's well over a generation of research in this area. But there are details and deviations on the margins which I think need a more complex model to explain. Some of these are in deep prehistory, such as the possibility of admixture between very divergent human lineages (Neo-Africans and Denisovans). But many of them are very recent. We are only ~10 years into the post-genomic era. I suspect that in a few years we'll feel that the coverage geographically given by data sets such as the HGDP are coarse indeed. As we drill-down to a finer-grain I suspect we'll get a better sense of the deviation of human genetic variation from the null,
the tortoise of constant and continuous genetic exchange and banal fission of tribe upon tribe,
buffeted by animal Malthusian pressures. Into the landscape of the tortoise ~10,000 years ago arose
the dynamic of the frog, protean, leaping to and fro, exploring the ecological niches on the margins, and creating them anew.
Whereas behavioral modernity ~40,000 years B.P. is termed the "Great Leap Forward," the past ~10,000 years have been an ever more rapid succession of leaps and lunges. Most of this is clearly cultural, due to the flexibility and plasticity of memes. But some of this has almost certainly has been genetic, as the gentle accumulation of thousands of years of genetic variation upon a demographic palimpsest is torn to shreds by cultural revolutions which have genetic import. In short, the distance between 8,000 B.C. and 12,000 B.C. in terms of the range of potential possibilities may have been far greater than that between today and 8,000 B.C. Agriculture may have heralded the era of morbid misery, but it also unlocked the keys to startling possibilities.
Image credit: Francois Marchal