Advantageous gene variants certainly spread by people marrying someone from the next village, but they can also be spread by population movements – settling virgin lands, farmers pushing aside foragers, and of course conquest, our old friend. If a Fisher wave is diffusion, genetic transport because of those population movements could be compared to convection, as our commenter RCB has suggested.
People are sometimes interested in estimating the point of origin of a sweeping allele: this is probably effectively impossible even if diffusion were the only spread mechanism, since the selective advantage might well vary in both time and space. But that’s ok, since population movements – genetic convection – are real and very important. This means that the difficulties in estimating the origin of a Fisher wave are totally insignificant, compared to the difficulties of estimating the effects of past colonizations, conquests and Völkerwanderungs. So when Yuval Itan and Mark Thomas estimated that 13,910 T LCT allele originated in central Europe, in the early Neolithic, they didn’t just go wrong because of failing to notice that the same allele is fairly common in northern India: no, their whole notion was unsound in the first place. We’re talking turbulence on steroids. Hari Seldon couldn’t figure this one out from the existing geographic distribution.
Same thing with the EDAR allele: Kamberov et al estimate that it originated in central China, but there’s no reason to think that they’re right. Not least because we don’t even understand what the advantage is.
It looks as if the EDAR mutation was fairly common among the original Amerindians. If so, how rapidly did it spread in the Americas? Just as fast the the place was colonized : deep into South America in a thousand years.
On the other hand, the mere fact that an allele has spread very far is a strong hint that it was carried by population movements, not just a Fisher wave. As we gradually figure out ancient population movements, to a large extent using ancient DNA, we will have a better idea of the origin and trajectory of such mutations. Seeing LCT 13910 in both Europe (especially northern Europe) and India suggests that was it was carried along by the Indo-European expansion. The delf508 Cystic fibrosis mutation (also found in India) probably was as well, and perhaps the common 35delG deafness mutation. On the other hand, SLC24A5 and Factor V Leiden probably came with the Middle Eastern farmers.
Many of these allele look like defenses against infectious disease, or some kind of adjustment to an agricultural diet: you’d expect that they originated among either the EEF farmers or the Indo-Europeans, not the old Mesolithic foragers of Europe.