There’s a simple model of the spread of an advantageous allele: You take σ, the typical distance people move in one generation, and s, the selective advantage: the advantageous allele spreads as a nonlinear wave at speed σ * √(2s). The problem is, that’s slow. Suppose that s = 0.10 (a large advantage), σ = 10 kilometers, and a generation time of 30 years: the allele would take almost 7,000 years to expand out 1000 kilometers.
The European lactose-tolerance allele, T-13910 has spread much further than this model would predict. It’s found all over Europe ( very common in northern Europe) but is also found in South Asia (30% in Pathans) and even in Africa (48% in Sudanese Fulani).
This big expansion didn’t just happen from peasants marrying the girl next door: it required migrations and conquests. This one looks as if it rode with the Indo-European expansion: I’ll bet it started out in a group that had domesticated only horses.
The same processes, migration and conquest, must explain the wide distribution of many geographically widespread selective sweeps and partial sweeps. They were adaptive, all right, but expanded much faster than possible from purely local diffusion. We already have reason to think that SLC24A5 was carried to Europe by Middle Eastern farmers; the same is probably true for the haplotype that carries the high-activity ergothioniene transporter and the 35delG connexin-26/GJB2 deafness mutation. The Indo-Europeans probably introduced the T-13910 LCT mutation and the delta-F508 cystic fibrosis mutation, so we should see delta-F508 in northwest India and Pakistan – and we do !
All these alleles had to confer an advantage, but population movements let them expand much farther and faster than girl-next-d0or ever could.
The same must be true for many of the European variants influencing skin, eye, and hair color. Blue eyes seem to come from WHG (the mesolithic hunters); likely the wide distribution happened as people expanded (rapidly) out of glacial refugia at the end of the Ice Age. Blond hair maps pretty well onto Corded Ware territory, which suggests that it came in with the Yamnaya. Blond, swarthy savages. Red-heads? Bell Beakers.
As long as the conquerors incorporate even a moderate fraction (~20% ?) of the previous inhabitants, the sweeping genes cross over and can become common by the present. Given enough time, this can happen even with far lower levels of admixture, as seen with the adaptive alleles that originated in Neanderthals and Denisovans.
In a region without so many rapid, large-scale expansions, you won’t see adaptive alleles spread as rapidly.