It has been suggested that red hair could have originated in Paleolithic Europe, especially since Neanderthal also had red hair. The only Neanderthal specimen tested so far (from Croatia) did not carry the same MC1R mutation responsible for red hair in modern humans (the mutation in question in known as Arg307Gly). But since Neanderthals evolved alongside Homo Sapiens for 600,000 years, and had numerous subspecies across all Europe, the Middle East and Central Asia, it cannot be ruled out that one particular subspecies of Neanderthal passed on the MC1R mutation to Homo Sapiens. It is however unlikely that this happened in Europe, because red hair is conspicuously absent from, or very low in parts of Europe with the highest percentages of haplogroup I (e.g. Finland, Bosnia, Sardinia) and R1a (Eastern Europe), the only two lineages associated with Mesolithic and Paleolithic Europeans. We must therefore look for the source of red hair, elsewhere. unsurpisingly, the answer lies with the R1b people – thought to have recolonised Central and Western Europe during the Bronze Age.
The origins of haplogroup R1b are complex, and shrouded in controversy to this day. The present author favours the theory of a Middle Eastern origin (a point upon which very few population geneticists disagree) followed by a migration to the North Caucasus and Pontic Steppe, serving as a starting point for a Bronze-age invasion of the Balkans, then Central and Western Europe. This theory also happens to be the only one that explains the presence of red hair among the Udmurts, Central Asians and Tarim mummies.
Haplogroup R1b probably split from R1a during the Upper Paleolithic, roughly 25,000 years ago. The most likely location was Central Asia, around what is now the Caspian Sea, which only became a sea after the last Ice Age ended and the ice caps over western Russia melted. After the formation of the Caspian Sea, these nomadic hunter-gatherers, ended up on the greener and richer Caucaso-Anatolian side of the Caspian, where they may have domesticated local animals, such as cows, pigs, goats and sheep.
If the mutation for red hair was inherited from Neanderthal, it would have been from a Central Asian Neanderthal, perhaps from modern Uzbekistan, or an East Anatolian/Mesopotamian one. The mutation probably passed on to some other (extinct?) lineages for a few millennia, before being inherited by the R1b tribe. Otherwise, it could also have arisen independently among R1b people as late as the Neolithic period (but no later).
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