This is a question I've been pondering about for many years. As far as I can tell, the Neanderthals were light and blue eyed. Some dispute that. I don't know. If that however is the case, it seems as if the region of distribution of Neanderthals concur roughly with the area where light humans are distributed i.e. caucasians. My thought was that we might have gotten the fairness and blue eyes from mixing with them. That they didn't disappear or where exterminated but that they are us. Mixed and integrated over time.
Hardly scientific, but something that I thought about for a long time. It probably has no merit at all. Subjects like this are probably rarely as simple as that.
That's what I also hypothesised
here and
here.
Central Asia appears to be the most likely place for Homo Sapiens-Neanderthal intermingling. Blond and red hair as well as blue eyes might well have come to Europe with the Indo-Europeans from the Eurasian plain. I think it is very probable that modern humans got fair skin, hair and eyes from Neanderthal in Central Asia around 45,000 years ago. These new hybrid modern humans would have belonged to Y-haplogroup K, who has spawned haplogroups L, M, N, O, P, Q, R, S and T.
L and T moved back to South and South-West Asia (T as far as North-East Africa). M and S went all the way to Australia and Papua. N moved north to Siberia, O east to East Asia. P, Q and R remained in Central Asia for many millennia, then Q moved to north-east Siberia and the Americas around 20,000 years ago. R1 and R2 developed in Central Asia. R2 moved to northern India and Pakistan. R1 split into R1a and R1b. R1a remained all over Central Asia, with a branch in the Pontic steppe. R1b moved to northern Mesopotamia and Anatolia, the rejoined the western R1a branch across the Caucasus. Their fusion gave birth to Indo-European culture and people, then expanded into Europe and back to Central and South Asia.
That's a very brief and schematic summary of how Neanderthal genes spread all over Eurasia.
As for why fair hair and eyes are not found among the first branches to depart from Central Asia (N, O and Q), there are several possibilities.
1) N, O and Q people mixed early with another human population and lost the fair hair and eyes gene before expanding. My guess is that they mixed with another hybrid, of Homo Sapiens and the descendants of the Peking Man, which gave the Mongoloid features to East Asians, Siberians and Native Americans. These older Homo Sapiens in East Asia belonged to Y-haplogroup C and D. N, O and Q might have replaced them as paternal lineages for
any of the reasons that R1a and R1b replaced older Y-lineages in Europe. I am increasingly in favour of a
genetic predisposition for these haplogroups to father more boys.
2) The fair hair and eyes mutations were not present in the people who migrated north and east from Central Asia. It was only inherited by another tribe, who later became the R people.
3) The fair hair and eyes mutation did not come from Neanderthal but was a later independent happening.