The question to look into is how long it takes to evolve new skintype to match solar input levels and when migration moved people into different locations.
There was a recent show on PBS on pre-historic immigration into Australia and the US and SAmerica (become natives) with genetic data and a small discussion of the evolution of fair skin from the urals back west to europe.
The show was called "The Journey Of Man"
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It has some interesting information, that may help anwer your question, but I am not sure I buy all the story on it myself.
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