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In the Episode "Let's Kill Hitler" we meet Mels. It later transpires that her parents are, in fact
Rory and Amy
Since she has two white parents why would she be black? Is there a specific in-universe reason for this or is it just because the producers wanted certain actors to play specific characters?
You may have missed the fact that the little girl we saw in the astronaut suit in Day of the Moon turned out to be an even younger River Song, and that she regenerated at the end of that episode, changing her into a different body than the one she was born with (as regeneration always does). Apparently Mels was the result of this first regeneration.
The young River in Day of the Moon (who still had the body she had been born with) was white, as you'd expect for Amy and Rory's child. The "biography" section of the TARDIS wikia article on River Song gives more details.
She was conceived on the TARDIS as it went through a space-time vortex which gave her genetic traits similar to a time lord. This allows her to regenerate which as we know can change you from male to female; so changing skin colour doesn't seem so far-fetched.
(It is likely that the Doctor will change race* at some point in the future)
*Race defined as our races on earth not an alien race.
In "A Good Man Goes to War" her conception is revealed.
We see her regenerate in:
