[Elpasser]

“Let’s say you have a population of 100,000...”

2 problems with this:
a. All the other women are having children too, and unless the “blonde” woman is a serious racist and her offspring are, too, they are all intermarrying with dark skinned people.

b. Light skin coloration is a recessive (non-dominant) gene. So the chances of the woman’s offspring being light skinned, short of cloning, are pretty low.

[John Will]

Skin color is not nessicarly dominant or rcessive. Mulattos have skin that is a half way between black and white.

[shuckmaster]

All the other women are having children too,

Ancient people lived and traveled in relatively small tribes. Any environmental breeding advantage one tribe obtained (such as immunity to vitamin D deficiency) could easily trigger a widespread expansion and replacement in just a few centuries.

[muawiyah]

The error is thinking that skin color actually exists. There are only two colors of pigment (with the "red" version having been discovered only recently.

You are speaking only of degrees of pigmentation with some folks having a darker appearance due to a higher pigment content in the upper layers of skin.

Many factors control the amount of pigment in the skin and some may or may not be as "dominant" as you might imagine.