Is this true? "Individuals with an increased pigmentation, survive and reproduce more near the equator."

Yes. The darker pigmentation of their skin helps them survive in the sun. Therefore they will thrive more so then someone with fair skin. Darker and lighter pigment in skin, is an adaptation humans went through based mostly on the amount of sun. If you lived in the heat with a lot of sun exposure ex: Africa, you would need to have darker skin to keep from being sun burnt as badly. Someone far from the equator with less sun or: Russia, wouldn’t need as much pigmentation in their skin for this reason. Heat also plays a role in it I believe.