Hypothesis: Red hair is a Neanderthal trait

They've constructed a Neanderthal model based on DNA. One finding: red hair.
http://www.dailymail.co.uk/sciencetech/article-1058538/Meet-Wilma-The-face-Neanderthal-woman-revealed-time.html

They have found that modern humans share 1 to 4% of their DNA with Neanderthals. Present-day Africans do not have Neanderthal DNA. This suggests to me that breeding with Neanderthals is responsible for a fair amount of the diversity of human morphology, including red hair and fair skin.
http://www.time.com/time/health/article/0,8599,1987568,00.html

Another recent discovery : redheads have different pain pathways. They are less sensitive to pain, and less susceptible to pain blockers. There's something genetic there, and my hypothesis is that it's in those Neanderthal-introduced genes.
http://gizmodo.com/5890532/redheads-feel-pain-differently-to-the-rest-of-us

Also, the redhead at the top of the Gizmodo article bears a passing resemblance to Wilma, the Neanderthal model.