So asks a commenter below in relation to the question above. First, why would one even presume that they were red-haired, see my 2007 post, or the paper in Science: A Melanocortin 1 Receptor Allele Suggests Varying Pigmentation Among Neanderthals. In humans loss of pigmentation can usually be thought of as loss of function on genes. That’s probably one reason that there are several different genetic architectures for light skin, but only one for very dark skin. There might be only one way for an engine to operate as designed, but there are many different ways you can tweak a part and render it broken.
The reason that scientists have posited that Neanderthals were red-haired is that they examined the region around a melanocortin receptor gene which serves as something of a master regulator in terms of melanin production. Their sample was of two Neanderthals, one from Italy and one from Spain, and both exhibited signs of loss of function within this region. An N = 2 is small, but one must recall the fact that they are independent draws as they were sampled from different regions. Also, since then from what I recall in the Denisovan paper the authors noted that all four of their Neanderthals, from Spain, to Italy, to Croatia, to the Caucasus, seem to have a shared recent common history back to an extreme population bottleneck. If Neanderthals were relatively genetically homogeneous spatially, they may also have exhibited phenotypic similarities (thought perhaps not, due to the power of natural selection to reshape populations).
But back to the question about what Neanderthal looked like. I’m sure you’ve heard the old chestnut that if you made a few hygienic changes and had a Neanderthal don modern clothing no one would bat an eye. I’ve obtained an artist’s reconstruction of a red-haired Neanderthal in contemporary dress after a visit to a barber:
Image credit: Hoggarazzi Photography