Beards?

Why do men have beards?
   And I don't mean the physiological basis, androgens and all that mess. I get that. I want to know why men have bears on a more evolutionary basis. What advantage does having a beard convey to men? And why do some men have relatively hairless chins - like many Native Americans - and others look like insane mountain men after two days of not shaving?
   This is interesting to me because 50,000 years ago, before there were razors, cavemen would have sported long, luxurious beards. To go along with their back hair. But cavewomen would have remained mustache-less, at least until cavewoman menopause. They shared the same environment, ate the same things, did much the same work, and yet men evolved beards and women did not.
   Por que?
   Maybe it's really just a side effect of the hormones that make men more aggressive, stronger, and predisposed to hunt instead of gather. Women have the same shoulder muscles men do, after all, but more slender versions that will never bulk up the way men's shoulders do. But if it were just a side effect, then presumably all men would have beards. And yet, as we discussed earlier, not all men grow facial hair. The difference is by global region, which points to some sort of evolutionary adaptation.
   Do Native American men have more naturally warm faces? So that when it gets cold outside they don't need the same kind of insulation European men do? Maybe ancient European women found beards much more attractive than hairless chins, and so there was natural selection for beardy-ness in European men? Maybe ancient Native Americans didn't scalp their enemies, they 'bearded' them? I'm just shooting in the dark here.
   This needs funding and serious research. Because I want to know.