There was a recent journal article about the East Asian variant of EDAR, v370 A. This variant influences the development of the ectoderm in many ways, and is responsible for many of the phenotypes characteristic of East Asia. In the study, they inserted this variant into mice in order to better understand its effects.
It causes increased scalp hair thickness, shovel-shaped incisors, an increase in the number of eccrine sweat glands, and smaller breasts.
Katy Perry does not have this EDAR variant, but Li Bingbing almost certainly does.
The authors modeled the spread of this allele, concluding that it conferred an advantage of about 7%, is about 30,00o year old, and originated in central China. In my opinion, that estimate of the geographical origin is worthless, because moderate geographical differences in the strength of selection would completely bollix that calculation. Such differences often exist, especially for alleles that protect against infectious disease. The date is reasonable, not least because the same variant is common in Amerindians.
Because the selected variant has so many different effects, it is hard to know which one conferred a selective advantage. We probably don’t know all the effects yet: they found one new one, more eccrine sweat glands, in this study.
The authors certainly had trouble explaining the advantage. They had several suggestions, all silly. They suggested that more sweat glands might been useful in dissipating heat back in the Ice Age. One idea was that different effects had advantages at different times, but that’s wrong thinking. The chance that any particular phenotypic change confers a strong fitness advantage is very low: by far the most likely case here is that one effect gives the advantage while others are close to neutral.
They suggested sexual selection: maybe East Asian men just like smaller breasts. Of course any such fashion would have to have endured a very, very, very long time, about five times the length of recorded history. I’m not really sure that any such preference exists today. I remember reading about the day that China relaxed the ban on foreign movies, back in 1979. When they showed that first movie, virtually all activity in the Nationalities Hotel came to a halt. Waitresses, elevator operators, room boys, and interpreters all sat watching The Hunchback of of Notre Dame, starring Anthony Quinn and Gina Lollobrigida.
I would guess that the real advantage comes from an as-yet undiscovered effect of this highly pleiotropic variant. It has to be something that worked in a number of places, including the Americas, and over a long time period.