Since I realized that out of two Karelian EHGs one was Uralic looking person (the anthro description of sample that turned out R1a) and the other was (proto) Europoid (description of sample that turned out J*), I am no more sure if there is a big link between autosomal make-up and looks.
There has to be some link. I think the problem comes with expecting that there is going to be some perfect correspondence between percentage of a certain autosomal component and "phenotype".
It doesn't work that way because the alleles that determine phenotype are a very small set compared to the whole, and after a lot of admixture can become detached from the other alleles with which they were originally associated.
I see it all the time with African-Americans. Years ago I worked with a Jamaican woman who married a "white" American. Her daughter looked just like her and unmistakably African-American, the son looked like what Americans would see as "Hispanic" or mixed, and the daughter looked totally "white". It caused her more than a few problems in terms of identity issues, unfortunately. That's why in the past in these kinds of biracial families one child could "pass", but the others couldn't.
As regards ANE, didn't Russian scientists see what they called "Mongoloid like" features in Mal'ta, who is how we define ANE? IF that's true, then ANE type people might have carried those traits from the very beginning. For all we know those kinds of phenotypical traits might have been widespread but in varying degrees in all the ancient North Eurasian and ENA populations. Who says that they specifically originated in the Han, for example? That's a population that formed later where a certain combination of traits became fixed. I also don't know how we could possibly "pin" it on a certain y or mtDna. Those don't carry phenotypical alleles. It must have arisen in a group carrying certain uniparental markers, but I don't know how we'd go back and figure out which ones.
We also have the intriguing appearance of EDAR in the SHG. That might have been one of those widespread traits which were selected against in Europe but selected for, for some reason, in East Asia. Or, it might just be a question of drift. Still, who brought it? When?
Subsequent "Mongoloid" gene flow in quasi historical times is a totally separate issue. We're talking here about gene flow long before that time.
What I don't understand (and this is totally separate from "phentype" issues) is how the Admixture runs and other statistical analyses can show admixture of a "Mansi-like" population into the EHG (and they do sometimes call it a "Mansi-like" population), the Mansi are by definition both West Eurasian and East Eurasian as those terms are commonly understood today, and at the same time we have analyses that show EHG have no ENA affinity.
Perhaps someone can refresh my recollection as to whether Lazaridis et al or Haak et al or Allentoft et al, produced stats showing that ANE had no ENA affinity, or whether that was done by internet people.
For what it's worth, I don't find the reconstructions of the Jomon particularly "Caucasian" looking.
They look more like Polynesians:
Whoa Nellie! Did I miss something? Who said they're "undesirable" traits? I guess I'd better go back and read the intervening posts.