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A reading of the whole paper shows that the authors are extremely circumspect and cautious in what they say, and in fact are left with more questions than answers.
They summarize the results of previous studies about the possible impact of the transition to the Neolithic on cranial and facial morphology. Those studies were inconsistent as to the effect on facial morphology, here mostly having to do with the mandibles. As to the effect on the crania, they appear to have been more consistent in showing increased brachycephalisation as well as skeletal gracilisation.
Here is their summary:
Carlson and van Gerven9 measured the cranial and mandibular morphology of Nubians across the transition from hunter-gatherer populations to agriculturalists... they also found a decrease in cranial length and increase in cranial height. Similar patterns have been observed to varying degrees in numerous studies using both standard craniometric measurements5,10,11 and geometric morphometrics6,7."
The areas studied were the southern Levant (a study done by the Pinhasi group itself) and in Iberia (Lalueza-Fox).
The purpose of this study was to see if the same pattern would hold in these widely spaced groups. What they found was that once again the results were inconsistent for facial morphology. However, they also found that in only one group was there a shift in the crania, and that was in the Ukrainian samples.
So, why is that the case? They basically say they don't know. They do raise the possibility that the migration of groups from the Caucasus into the Ukraine might have had an impact, but as they themselves say, why then didn't the same change occur in Iberia, which also experienced the inflow of new populations at the time of the Neolithic transition?
One could argue that it's because we're talking about two different incoming groups, with different cranial morphology.
Still, we have a situation here where prior studies showed a change to increased brachycephaly in Iberia with the advent of the Neolithic, and here they couldn't find evidence of this change.
In the Ukraine, on the contrary, one sees the change and yet the diet didn't change all that much...
"Despite these fundamental cultural changes, it is interesting to note that isotopic evidence suggests very little consistent change dietary composition41,42, with evidence for the consumption of both freshwater and terrestrial resources through prehistory."
My take away is that no one really seems to understand the reason for these changes, changes that continue to take place, since it appears that brachycephaly has continued up until the present.
I'd also add that however interesting it is to look at photographs, they're not reliable. You need the measurements.
Non si fa il proprio dovere perchè qualcuno ci dica grazie, lo si fa per principio, per se stessi, per la propria dignità. Oriana Fallaci