Okay, now explain how mainland Europe gained on average 3 inches of height in a century, if not for nutrition.
This is a tough nut to crack. For one, height isn't related to just one gene.
Secondly, there's a big association in early childhood health and final height. So it was not only nutrition over the generations, but the fact most kids were being disease and parasite-free.
Bear in mind the study linked here also said height plateaued in countries like Japan, after a big period of growth.
Change in height around the world over 100 yearsOn Japan:The pace of growth in height has not been uniform over the past century. The impressive rise in height in Japan stopped in people born after the early 1960s (Figure 6). In South Korea, the flattening began in the cohorts born in the 1980s for men and it may have just begun in women. As a result, South Korean men and women are now taller than their Japanese counterparts. The rise is continuing in other East and Southeast Asian countries like China and Thailand, with Chinese men and women having surpassed the Japanese (but not yet as tall as South Koreans). The rise in adult height also seems to have plateaued in South Asian countries like Bangladesh and India at much lower levels than in East Asia, e.g., 5–10 cm shorter than it did in Japan and South Korea.
So it seems different peoples (genes, for all intents and purposes) have different peak levels.
Considering the tallest people in the world a century ago are also the tallest people in the world nowadays (the Dutch, Montenegrin, Scandinavians), this is clearly the work of nutrition in association with genetics and better early childhood health.
So, again, the claim that height differences among countries is mostly explained by factors other than genetics is bs.
There's a German member of this forum with a 170cm (5'7) dad and a mother around 160cm who grew to 182cm (~6 feet). This would most likely never happen in a couple of Portuguese, Japanese or Peruvian origin. This seems obviously the result of German genetics, the same genetics that allowed them to get such a big height increase over a century.
What can happen
now is that if height starts being heavily sxxually selected for in countries where the height has already plateaued, like Japan, then their average height will probably start increasing little by little, as they'll be selecting for the genes with taller height potential.
Now, this is also all my theory based on all that I've read and observed so far. If an actual researcher on this subject is reading my post and wants to call bs on anything that I said, please do. It'd be highly appreciated and enlighten us all.
tl;dr I think different genes have different peak height potentials. Nutrition, genetics, and early childhood health over the generations are the main factors defining height increase and final height.