Young children from Guatemala who are adopted into the United States gain considerable height relative to the standards. So the height difference cannot be genetic.

I agree that zinc is one of the important micro-nutrients but people require a balanced blend of food for our biological engines.

Africans are not as tall as northern Europeans. But Manute Vol and other sports figures in basketball and football receive a lot of press coverage.

A rich diet does lead to earlier puberty but to my knowledge it does not student the adolescent growth spurt. Early pregnancy, before reaching adult height, does slow or stop growth.

There are some effects of the biome. Compact bodies tend to conserve heat relative to linear ones. This can affect average height as well as body proportions. The study participants Europeans and Americans do not fall into the range where this effect is powerful, however.

All the Americans in the study were native born, but the height of the mother does affect the growth potential of the child. So, there is a second generation effect. But this can explain only a small portion of the height difference between Americans and northern Europeans. Regarless of continent of origin, children who grow up under conditions of good health and nutrition are about the same height, on average.

People tend to shrink with age, especially after age 50 or so. It has to do with spaces between the joints amount of cartilage and posture. Bone length does not change.