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.

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.

Being shorter or taller depends on details of the diet. Vegetarians can obtain a balanced diet, with sufficient complete protein, vitamins, minerals and micro-nutrients. It's trickier for vegans but it can be done.

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.

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.