Genes are very important at the individual level but these differences tend to cancel at the national level.

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.

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.

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.

The second and third generation effect of immigration accounts for only a small portion of the height shortfall between Americans and northern Europeans. Besides the slowdown in American heights began in the 1950s, well before large-scale immigration into the country.

The English were relatively short in the mid-nineteenth century and so their expeditions return with stories some exaggerated, not doubt about "giants" who lived in other parts of the world.