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.
Richard H. SteckelGenes are very important at the individual level but these differences tend to cancel at the national level.
Richard H. SteckelAfricans are not as tall as northern Europeans. But Manute Vol and other sports figures in basketball and football receive a lot of press coverage.
Richard H. SteckelYoung children from Guatemala who are adopted into the United States gain considerable height relative to the standards. So the height difference cannot be genetic.
Richard H. SteckelA 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.
Richard H. SteckelAll 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.
Richard H. Steckel