Different species were domesticated in the New and Old World. New and Old World cultures eat different foods. Migration and gene flow was limited between the New and Old World. Similar species of pests and diseases attack crops worldwide. The diversity of plants differs between the New and Old World.
Natural selection acts on differences between populations.
Evolution by natural selection is a very slow process. Evolution cannot occur in populations made up of different clones. Natural selection acts on differences between individuals within populations. Evolution occurs because individuals can evolve. Less than one percent of the genes sampled were variable.