Over the last few centuries, migration patterns have strongly affected population patterns in the Americas. This is true both between countries and within countries. The migration patterns have been determined largely by economic factors.
Some of the countries in the Americas have received a great deal of migration. (We are talking about voluntary migration here, not forced migration through slavery.) This has affected population patterns. For example, there has been a great deal of migration from Europe both to the United States and to Argentina. This has affected the demographics of those countries significantly.
Relatedly, some countries in the Americas have been the source of migration to other countries. The major example of this is migration from Mexico to the United States. This has hollowed out populations in some parts of Mexico while adding to that of the US.
There have been migration patterns within countries as well. The most common of these patterns is from the countryside to the city. As countries have industrialized, they have also urbanized. This has led to a situation in which the rich countries have a very large percentage of their population living in cities.
In these and other ways, migration patterns have affected population patterns in the Americas.