How did the incorporation of western territories into the United States affect Indian nations such as the Sioux or the Nez Pierce?

The formal addition of Indian lands into territories of the United States served as a population magnet for land hungry immigrants, prospectors, and railroad barons.  The frontier always represented opportunity for America, and especially in the Gilded Age of laissez faire capitalism.  This meant that population pressure on Indian tribes would inevitably grow, resulting in conflict, the spread of disease, and the decimation and conquest of the native peoples, including the Sioux and the Nez Perce.

The Sioux were particularly vulnerable to such expansion, as they were a nomadic buffalo culture, roaming the Great Plains, and living on prime land for white settlement, farming and the intercontinental railroad.  In short, the addition of the western territories to the US was the beginning of the end for native tribes and their independence in America, as well as their cultural integrity.