In what ways did American Indian tribes organize themselves prior to contact with Europeans?

E.g. why were some patrilineal and others matrilineal? Why might these regional differences existed? How did women's roles in American Indian societies vary across the regions? In what ways do women's roles in these societies reflect similarities in their life cycles (infancy and childhood, puberty, sexuality, courtship and marriage, pregnancy, and childbirth, adult work, spirituality)?