Richard L. Evans says the Book of Mormon peoples are among the ancestors of modern Native Americans.
Richard L. Evans, "What is a Mormon?" 1955, rep. Religions of America: Ferment and Faith in an Age of Crisis: A New Guide and Almanac, ed. Leo Rosten (New York: Simon and Schuster, 1975), 190
The Book of Mormon is part of a record, both sacred and secular, of prophets and peoples who (with supplementary groups) were among the ancestors of the American Indians. It covers principally the peoples of the period from about 600 B.C. to A.D. 421. These peoples were of Asiatic origin, of the House of Israel, and left Jerusalem during the reign of King Zedekiah, eventually to cross the sea to the Western world, where they built great cities and civilizations. Ultimately, they all but destroyed themselves in warring with one another.