The Book of Mormon 8/18
In the introduction to the BOM, it says that of the three groups written of in the BOM--the Jaredites, the Nephites, and the Lamanites--all were destroyed except for the Lamanites, and the Lamanites "are the principle ancestors of the American Indians."
DNA tests have confirmed that Native Americans came to the Americas from Asia, not the middle east. Mormons are well aware of this. The explanation I've heard most often is that there were other natives here when Lehi's people migrated to America from Jerusalem, and that Lehi's people made up a small percentage of the population of north and south America. Essentially, they are arguing that the Lamanites are not the principle ancestors of the American Indians, and that's why they haven't shown up in DNA tests. These DNA tests have been done extensively in both North and South America, and there have been no traces of any native Americans of Jewish descent.
The BOM itself seems to support the notion that the Lamanites are the principle ancestors of the native Americans. Shortly after Lehi's people got to America, Lehi made a speech in which he said:
And behold, it is wisdom that this land should be kept as yet from the knowledge of other nations; for behold many nations would overrun the land, that there would be no place for an inheritance. Wherefore, I, Lehi, have obtained a promise, that inasmuch as those whom the Lord God shall bring out of the land of Jerusalem shall keep his commandments, they shall prosper upon the face of this land; and they shall be kept from all other nations, that they may possess this land unto themselves. (2 Nephi 1:8-9)The BOM doesn't mention any civilizations that were already in America that didn't come from Jerusalem, and I get the impression from this passage that there were no natives in the land. They must've spread pretty wide, too, because they built cities, had large populations, and waged massive wars. The "promised land" had to have been pretty big.
In Alma 22, it talks a little bit about the geography of some of the land. In verse 31-32, it mentions two areas of land that share a boarder--Desolation to the north and Bountiful to the south. There is a sea on the east and west of these lands, and it takes a day and a half to walk from the east sea to the west sea along the boarder between Desolation and Bountiful. It goes on to say, "and thus the land of Nephi and the land of Zarahemla were nearly surrounded by water, there being a small neck of land between the land northward and the land southward." That sounded to me like a good description of central America. That's the only place where one can walk a day and a half to get from the east sea to the west sea.
But then later we find both the Lamanites and the Nephites in the land of Cumorah, by a hill called Cumorah. That's where the final battle between the Lamanites and the Nephites took place, and according to the official LDS website, the hill Cumorah is in New York. It's where the prophet Moroni hid the gold plates, and that's where Joseph Smith found them. Surely, the Nephites and Lamanites were spread more widely than Mormon apologists seem to think.
And now I, Mormon, would that ye should know that the people had multiplied, insomuch that they were spread upon all the face of the land, and that they had become exceedingly rich because of their prosperity in Christ. (4 Nephi 1:23)The Lamanites eventually wiped out the Nephites. In Mormon 6:12-15, it says 220,000 Nephites were killed. But this slaughter was merely the last of a long series of battles in which massive numbers of Nephites were killed. And if there were that many Nephites, think how many Lamanites there must've been! In Mormon 5:6, it says the Lamanites were beating the Nephites because the Lamanites were so great in number. Surely, they outnumbered the Nephites. I think it is unlikely that such large numbers of people would be confined to an insignificant area of land.
And it came to pass that they did multiply and spread, and did go forth from the land southward to the land northward, and did spread insomuch that they began to cover the face of the whole earth, from the sea south, to the sea north, from the sea west, to the sea east. (Helaman 3:8)
Toward the end of the BOM, after the Nephites had all been wiped out except for maybe five people, it says, "And now, behold, I say no more concerning them, for there are none save it be the Lamanites and robbers that do exist upon the face of the land" (Mormon 8:9). The Lamanites are descendents of Lehi, who was a Jew who migrated from Jerusalem in 598 BCE.
There is one more piece of evidence that I think indicates the BOM intends to make the Lamanites out to be the principle ancestors of the native Americans. There are two prophecies concerning the Gentiles' interaction with the descendents of the Lamanites.
Nevertheless, thou beholdest that the Gentiles who have gone forth out of captivity, and have been lifted up by the power of God above all other nations, upon the face of the land which is choice above all other lands, which is the land that the Lord God hath covenanted with thy father that his seed should have for the land of their inheritance; wherefore, thou seest that the Lord God will not suffer that the Gentiles will utterly destroy the mixture of thy seed, which are among thy brethren. Neither will he suffer that the Gentiles shall destroy the seed of thy brethren. (1 Nephi 13:30-31)These two prophecies seem to be about Europeans coming over to America. They did not "utterly destroy" the native Americans, but they did kill a bunch of them. The native Americans did "dwindle in unbelief," assuming they ever believed in the first place. The "fulness of the gospel" came to the gentiles by way of Joseph Smith restoring the church of Christ. From there, the gospel ought to reach the native Americans. So the BOM presumes that the descendents of the Lamanites are still around, and that they will convert to Mormonism. They must be among the native Americans. That seems to be the assumption of these "prophecies."
And now, the thing which our father meaneth concerning the grafting in of the natural branches through the fulness of the Gentiles is, that in the latter days, when our seed shall have dwindled in unbelief, yea, for the space of many years, and many generations after the Messiah shall be manifested in body unto the children of men, then shall the fulness of the gospel of the Messiah come unto the Gentiles, and from the Gentiles unto the remnant of our seed--And at that day shall the remnant of our seed know that they are of the house of Israel, and that they are the covenant people of the Lord; and then shall they know and come to the knowledge of their forefathers, and also to the knowledge of the gospel of their Redeemer, which was ministered unto their fathers by him; wherefore, they shall come to the knowledge of their Redeemer and the very points of his doctrine, that they may know how to come unto him and be saved. (1 Nephi 15:13-14)