John L. Sorenson reviews DNA question; concludes DNA cannot be used to prove or disprove Book of Mormon.
John L. Sorenson, Mormon's Codex: An Ancient American Book (Salt Lake City: Deseret Book; Provo, UT: Neal A. Maxwell Institute, 2013), 247–254
What do the genetic data say about whether Near Eastern people were involved in the Mesoamerican gene pool? Results obtained so far do not provide enough evidence to be certain.
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A considerable to-do has been made about a supposed lack of Jewish DNA in American Indians in the light of the Book of Mormon report of migrations from Jerusalem to Mesoamerica. Such assertions have been discussed at length by DNA scientists and other scholars. Their views suppose that attempts to answer the question are premature at best and possibly futile. The key problem is still the same as Mourant pointed outsome time ago; that is, we don't know the genetic composition of the Jews at the time of the Diaspora when the Lehite and Mulekite parties left the land of Israel. Given that basic lack of data, no valid comparison can be made. Even in the unlikely case of such information becoming available, formidable methodological problems would make fruitful investigation of the issue unlikely.
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It is a rational conclusion that this picture of human physical variation within the Americas, limited as it is, points to Old World populations having reached this hemisphere by sea voyages. This constitutes a fundamental correspondence or convergence between the scientific evidence and the historical account in the Book of Mormon, regardless of any unanswered questions.