FairMormon is a non-profit organization dedicated to providing well-documented answers to criticisms of the doctrine, practice, and history of The Church of Jesus Christ of Latter-day Saints.
Question: Does the Church claim that Native Americans were the ''exclusive'' descendants of Lehi or Mulek?
Southerton (2014): "It's true that if a small group (say 10 people) entered a massive population (say 1 million), that it would be hard to detect their mitochondrial or Y chromosome DNA."
Dr. Simon Southerton is one of the most outspoken critics of the Church with regard to DNA and the Book of Mormon:
2008: In case anyone from FAIR is unclear I will repeat what I wrote four years ago…“IF A SMALL GROUP OF ISRAELITES ENTERED SUCH A MASSIVE NATIVE POPULATION (SEVERAL MILLIONS) IT WOULD BE VERY, VERY HARD TO DETECT THEIR GENES.” Now that FAIR has finally conceded that American Indian DNA is essentially all derived from Asia, I also agree with them that the debate should be about the theology. 
2014: I made the original statement at a time when whole genome sequence analysis was a long way off. It's true that if a small group (say 10 people) entered a massive population (say 1 million), that it would be hard to detect their mitochondrial or Y chromosome DNA. Your odds would be roughly 1 in 100,000 (10 in 1 Million). But technology has moved very rapidly and whole genome studies are now almost routine. So, my original statement is no longer true. 
- Simon Southerton, "Finally, I agree with LDS scientists-apologists," posting to an ex-Mormon discussion board, Sept. 6, 2008. (emphasis in original)
- Simon Southerton, cited in Jeremy Runnells, Letter to a CES Director (February 2014).