The Church web site includes this interesting study of the Book of Mormon and DNA.
To sum up:
Much as critics and defenders of the Book of Mormon would like to use DNA studies to support their views, the evidence is simply inconclusive. Nothing is known about the DNA of Book of Mormon peoples. Even if such information were known, processes such as population bottleneck and genetic drift make it unlikely that their DNA could be detected today. As Elder Dallin H. Oaks of the Quorum of the Twelve Apostles observed, “It is our position that secular evidence can neither prove nor disprove the authenticity of the Book of Mormon.”
This study seems like basic common sense to me. Take some time to read it.