An essay on Book of Mormon and DNA Studies was added on 1/31/14 in the topical guide of the LDS.org website. The essay asserts that DNA studies cannot be used decisively to either affirm or reject the historical authenticity of the Book of Mormon. The essay is found here: Book of Mormon and DNA Studies
The essay contends that there were other inhabitants in the Americas before the BOM people arrived. The essay does not address many statements from the Church and scriptures that contradict this.
Many General Authorities have written about how no one was in the Americas before the BOM people. Here's remarks from Apostles Jeffrey R. Holland (A Promised Land, The Ensign, June 1976) [emphasis added]:
“Holy scripture records that “after the waters had receded from off the face of this land it became a choice land above all other lands, a chosen land of the Lord; wherefore the Lord would have that all men should serve him who dwell upon the face thereof.” (Ether 13:2.) Such a special place needed now to be kept apart from other regions, free from the indiscriminate traveler as well as the soldier of fortune. To guarantee such sanctity the very surface of the earth was rent. In response to God's decree, the great continents separated and the ocean rushed in to surround them. The promised place was set apart. Without habitation it waited for the fulfillment of God's special purposes.
With care and selectivity, the Lord began almost at once to repeople the promised land. The Jaredites came first, with stories of the great flood fresh in their memories and the Lord's solemn declaration ringing in their ears: “Whoso should possess this land of promise, from that time henceforth and forever, should serve him, the true and only God, or they should be swept off when the fullness of his wrath should come upon them.” (Ether 2:8.)
A Promised Land
By Jeffrey R. Holland
And this scripture from the Book of Mormon. 2 Nephi 1:8:
"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. "
Nor does it mention how these other people survived the Global Flood from the time of Noah, which the Church teaches as a literal event.
A former bishop and DNA geneticist Simon Southerton is very familiar with this topic and has been writing about it for years. We list his knowledgeable response: Response from Simon Southerton
Also, this excellent podcast adresses the DNA essay as well as apologetic defenses:
Mormonstories episode 571: Three Geneticists Respond to the LDS Essay on DNA and the Book of Mormon, and to Apologist Michael Ash
Also, more information from MormonThink's section on the Book of Mormon and DNA