DNA and the Book of Mormon
Here I will go a little in depth on a subject that made news a few months ago: the relationship between DNA evidence and the claims made by the Book of Mormon. Many people think that the Book of Mormon specifically says that all Native Americans in the Western Hemisphere are descendants of the Lost Tribes of Israel. Thus, when DNA is analyzed and no link is found between Middle Easterners and native Americans, the Book of Mormon is shown to be false.
This is not the case. First of all, the group that left Jerusalem and immigrated to the New World was not from the Lost Tribes. Although the leader of this group, the prophet Lehi (from which many Mormons refer to this group as "Lehites") was an Ephraimite, he and his family were living in Jerusalem over a century after the destruction of the kingdom of Israel by the Assyrians, which is how the Ten Tribes were lost. And the entire group only numbered between about 20 to 30 individuals, according to the Book of Mormon's description.
Second, from the very beginning of Church history there were 2 different views of where the Book of Mormon took place. Some said that it occured over the entire New World, with the descendants of the Lehites being the ancestors of all New World people. This view would require that DNA from modern Middle Easterners and modern Native Americans bear similarities.
However, it has been held by others, since even before the discovery of DNA, that the New World was already populated when the Lehites arrived in 600 BCE and that these pre-existing people are the ancestors of modern Native Americans. In fact, some would even say that the Nephites and Lamanites - the two main groups of the Book of Mormon, named after two of Lehi's sons - were descended primarily not from Lehi's group but from the natives already there. In other words, the Book of Mormon is a story not of Israelites in the New World but of natives who had to a degree picked up Israelite culture, religion, and history.
If this is the case, there would be no DNA evidence to confirm or deny it. A group of 20-30 people, living 2600 years ago, cannot be expected to leave a large marker in the DNA of their descendants, especially if it is not known where these descendants are.
The Book of Mormon itself gives not details, and the Church has never taught that one model or the other is correct (although church leaders have expressed opinions). The Book of Mormon gives a vague account of topography, but the Church doesn't try to place it anywhere specific. However, certain elements of Book of Mormon culture are similar to Mesoamerican culture, so most Mormons believe that the Book of Mormon took place somewhere around Mesoamerica.
Additionally, the Book of Mormon implies some assimilation with other groups - a prophet or king may identify himself as a descendant of one of the founders of the Lehite group, which only makes sense if most people aren't. And within a generation or so of the arrival in the New World, each group is much larger than it could be if it started with a dozen members.
DNA cannot be used to confirm or deny the Book of Mormon story, as long as one understands what the Book of Mormon is actuall saying about geneology and what should be expected. In fact, in general it can't be judged by history or science, but rather on its spiritual qualities.