Well, this is interesting: the NY Times reports on Studies Showing Jews' Genetic Similarity. There is so much shared genetic material among Jews that "members of any Jewish community are related to one another as closely as are fourth or fifth cousins in a large population, which is about 10 times higher than the relationship between two people chosen at random off the streets of New York City."
Not only can the geneticists who conducted the studies determine how closely the various communities are related, they have also
developed a way of timing demographic events from the genetic elements shared by different Jewish communities. Their calculations show that Iraqi and Iranian Jews separated from other Jewish communities about 2,500 years ago. This genetic finding presumably reflects a historical event, the destruction of the First Temple at Jerusalem by Nebuchadnezzar in 587 B.C. and the exile of many Jews there to his capital at Babylon.
Why am I writing about this, given that I'm neither a geneticist nor Jewish? Because the Book of Mormon claims that Native Americans (or, in Mormonspeak, the "Lamanites") are descendants of Jews who left Jerusalem in 600 BC shortly before the destruction of the temple, traveled to the sea, then got on boats and sailed to the American continents. (Where they arrived is shrouded in mystery; where they ended up is, in Mormon belief, uncontested: upstate New York. 'Cause that's where the golden plates the BOM is translated from were buried.) And accepting the Book of Mormon as a factual document written by those errant Jews detailing their history is a linchpin of Mormon belief and orthodoxy.
The Foundation for Ancient Research and Mormon Studies (FARMS) is always trying to find scientific or geographic or whatever kind of evidence to "prove" that the Book of Mormon is what Joseph Smith said it was, and not just something he made up. Well, if they really think the people living in North and/or South America when Columbus showed up are another offshoot of the children of Israel, they should commission a study adding Native Americans to the mix, to see how genetically close they are to these other communities.
But they won't, because they don't really believe it--they just know it, which is not the same thing. And when there is irrefutable proof that the indigenous (insofar as one can be indigenous of any continent but Africa, which is where we all came from originally) people of the Americas are not actually related to Jews any more closely than they're related to, say, Celts or Gauls or Romans, they'll find some way to dismiss it, and to say that all the logical, scientific evidence in the world is trumped by their emotional reactions to Mormonism, aka "personal revelation," which "proves" to them that everything they already believe is true.
Aside from the specifics of this study, I'm pretty sure that there have been genetic comparisons of the Native Americans with other groups before, and that they have been shown to be most closely related to East Asians (unsurprising, since they came to the Americas over the Alaskan land bridge, i.e. from the North-east of Asia). I've seen this cited in discussions of Mormonism, in fact.
You're absolutely right, Stephen--I've also seen studies like the ones you mention. Of course, FARMS and FAIR always find ways to dismiss the findings: they don't cover everyone; genetic dilutions could have occurred; etc. Which is why I say that even if Native Americans were included in this study and it showed, conclusively, that they are NOT any more closely related to Jews than any other group of humans, FARMS and FAIR would find a way to dismiss the results.