Those studies have been done and more. For example, the National Geographic Genome Project is putting many of the pieces together -
https://genographic.nationalgeographic.com/genographic/index.html
As Ash points out in the article above there is no support from DNA for the bom story. However, this does not stop the valiant mormon apologists. One common defense is that the bom does not PRECLUDE others being in the americas at the same time and thus their genetic pool was eventually cut off/overwhelmed by the asian/mongoloid dna. This is currently the working premise of Sorenson's/BYU limited geographic theory. However, to accept this answer, one must then reject the prophetic teachings of lds presidents and church since its inception.
Throw in the inexplicable LACK of archeological evidence, anthropological and linguistics and other applicable sciences - the evidence becomes even more overwhelming against the bom.
Asakanasi Jews look more European than their ‘never left the Middle East’ brethren, but the origins of the Jewish people are Semitic, not Caucasian.
And yes, there is not a SHRED of evidence, DNA, archaeological or linguistic that the Book of Mormon is anything other than the creation of Joseph Smith with no basis in actual history.
--MormonDude(But I am starting to doubt the whole basis of my chosen 'religion'.)