There has indeed been a significant amount of DNA research on native Americans. This is addressed in Rod Meldrum's DVD set with a one of about five of the set specifically addressing it.
Rod Meldrum seems a bit hokey to me on some points. But not all. Of interest in particular to the point of a "Nephite/Hopewell" connection is the presence of a mitochondrial RNA marker that is present in the tribes of the Algonquin area that matches up with some European and particular a middle-eastern group. . . The Druze, I think is what they're called. . . . a small sect of Hebrew origins who have kept a strict ban against marrying "outsiders" for over a thousand years. . . . The marker is present in one particular tribe in American at the level of 25%, which is about it's frequency in the Druze in Jordan/Syria.
So here's my own little discussion. . . . I've satisfied myself that there were people here, and everywhere on this planet, over twenty to fifty thousand years ago. . . . not an issue with me. We can talk about Adam and follow the fabulous "genealogies" of the Bible for whatever purpose we want, except I don't accept that data as "factual". . . . It's a flawed history, perhaps with allegorical or metaphorical values, and a nice story. The fact is, people were here before twenty to fifty thousand years ago. . . .
In relation to DNA, I profess to know a little about DNA, and fancy myself to be a "breeder" of sorts, following what I think I learned in college about genetics. There are a number of exceptional phenomena that do happen in genetics. We have learned to do them in the lab, but there is a non-zero probability that these things can occur in nature as well, and a possibility that an interested actor on the universal scene could have, somewhere or sometime. . . . possibly billions of years ago. . . . done the same sorts of things on purpose. . . .
There is a lot we just don't know, for sure. . . .
But in the line of natural and ordinary events, we need to understand a few facts about population genetics before we start jumping to unfounded conclusions about the past. . . .
If any of us will do a factual genealogical research back twenty generations. . . . we will be looking at over a million ancestors. . . way back then. . . . only six hundred years ago. Whether hutched up in Europeans hovels, or Asiatic, or African. . . . it would mean we have a significant chance of being a descendant of any particular one of several million total people living then, in that area. . ..
And yet we only have 46 specific elements of DNA, and that means almost all. . . . over 99%. . . . of those ancestors from 600 years ago. . . . lost out on passing one of their chromosomes to a specific living person at this time. . . .
Only the maternal extranuclear ribosomal DNA and the male Y chromosome can be followed across time in a manner that can generate a positive statement of inheritance. one mother to daughter, the other father to son.
The Book of Mormon story brings four groups of people into America. . . . one supposedly about five or six thousand years ago, two about 2600 years ago. One group that left, and came back, and some of which left again with others, about 2400 years ago. So if it were the Hopewell/Nephite identity, the Nephites would be practically gone. The displacing culture would be Lamanites from the south and the western plains. Nothing is said about Lamanite contacts with other groups, but it should be presumed that there were other groups "out there".
We are told about the Nephites encountering and assimilating one other group. Any reputable "scientist" trying to debunk the Book of Mormon story should address the genetic implications of this basic history, and I have not seen one such erudite "scientist" who has done so. None of them read the Book of Mormon past the title page, and none of them actually understand even what it says there.
So, the reasonable position is that the "Lamanites" we might encounter today have been in long contact with larger groups around them, particularly to the north and west, and the genetic fact is we should expect the genetic "markers" for the smaller group to get "washed out" over a long period of time. . . as the 1400 years since the close of the Book of Morman account should be considered to be. . . . .
so, any, as erudite as it may seem, the DNA "disproof" is BS.