Here is the beginning of the paper (Rohde et al., 2004):
If a common ancestor of all living humans is defined as an individual who is a genealogical ancestor of all present-day people, the most recent common ancestor (MRCA) for a randomly mating population would have lived in the very recent past. However, the random mating model ignores essential aspects of population substructure, such as the tendency of individuals to choose mates from the same social group, and the relative isolation of geographically separated groups. Here we show that recent common ancestors also emerge from two models incorporating substantial population substructure. One model, designed for simplicity and theoretical insight, yields explicit mathematical results through a probabilistic analysis. A more elaborate second model, designed to capture historical population dynamics in a more realistic way, is analysed computationally through Monte Carlo simulations. These analyses suggest that the genealogies of all living humans overlap in remarkable ways in the recent past. In particular, the MRCA of all present-day humans lived just a few thousand years ago in these models. Moreover, among all individuals living more than just a few thousand years earlier than the MRCA, each present-day human has exactly the same set of genealogical ancestors.Please note that finding a common ancestor is a much easier task--and one that requires less digging into the past--than finding a common ancestor along purely maternal or purely paternal lines, the kind that are analyzed using mitochondrial DNA and Y-chromosome tests.
The implications for the book of Mormon, as I discuss on my Mormon Answers page about DNA and the Book of Mormon, is that it is entirely possible for the majority of Native Americans to be direct descendents of Lehi with some of his DNA, even though there may not be anyone with his Y-chromosome or with Sariah's mitochondrial DNA. Lehi may be a common ancestor for most Native Americans without requiring that they all have clearly discernible "Jewish DNA."
There are also implications for the issue of race. It is very likely that we all share some African DNA. The old Mormon folklore about blacks being descendants of Cain - and white "Gentiles" or House of Israel members not having a drop of that blood - was simply an attempt to resolve questions about race and the limitations on priesthood and has no doctrinal basis. Alma Allred devastates those old myths in his chapter, "The Traditions of Their Fathers: Myth versus Reality in LDS Scriptural Writings" in the outstanding new book, Black and Mormon, edited by Newell G. Bringhurst and Darron T. Smith (Urbana, Illinois: University of Illinois Press, 2004, 172 pages). Tomorrow or later this week I'll dig into the issue and the fascinating topic of Abraham 1 and the patriarchal privilege of presiding called the "right of priesthood" that was denied to Pharaoh, not the ability to hold the priesthood at all.