There is an interesting article on Slate today about genealogy and ancestry. Since the farther back you go in time, the more ancestors you had, virtually everyone alive today is descended from virtually everyone in the ancient world.
Say you go back 120 generations, to about the year 1000 B.C. According to the results presented in our Nature paper, your ancestors then included everyone in the world who has descendants living today. And if you compared a list of your ancestors with a list of anyone else's ancestors, the names on the two lists would be identical.
You may have heard of people who can trace their ancestry back to Charlemagne. Well, if you had better records, you probably could, too. And the farther back you go, the more likely you are to be related. I am almost certainly descended from the Roman caesars, and even more certainly descended from King Solomon.
Keep these observations in mind the next time you read about people being linked to famous ancestors. Newsweek recently gushed that "one in five males in northwest Ireland may be a descendant of a legendary fifth-century warlord." In fact, virtually everyone with any European ancestry is descended from that man. One-fifth of Irish males may be descended from him in a direct male line—that is, through their father, grandfather, great-grandfather, and so on. That's what genetic tests can measure. But almost everyone else in Europe, and many people living elsewhere in the world, is descended from him through genealogical lines that include women. And of course, we're just as much descended from our mother's parents and from our father's mother as from our father's father.
Mormons (myself included) believe that they are in some way the descendents of the Israelites. (To be specific, most Mormons believe they are of the tribe of Ephraim.) Some of the more skeptical Mormons contend that we are spiritual, not literal, descendents of Israel: adopted into that lineage through covenant. However, if the theories discussed above are correct, it is likely that almost every Mormon is a literal descendent of not just one Israelite, but almost every Israelite.