As both a member of the Old Edgefield District Genealogical Society (OEDGS) and a mathematician, I have often thought about how sure we all are about our ancestry when Edgefield County was first settled by European-Americans and African-Americans, in the early 1700’s.
One is never certain about paternity, of course. One trusts his/her partner’s morality in most cases, but can you trust your youthful great-grandmother’s, whom you’ve never met? In addition, how do you really know whether your great-grandmother herself may actually have been a foundling left on the doorstep and raised as if she were one of the children? Your supposed great-great-grandparents may not really have contributed to your ancestral DNA after all.
Figure the odds. Let’s say you are 95% sure of parentage at each step (on both the maternal and paternal side, which is probably overly generous). So “n” generations back, you are only (95%) times itself “n” times, or (0.95^n), sure. It’s easy to solve the equation (0.95^n) = (1/2); n is about 14. After 14 generations (that’s about 300 years), even if you are 95% sure of your data at each step, you end up less than 50% confident in the identity of any given ancestor.
Anybody who ponders their ancestry around or before the year 1700 is, in reality, just guessing.
Yes, you may have traced your family back to a Scotch-Irish immigrant named Mr. McElmurry, and your DNA probably included a contribution from Ireland. But it probably doesn’t include Mr. McElmurry, at least not the one living in the year 1700. Unless it’s a small community – which Ninety-Six District was – and Mr. McElmurry is actually hiding in another branch of your family tree!
Going back to a much earlier migration, modern science asserts that our collective ancestors migrated from Africa several millennia ago and spread throughout the world, including some who returned to Africa. We’re all cousins. But we all have common ancestors, a lot more recently than that group who left Africa.
We each have (2^n) ancestors n generations ago, not necessarily distinct (meaning that the same name shows up more than once in your family tree). Thinking of the McElmurrys, it doesn’t take long before (2^n) exceeds the populations first of Ireland, then of Britain, then of Europe, then of the world. The mathematics implies that there is at least one common ancestor of us all (including all “races” as we now consider them) living around the time of Christ. Some people living back then have no current descendants, of course, and the set of people eligible to be our ancestors diminishes the further back you go. Those who have studied the situation state that a relatively small set of people who were alive at the same time, around the time of Egypt’s first dynasty – only 5000 years ago – form the entire group of our ancestors of that era. We are all descended from every one of them. We are different from each other DNA-wise today, only because some of those ancestors show up more often in my family tree, others more often in yours. And, of course, because of the influence of mutations and evolutionary biology. Thank God for that intelligent design!
Is young Prince George of Cumberland really descended from William the Conqueror? Almost certainly he is. But then again, almost certainly you and I are descended from him, too, and everybody else who has at least one European ancestor. (2^n) is a very large number, that many generations ago. White or black, William the Conqueror is almost certainly not only Prince George’s ancestor. He’s your ancestor, too.