When you draw your family tree, you start with yourself, then add your parents, and their parents, and so on: one person, then two in the next generation, then four, then eight, then sixteen ... in a geometric progression.
But if you keep this up, it gets out of hand. Add them up, and at some point the number of people in one generation will exceed the total population on the planet.
There are two possible reasons for this: Your family tree includes billions of aliens back to the Middle Ages and earlier; or your family tree includes cases of pedigree collapse.
You probably don't need to go back thirty or forty generations to see it. Chances are, eight or ten will do. In my own family tree, ten generations back I see the same person three times. John Barlow, one man, is three of my great-(eight times)-grandfathers.
No, this isn't a case of the old song, "I am my own grandpa." All it takes to haul this off—for one person to take up several slots in a single generation of your ancestors—is a little bit of cousin-marrying. Or second-cousin-marrying ... that kind of thing.
Here's how it happened with John Barlow:
He and his wife Anne had several children, among whom were Deborah, Ruth, and John.
Deborah married John Sturges, and had a son Joseph, who married Sarah Judson, and they had a son Solomon Sturges, who married Abigail Bradley *. Then Solomon and Abigail had a son Hezekiah, who married Abigail Dimon **
Ruth married Francis Bradley, and they had a son Daniel, who married Abigail Jackson, and they had a daughter Abigail Bradley * — who's the same Abigail Bradley who married Solomon Sturges.
John married Abigail Lockwook, and they had daughter Deborah, who married John Burr, and they had a daughter Mary, who married Ebenezer Dimon, and they in turn had a daughter Abigail Dimon** — who's the same Abigail Dimon who married Hezekiah Sturges.
So in summary (if I've got my cousins terminology right):
- Solomon Sturges married his third cousin, Abigail Bradley
- Ebenezer Dimon married his third cousin, Mary Burr
- Then in the next generation, the son of Solomon and Abigail married the daughter of Ebenezer and Mary.
Right there, in the space of a few generations, a huge piece of the geometric progression is lopped off. And there you have it: pedigree collapse.
And in case you're thinking, "Hm. A little in-breeding, there, eh?" consider your own family tree: Millions of aliens, or some cousins marrying. Has to be one or the other.
Image: Sturges Family Arms. From stationery printed for the family of James D. Sturges sometime in the late 1800s.