Something Doesn't Add Up

It took me a few minutes to figure this out:

By the time you have found your x5 great grandparents (around 150 years ago) you will potentially have a list of 148 ancestors – and of course it doubles up with every further generation! [Link]

OK, barring incestuous liasons between cousins, each of us has 128 "x5 great grandparents." Adding in all the intervening generations gives us 254 ancestors. Subtract the 106 ancestors whose prison records and gambling debts make us ashamed and we arrive at ... 148!

You Have More Grandmas Than Grandpas

Transylvanian Dutch links to a New York Times blog post claiming that more of our ancestors are women than men.

While it’s true that about half of all the people who ever lived were men, the typical male was much more likely than the typical woman to die without reproducing. Citing recent DNA research, Dr. [Roy F.] Baumeister explained that today’s human population is descended from twice as many women as men. Maybe 80 percent of women reproduced, whereas only 40 percent of men did. [Link]

An update to the post gives a good explanation of how this is possible. In short, the difference in reproduction rates combined with pedigree collapse makes it more likely that men will appear multiple times in your family tree with different mates than will women.

We're More Dead Than Alive

Nancy Bovy sent a link to a cool SciAm article that debunks the myth that 75 percent of all people ever born are currently alive.

To calculate how many people have ever lived, [Carl] Haub followed a minimalist approach, beginning with two people in 50000 B.C.—his Adam and Eve. Then, using his historical growth rates and population benchmarks, he estimated that slightly over 106 billion people had ever been born. Of those, people alive today comprise only 6 percent, nowhere near 75 percent. "[It is] almost surely true people alive today are some small fraction of [all] people," says Joel Cohen, a professor of populations at the Rockefeller and Columbia Universities in New York City. [Link]

I wonder how many of those 106 billion people left enough evidence of their existence that they may be genealogically (and not just genetically) linked to persons alive today, and how many are ancestors we will never find.

An Argument for Inbreeding?

Every genealogist knows that the number of one's ancestors increases exponentially the further back one goes. Each person has two biological parents, four grandparents, eight great-grandparents, and so on. In the tenth generation (counting oneself as the first) one has 512 ancestors; in the twentieth one has 524,288; in the thirtieth one has 536,870,912. Adding up the members of each generation from the second to the thirtieth, we find 1,073,741,823 total ancestors. Go back a few more generations, and we have exceeded the number of persons who have ever lived on Earth. And yet, thirty generations (assuming each to measure 25 years) takes us back only to the thirteenth century!

Of course we haven't each had a billion distinct ancestors since the Middle Ages. We have all found (or will eventually find) loops in our family trees—near or distant cousins who marry, and so share common ancestors. If my father and mother were first-cousins (shared one set of grandparents), I would have only three sets of great-grandparents, and my family tree in previous generations would be reduced by a quarter.

There is an upper limit to the number of ancestors one can have at any given generation. But is there a lower limit?

Consider a society which allows siblings to marry. If a brother and sister married in every generation, one would have two parents, two grandparents, two great-grandparents, and so on. One would then have only 58 ancestors to track down through the thirtieth generation!

Now suppose that one's parents are first cousins who share both sets of grandparents—in other words, the father's parents are siblings of the mother's parents—and that this pattern is repeated in each preceding generation. One would then have four grandparents, four great-grandparents, and so on. Through the thirtieth generation, one would have 114 ancestors—still a very manageable number.

More Reading:

• Straight Dope: 2, 4, 8, 16 ... how can you always have MORE ancestors as you go back in time?
• Redundancy in Ancestry
• The Olive Tree Genealogy: How Many Ancestors Do We Have????
• Some Thoughts on Ancestry and Nobility
• A Simple Way to Count Parental Lineage
• Historical Text Archive: Number of Ancestors We Have