Sunday, June 05, 2005

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.

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