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Straight Dope Classic from Cecil's storehouse of human knowledge21-Aug-1987
Dear Cecil:
Have you ever considered the puzzle of doubling ancestors? Everybody has two parents, four
grandparents, eight great grandparents, and so on back through time, with the number of
ancestors doubling in each generation. Go back 30 generations and the number of ancestors
tops one billion. Eventually we arrive at a time when we have more ancestors than there
could have been people in the world. How can this be? Common sense, not to mention the
book of Genesis, suggests the human race started off with a handful of individuals whose
numbers steadily increased. What are the implications of these two surging numerical
tides, ancestors and descendants, butting head to head? Enclosed is a $10 check for the
trouble of a personal reply. --George M., Monrovia, California
Dear George:
You ask a question as cosmic as this one and you think a lousy sawbuck is going to cover
it? Keep your money until you can fork over some real cash. The ancestor puzzle has its
explanation in what one genealogist has called "pedigree collapse." This occurs
when relatives, usually cousins, marry, in effect narrowing the family tree. (Fortunately
for the gene pool, most of the cousins are only distantly related.) When this happens you
find that many of the "slots" in a given generation of your family tree are
filled by duplicates.
Consider an extreme case. Mr. and Mrs. Nosepicker have two children, a girl and a boy.
These two develop an unnatural yen for one another and marry. Six months later the girl
gives birth to an eight-pound horseradish with a lisp. In theory, the horseradish has four
grandparents. In reality, its maternal and paternal grandparents are identical. Two of the
four grandparent slots are thus filled by duplicates--pedigree collapse with a vengeance.
Only slightly less extreme is the case of Alfonso XIII of Spain (1886-1941). Because of
inbreeding in the royal family, he had only ten great-great-grandparents instead of the
expected 16.
If you go back far enough, however, pedigree collapse happens to everybody. Think of your
personal family tree as a diamond-shaped array imposed on the ever-spreading fan of human
generations. (I told you this was cosmic.) As you trace your pedigree back, the number of
ancestors in each generation increases steadily up to a point, then slows, stops, and
finally collapses. Go back far enough and no doubt you would find that you and all your
ancestors were descended from the first human tribe in some remote Mesopotamian village.
Or, if you like, from Adam and Eve in the Garden of Eden.
These simple facts have given rise to some remarkable displays of statistical
pyrotechnics. Demographer Kenneth Wachtel estimates that the typical English child born in
1947 would have had around 60,000 theoretical ancestors at the time of the discovery of
America. Of this number, 95 percent would have been different individuals and 5 percent
duplicates. (Sounds like Invasion of the Body Snatchers, but you know what I mean.) Twenty
generations back the kid would have 600,000 ancestors, one-third of which would be
duplicates. At the time of the Black Death, he'd have had 3.5 million--30 percent real, 70
percent duplicates. The maximum number of "real" ancestors occurs around 1200
AD--2 million, some 80 percent of the population of England.
Pedigree collapse explains why it's so easy for professional genealogists to trace your
lineage back to royalty--go far enough back and you're related to everybody. For that
matter, you're probably related to everybody alive today. Some geneticists believe that
everybody on earth is at least 50th cousin to everybody else. For a fuller discussion of
the above, see The Mountain of Names, by Alex Shoumatoff (1985).
--CECIL ADAMS
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