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Archiver > GENEALOGY-DNA > 2004-01 > 1075062418


From: Amelia <>
Subject: Re: [DNA] Charlemagne's DNA?
Date: Sun, 25 Jan 2004 12:26:58 -0800
References: <20040125170439.84607.qmail@web41807.mail.yahoo.com>
In-Reply-To: <001901c3e37c$a32b9c60$606660cb@Marsh>


This is a very interesting
link: http://www.oz.net/~lee/Genealogy/charlemagne.html, which is quoted here:

there is virtually no chance that anyone of European ancestry is not
directly descended from Charlemagne...

Charlemagne was approximately 40 generations back from the present day.
Each person has 2 parents, 22 = 4 grandparents, 23 = 8 great-grandparents,
... and 240, or approximately 1,000,000,000,000 (one trillion),
40th-generation ancestors, which means half a trillion male ancestors. Of
course, since the entire male
<http://www.fordham.edu/halsall/source/pop-in-eur.html>population of Europe
at the time of Charlemagne was only about 15 million, these half trillion
ancestors cannot all have been different men -- obviously there has been a
lot of cross-breeding, and many of our ancestral lines cross and re-cross,
eventually ending up at the same person. Let's assume that each of my
40th-generation male ancestors is a randomly-chosen man from eighth-century
Europe (this is not really valid, but more on that below). Choosing any one
such ancestor, say my father's father's ... father's father, the
probability that that particular person is Charlemagne is one in 15
million. Pretty small. To put it another way, the probability that any
particular ancestor was not Charlemagne is 1 - 1/15,000,000, or
approximately 0.999999933

But now consider the probability that none of my 40th-generation ancestors
is Charlemagne. For that to happen, every one of my half trillion male
ancestors has to not be Charlemagne, which would be an amazing coincidence.
To see how amazing, let's compute the probability. Assuming all of these
various not-being-Charlemagne occurrences are independent of each other
(more on this below), the laws of probability state that the probability of
all these events occurring simultaneously is obtained by multiplying
together their individual probabilities:

(0.999999933)·(0.999999933)·...·(0.999999933) = (0.999999933)500,000,000,000.

This turns out to be an incredibly small number: about one chance in
1015,000. That's a one with 15,000 zeroes after it, a number that's too big
even to display in a browser window. This is way more than the number of
atoms in the universe (which is estimated to be about 1080). Therefore, if
this analysis is even remotely close to correct, it's virtually impossible
that Charlemagne is not among my direct ancestors.

Of course, there are a few sources of errors in this analysis, so there are
various corrections one could make that might yield a more accurate
estimate. Most obviously, one's ancestors are not in fact randomly chosen
people from eighth-century Europe. For example, anyone who had no children,
or no grandchildren, cannot be an ancestor of someone living now.
(Charlemagne has well-documented descendants down to the present day.) More
generally, wealthy people survived at a far higher rate than the rest of
the population, and so were much more likely to produce descendants - thus
one's ancestors are more likely to be found among the relatively small
population of royalty and nobility, including Charlemagne. You might think
of other, smaller, corrections, such as the fact that the probabilities of
different ancestors being Charlemagne are not really independent: for
example, if my father's ... father's father was Charlemagne's brother, then
the probability that my father's ... mother's father was Charlemagne
himself is very small. And, of course, some of my ancestors came from
outside of Europe. But I believe these effects cannot change the fact that
the probability we're talking about is so tiny as to be zero for all
practical purposes.


At 08:50 AM 1/26/2004 +1300, you wrote:
>In calculating if any one of us might still have any significant part of
>Charlemagne's DNA, a simplistic approach might be to say that if in
>Charlemagnes day say 100,000,000 people lived in the World (or whatever the
>number was) then in his day his genes reperesented one one hundred millionth
>part of the world's DNA pool. If he left descendants at the same
>proportional rate as all other persons living in his day, then when the
>stage is reached where his genes are uniformly mixed in the whole World
>population, each person in the World would on average have one one hundred
>millionth part of their DNA from Charlemagne. From then on until the end of
>human history, everybody would always have on average one one hundred
>millionth part of their DNA from Charlemagne, regardless of the population
>of the world.
>
>If most of Charlemagne's DNA was still currently in Europe and not fully
>dispursed, and if the advantage his descendants had had enabled them to
>breed a bit better than average, it might be today that on average all
>Europeans have perhaps one ten millionth part, or perhaps one millionth part
>of their DNA from Charlemagne.
>
>I have some supposed lines from Charlemagne. If they were correct, and not
>interupted by "non paternity events" along the way, I suspect I could show
>1,000 separate "paper trail" lines to Charlemagne, and there is nothing
>remarkable about my family. And I only know a tiny tiny fraction of my
>lines of descent back to Charlemagne's day.

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