Early ancestors

I recently came across a reference to a theory by Joseph Chang, a
statistician at Yale University, suggesting that 80% of people living about
800 years ago were ancestors of *all* people living in a particular area
today, e.g. Europe; the other 20% were ancestors of nobody alive today.

Don Aitken...

This is pretty generally accepted as true *if* one puts in a few
provisos. One version is "by going about thirty generations into your
past, you and all your contemporaries will be related to averyone who
lived then, or at least to those who had offspring and who lived
within that particular geographical and cultural realm". The main
difficulty is in defining the "geographical and cultural realm"; even
in mainly homogeneous populations, there may be genetically isolated
communities - Swiss mountain valleys are one of the classical
examples. You also have to exclude recent immigrants. But, if you
pick your area carefully, the statement is very likely true; England
probably qualifies.

This is based on the fact that the number of ancestors doubles each time you
go back a generation. Thus 800 years ago, or approximately 40 generations
ago, each of us had many millions of ancestors (2 to the power of 40); even
allowing for the increasing number of occasions when people married people
distantly related to them, this amounts to more than the population of
Europe of the time of about 50 million.

Don Aitken...

Actually, it isn't based on any such thing; this "doubling fallacy"
just confuses people.

There ia a good example of how it should be done in Appendix 8 of Ian
Mortimer's recent biography of Edward III. He sets out to determine
the truth or otherwise of the traditional description of Edward as
"father of the English people" (Edward is separated from us by 20-24
generations, on average). His method is to actually count his living
descendants several generations later; in 1500 there were 436 of them.
He then looks at the marriages of all these people, and finds what
proportion married other Edward III descendants; the answer is 13%. He
then estimates the number of descendants in subsequent generations by
doubling and applying the factor 100/113. (Note that this doubling
each generation as you come forward is simply the conservative
assumption that the population is self-sustaining, with each couple
having two children; it has nothing to do with the doubling as you go
back which you mention above). After a number of complications which I
won't go into, his conclusion is that the proportion of Edward III
descendants in the English-descended population of England is at least
80% and more probably 95%. Among those being born *now* it is probably
in excess of 99%.

T.M. Sommers...

However, as the percentage of the population descended from
Edward increases through the years, the probability of one of
them marrying another such descendant increases also, so that
100/113 factor can't remain constant (I'm not sure that is the
right factor, anyway; shouldn't it be 1 - 0.13?).

Don Phillipson...

One of the unstated and implausible assumptions underlying
this calculation is the supposition that people 400 or 800
years ago chose spouses at random -- which we know not
to be true. When parents chose their children's spouses,
they did so from a relatively short list, excluding unsuitable
candidates. No one choosing his or her own spouse could
do so from a larger population pool than they had personally
encountered in the first 15 or 25 years of life. Up to the
Middle Ages no one would ever meet in a lifetime social
equals born more than 20 miles away. Thus spouses
were chosen from a measurably small geographic population

This implies that there is no point in doing genealogical research prior to
the Middle Ages, even supposing it's possible to find reliable information
for that period. It is suggests, for example, that we're *all* descended

Don Aitken...

I don't see that that follows at all.

from William the Conqueror (referring back to a previous thread).

Don Aitken...

Not all, just "nearly all". It is a matter of probabilities. Proving
an actual descent for a particular person is quite a different kind of
exercise; all the probabilities in the world don't add up to proof.

I realise this topic may well have been covered previously, but I thought
I'd throw it in anyway.

Don Aitken...

It comes up every so often, but what the hell.