

How many genetic ancestors do I have? - maxerickson
http://gcbias.org/2013/11/11/how-does-your-number-of-genetic-ancestors-grow-back-over-time/

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DonGateley
Can it be calculated how far back we need go before each of us, with high
probability, is descended from everyone then living? Does the question even
have an answer?

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graham_coop
Yes, people have developed simple models to give us some intuition about this
question. The first thing to keep in mind is that not everyone at a particular
time in the past will leave descendants to the present day. But quite a high
proportion of the population will leave descendants to the present day. It's
been estimated that around 80% of the population at a given time will. So we
can ask how long far do we have to go into the past until we can expect
everyone in the population (who left any descendants in the present) to be our
genealogical ancestor.

Your number of ancestors grows very quickly, k generations you have up to 2^k
ancestors (2 parents, 4 grandparents etc). So if our population has N
individuals in it, we need to go back log2(N) generations until our number of
ancestors is on the order of the population size. So even if our population
was made up of a billion people it takes only 30 generations (~1000 years) for
us to reach the point where it is likely that you are descended from everyone
in the population. What’s happening here is that if we go back far enough
everyone in the population (who left descendants) is your ancestor many times
over (via various routes back through your family tree). Now this is only an
approximation, and this statement has been made more precise by Chang (1998)
[http://www.stat.yale.edu/~jtc5/papers/Ancestors.pdf](http://www.stat.yale.edu/~jtc5/papers/Ancestors.pdf)
.

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graham_coop
However, in the calculation above we have ignored the fact that populations
are structured, i.e. individuals any where in the world are not equally likely
to be your parents. This means going back a few generations in the past
individuals in your geographic area may be your ancestors, but individuals in
geographically remote areas may likely not be. This means that while in a well
mixed population (where individuals) move around a lot the above result will
hold, in populations where migration is geographically limited it may take far
longer for you to be descended from everyone (who left any descendants).

However, some individuals within populations do migrate, and so some
individuals in the population will have an ancestor in some distant geographic
location in the previous generation. You only need to trace part of your
family tree back to one of these migrant individuals in order for you to start
having ancestors at geographically distant locations. Given the vast numbers
of ancestors you have only a small number of generations back, it is quite
likely that you trace your ancestry back to many different migrant ancestors.
In turn these migrant ancestors quickly themselves have many ancestors further
back in time, and so your ancestry quickly spreads around the world. Indeed
Rhoades, Olsen, and Chang (2004) estimated under some fairly conservative
assumptions about human migration that you might well trace your ancestry to
everyone in the the entire world (who left descendants) may be just ~three
thousand years ago. See
[http://www.stat.yale.edu/~jtc5/papers/CommonAncestors/Nature...](http://www.stat.yale.edu/~jtc5/papers/CommonAncestors/NatureCommonAncestors-
Article.pdf)

~~~
graham_coop
Carl Zimmer has a really nice writeup on this,
[http://phenomena.nationalgeographic.com/2013/05/07/charlemag...](http://phenomena.nationalgeographic.com/2013/05/07/charlemagnes-
dna-and-our-universal-royalty/) , where he discusses Chang's result and Peter
Ralph and I's paper on this topic
[http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjo...](http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001555)

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QuantumChaos
We got both kinds of science here, simulation and theoretical approximation

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babesh
This doesn't take into account males who inherit the Y chromosome wholly from
the paternal side. It also does not factor in mutations that occur along the
way.

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Myrmornis
It says "autosomal" in the first sentence.

What makes you think the mutation process is relevant to this subject? He's
talking about ancestry of genomic segments. It doesn't matter what mutations
occur on those ancestral lineages.

If you don't understand the topic, I'm baffled as to why you would post two
sentences criticizing it.

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babesh
You know you're right. Bye bye Y Combinator.

