Xref: utzoo talk.religion.misc:33069 soc.history:2670 sci.bio:4128
Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!samsung!dali.cs.montana.edu!milton!felsenst
From: felsenst@milton.u.washington.edu (Joe Felsenstein)
Newsgroups: talk.religion.misc,soc.history,sci.bio
Subject: Re: Some statistical analysis of "Eve"
Summary: Eves should be about Nf generations back
Keywords: Eve mitochondria genetic drift
Message-ID: <12698@milton.u.washington.edu>
Date: 10 Dec 90 08:30:25 GMT
References: <15566@cs.utexas.edu> <1613@sun13.scri.fsu.edu <15644@cs.utexas.edu>
Organization: University of Washington, Seattle
Lines: 33

The theory of how far back a mitochondrial "Eve" should be is well-known.
It involves the time until Nf female lineages have a common ancestor up
the female line.  It is a bit too complex to explain here but is based
on old results in genetic drift theory.

Basically with Nf females (N-sub-f) in a randomly reproducing population
(one where each offspring comes from a randomly selected female independently
of all others -- the classical Wright-Fisher model), the time until two
randomly sampled females have a common ancestor up their female lines is on
average Nf generations.  For all females in the population the corresponding
result is 2Nf generations.

The result for two female lineages is easy to explain.  Each generation
going back there is a random chance with probability 1/Nf that they
come to the same ancestor.  Then it is just like tossing a coin with this
probability of heads.  The result for the time to first heads is a geometric
distribution with mean time Nf generations.

The result for all Nf females is more complex so I won't try to explain it
unless there is some overwhelming demand, but it comes out as twice that
time, on average.

Keep in mind that this "Eve" will then be (1) not the common ancestor of
other parts of the genome, and (2) by no means the only female in the 
population, and (3) by no means the only female in that generation
who contributes genes to the population of the present.

---
Joe Felsenstein, Dept. of Genetics, Univ. of Washington, Seattle WA 98195
DO NOT send to me at "milton" but instead please use:
Internet/ARPANet:   joe@genetics.washington.edu   (IP No. 128.208.128.1)
BITNET/EARN:        FELSENST@UWALOCKE
UUCP:               ... uw-beaver!evolution.genetics!joe