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From: "Dienekes Pontikos" <>
Subject: Re: [DNA] What shall R1b1c call themselves now?
Date: Wed, 17 Sep 2008 22:19:17 +0300
References: <mailman.6170.1221611606.2567.genealogy-dna@rootsweb.com><000d01c9186a$a93829c0$6401a8c0@alfap43400ak><REME20080916225634@alum.mit.edu><f3f05ce80809170322k3a5a5710ve413dde9da0a5669@mail.gmail.com><REME20080917142424@alum.mit.edu>
In-Reply-To: <REME20080917142424@alum.mit.edu>


On Wed, Sep 17, 2008 at 9:26 PM, John Chandler
<> wrote:
> Not true. If there is no expansion, and if nearly every man has 1
> son, then nearly every man of today is his own lineage's MRCA, and the
> expected time between founding and MRCA is essentially "forever".
> More generally, there is no theoretical limit on the amount of time
> that a lineage can flounder between the two extremes of extinction and
> saturation.
>
> John Chandler


Incorrect, I didn't say that every man has one son -that's
demographically unlikely anyway-, I said that men have 1 son _on
average_. The number of sons/man is Poisson-distributed with parameter
1.

Even under that assumption, the time from the founding of the lineage
to today is not much longer than the MRCA and today.

Here is an R function which makes this calculation. Write to me
off-list if it doesn't come right at your end:

mrcaFounder <- function(N=10000, g, m) {
COUNT <- vector(length=N);
MRCA <- vector(length=N);
for (i in 1:N) {
COUNT[i] <- 1;
MRCA[i] <- 0;
}
for (j in 1:g) {
for (i in 1:N) {
if (COUNT[i]>0) {
COUNT[i] <- sum(rpois(lambda=m, COUNT[i]));
if (COUNT[i]==1) {
MRCA[i] <- j;
}
}
}
}
sum(MRCA[COUNT>0])/(sum(COUNT>0)*g)
}

Paste the above in an R window. The function can be called as:

mrcaFounder(N=10000,g=100,m=1)

or with whatever values you are interested in:

N: number of lineages
g: number of generations since founding
m: average number of sons/man

The function outputs the expected time between the MRCA and the
founding divided by the time between the founding and today.

Some results:

0.08 for g=100, m=1
0.02 for g=100, m=1.1
0.06 for g=200, m=1

So, yes, the MRCA is expected to be close to the founder in age.

A little bit of explanatory info on the code:

COUNT: number of men per lineage: initially 1
MRCA: generation of the MRCA for each lineage

==== Results ====

g=100, m=1



--

Dienekes' Anthropology Blog
http://dienekes.blogspot.com


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