GENEALOGY-DNA-L Archives

Archiver > GENEALOGY-DNA > 2005-05 > 1117584718

From: (John Chandler)
Subject: Re: [DNA] Middle Eastern ancestral markers on new Euro 1.0 test
Date: Tue, 31 May 2005 20:11:58 -0400 (EDT)
References: <BKEPIIDHHKEPCMDIEBKBIEGFCHAA.andrew.en.inge@skynet.be>

I wrote:
> Here's the math. Suppose the probability of random individual
> extinction is 99%. That's pretty daunting odds. However, the
> extinction probability for a group is the Nth power of the individual
> probability (where N is the size of the group). With even just a
> thousand members, the group extinction probability goes down to
> 0.004%. Negligible.

Andrew replied:
> You say you'll show me the math, but then you don't, you only give the
> results. How do you calculate an extinction probability, and what does the
> term mean?

The individual or group extinction probability is the likelihood that
the individual's or group's lines would eventually end. In the
context of surnames or Y DNA, these would be the male lines, of
course. As for calculating the probability, it's much easier to
guess, and perhaps as accurate, too, since you need to have statistics
literally forever in order to calculate it. I'm being flippant here,
but I surmise that you really would not be interested in a discussion
with enough depth to arrive at the extinction probability. If all you
want is an example that has a 99% individual extinction probability,
here's one: suppose the likelihood is 40% that a man will have no sons
who live to maturity, 30% that he will have one son who lives, 20% two
sons, 9.5% three sons, 0.5% four sons, and no chance at all of more
than four sons. This example will have a 99% extinction probability.
The population will be almost stable: growing at a rate of 0.5% per
generation.

No, that's not the usual behavior. Probabilities tend to multiply
instead. Consider the familiar example of a coin toss. If the
probability is 1/2 that a coin will come up heads, then the
probability is 1/2 x 1/2 = 1/4 that two coins will both come up
heads. The same principle applies to group extinction.

> If a single "nuclear" Y-family can die out so
> can an extended one with thousands of male individuals.

You have to understand that something "can" happen as long as its
probability is greater than zero, but a low probability means that you
can't expect it to happen often. You've upped the ante to thousands,
so let's consider a group of 2000 individuals. Following the same
guess of 99% individual extinction probability, we get the probability
for the group as a whole to be 0.99 raised to the 2000th power, i.e.,
about 2 x 10^-9. It is virtually certain that any one person in the
group would face extinction eventually, but almost impossible for the
group as a whole.

> I don't have any references but I am aware of the fact, from reasing
> something in the past, that a simple random computer programe which assumes
> no selective advantage will show surnames or Y DNA dieing out even when they
> have been in a majority situation.

The devil is in the details. You could have read a description of a
simulation which enforced a rule of 100% extinction, i.e., everybody
dies out in the long run, or even in the short run. If the population
dwindles by 2% per generation, then obviously no surname will survive,
even if there was only one surname to start with. Similarly, a case
with 5 out 8 certainly has a majority situation, but 5 is not in the
same league with 2000. The group extinction probability for a group
of 5 is 95% when the individual probability is 99%.

John Chandler