GENEALOGY-DNA-L Archives

From: John S Walden <>
Subject: Re: [DNA] Re: Two one-step mutations between 3rd cousins
Date: Fri, 02 Aug 2002 07:01:05 -0400
In-Reply-To: <ea.2b8875f8.2a7b4ff5@aol.com>

At 11:01 PM 8/1/2002 -0400, you wrote:
>I'll welcome any comments. I'm very surprised that they differed so much on
>the 12-marker test. Isn't that the one that is supposed to be fairly
>definitive in grouping close relatives?

I take a stab at this and see if I remember how.
I we ignore the full test and just do the 12 marker and I use what
Ann wrote for yesterdays question "The expectation of matching at all 24 loci
is .998 ^ 24, or .953. The expectation that you will match your brother is
.953 x .953 = .908."

The 12 marker test (again using .002) the odds they all match
with no change would be .998^12 = .9763 for each birth in the line.
You said 4 generations (is that really 5?) two men who are 3rd
cousins. There are 4 births
in each line to get to 3 cousins so the odds of having no markers change
would be .9763^8 = .825 (the fraction for one marker to change is .175)
There are lots of ways to see two markers to change at end and that math
can get complicated. There could have been lots of changes along the way
some other markers could have changed plus one in one generation and minus
one the next.
Ignoring all that, and taking the simple approach the odds of a two marker
change is approximately .175^2 or .0306

So while 3% is not much when you think that we have over 200 surname
projects going on
and assuming they are only doing one such case then
one would expect to see about 6 projects have this happen.
Yours just happens to be one of the 6.

It is our testing a looking at the results that will tell us if .002 is
correct and if it
is the same for all markers. We just don't have enough cases to get a good
solid
number for it. If the mutation rate were .004 then the 3% becomes 10% and
we would
see more of this if it were .001 then the 3% becomes 0.8% (or about 2 out 200).

To the real statisticians: Is this close enough?

John W.

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