Archiver > GENEALOGY-DNA > 2002-11 > 1037731980

From: "John F. Chandler" <>
Subject: Re: [DNA] MRCA calculations
Date: Tue, 19 Nov 2002 13:53 EST
In-Reply-To: message <> of Tue, 19 Nov 2002 09:30:28 -0700

Orin wrote:
> Subject A is the brother of Subject B. Their father differed from both of
> them by one mutation, each on a different marker. The subjects passed
> these mutations on to their sons. What are the odds that two sons of a
> single individual would each have a mutation on different markers?

That's easy. Chance of ZERO mutations is 90%, ONE is 9%, TWO is 0.5%,
and so on. This is very unlikely, but obviously not impossible.

> One of
> the above also had a mutation at another site, Y-GATA-A10, where they
> picked up a double reading (13/14). This mutation/anomaly was NOT passed
> on to his sons. This sort of thing is not supposed to happen according to
> the tidy rules.

If it wasn't passed on to his sons, then it is presumably a coincidental
locus on some other chromosome, which happens to be ampmlified by the
same primers. Frankly, that makes A10 a bad marker to use in testing.
I wonder if that's why thes marker has not been given a DYS designation.

> I have a major discomfort with the "standard" assumptions being made as
> though mutation rates will always play by some nice tidy
> scientific/mathematical rules. They don't seem to.

The factor that giving you grief here is the essential rarity of
mutations. Anything that PROBABLY won't happen at all, but MIGHT
happen several times is going to play hob with your expectations.

> In one of our baseline families we have what amounts to 43
> transmissions. According to the tidy theory that should work out to
> .002x43x26 = 2.23 mutations. We experienced exactly 1.

Again, it's easy to figure the chances: ZERO 11%, ONE 24%, TWO 27%,
THREE 20%, FOUR 11%, and so on. If you flip a coin twice, and it
comes up heads both times, are you amazed? No, of course not. It's
roughly the same probability here.

> In other families we did experience more mutations. But the point is I
> question that you can apply the "average" theoretical mutation rate against
> any two individuals and really hope that it is going to give you accurate
> results. It may be a good "rule of thumb" but in any given instance it
> probably is not really correct.

True, but so what? Why would you need to know precisely how many
mutations you will find in a particular study? The whole field of
statistics rests on the tendency for these small-scale fluctuations
to average out after many cases have been added up. That's why
insurance companies need to be big, and that's also why companies
(and governments) that ARE big often decide to "self-insure".

> skew one way or another by the families where no mutations were encountered
> and those where several were encountered. To lump a family with a
> relatively high rate of mutation with one with a low rate of mutation seems
> to me to be wrong science. I believe there may be some other
> influences. They may be genetic or environmental but seem to impact one
> family over another and thus cause the "average" mutation rate to be
> overstated in one case and understated in another.

You may be right. However, if those other influences are not
correlated with observed factors, then they are effectively random.
If you collect enough statistics to DISCOVER such a correlation,
then you can subdivide the mutation rate into random and predictable
parts and be a lot more precise in the calculations. Note, in
particular, that a completely random mutation process will inevitably
lead to exactly the sort of disparities you are seeing.

John Chandler

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