GENEALOGY-DNA-L Archives

Archiver > GENEALOGY-DNA > 2007-02 > 1171612126


From: Jonathan Day <>
Subject: Re: [DNA] TMRCA
Date: Thu, 15 Feb 2007 23:48:46 -0800 (PST)
In-Reply-To: <BEB9170F-55B5-4C71-A297-81A2AE5AE9E7@vizachero.com>


You're technically correct. I'm assuming that there
can be variations in mutation rates and differences in
generation gaps - that instead of everything being
uniform and balanced, that actually a number of cases
will be seriously skewed.

Why is that important? Well, let's say you have a
genetic distance of 4. There are five possible ways
that can occur:

a) Person A has 4 mutations, person B has none
b) Person A has 3 mutations, person B has 1
c) Person A has 2 mutations, person B has 2
d) Person A has 1 mutation, person B has 3
e) Person A has no mutations, person B has 4

If you have to include all five possibilities (ie: the
entire bell-curve of possibilities) then you have a
gigantic range of possible times to consider, which is
why TMRCA calculators generally produce very ugly
results. They aren't able to factor in skew, so must
offer the widest possible range of answers and the
least possible confidence on any of them.

(Either that, or they assume that people have kids
exactly on their twentieth birthday, that mutation
rates are absolutely uniform between generations and
that all siblings have exactly double the genetic
difference than each has from the parent concerned. In
that case, you produce extremely accurate nonsense.)

If, however, you can definitely say that you're in the
peak area OR in one of the tail sections, you've
eliminated a significant part of that window. Those
timeframes simply don't compute, given the nature of
the changes.

Let's take our case of having a genetic distance of 4,
and let's say that this is a freak case and it turns
out that the changes map onto case (a) above.

The greatest possible time to TMRCA is the greatest
possible time in which you can sensibly have the
second group be subject to absolutely no mutations
over the N markers being looked at. This will be much
shorter than for the "average" case of two mutations.
All that time can be safely ignored. It simply doesn't
matter.

The shortest possible time to TMRCA is the shortest
possible time in which you can have the first group be
subject to four mutations over the N markers being
looked at. This will be longer than the "average" case
of two mutations. Anything shorter can be ignored.

Whereas the TMRCA must consider the full range of all
possible combinations, we've identified a very narrow
band by eliminating combinations that could not have
existed. In this scenario, we're probably looking at a
timeframe around 1% of the possible range of times for
a TMRCA with a GD of 4.

(In the "typical" case of a totally even split, you're
at maybe 75% of the possible range of times, which is
still a good deal narrower.)

By looking at intermediate steps, we should be able to
advance the shortest possible time, and reduce the
maximum possible time. Nobody, however impressive, can
be born after their descendants or before their
ancestors. Values that become impossible because of
some intermediate value can be rejected.



--- Vincent Vizachero <> wrote:

>
> On Feb 15, 2007, at 2:31 AM, Jonathan Day wrote:
>
> > It would seem to me that a good calculator must
> make
> > some attempt at figuring out what the common
> > ancestor's markers most likely were.
>
> That might be a useful tool, but it is not the
> function of a TMRCA
> calculator.
>
> Anyway, such tools already exist. PAUP* is one.
>
> Vince
>
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