GENEALOGY-DNA-L Archives

From:
Subject: Re: [DNA] How many STRs??
Date: Sun, 4 Apr 2004 14:46:08 -0400 (EDT)
References: <1ee.1d225d83.2da113a2@aol.com>
In-Reply-To: <1ee.1d225d83.2da113a2@aol.com> (AWNRDC@aol.com)

Anne wrote:
> I may be alone in this, but my concern is in trying to get a better handle on
> the probabilities between the "minimal" TMRCA and the maximum. If this has
> been addressed in any detail on this list, I either missed it or I didn't
> realize it!

We had some discussions like this a couple years ago.

> Example (using Dr. Walsh/'s calculations):
>
> "slow" mutation model [chosen because my two samples with 12 transmission
> events have 0 mutations, we don't have the 37 marker results yet,but for
> illustrative purposes let us assume 37/37]

Right choice. Wrong reason. The way to determine the average mutation
rate is by studying thousands of cases, not just a few.

> 12/12 match has P[MRCA<=14]= .50 P[MRCA <=53]=.9 P[MRCA<= 71] =.95
> P[MRCA>=72]= .05

NOTE: these are "a priori" probabilities computed from the assumption
that nothing whatsoever is known about the true relationship between
the two test subjects. If you have some such knowledge, then the
computation should be redone to include that.

> It appears a 43 marker match would be represented by P[MRCA<=4]=.5, but what
> is the effect of a 43/43 on the 5 - 26 generations probabilities?

Everything scales with the number of markers (assuming the average rate
is the same for all). If you multiply the number of markers by 43/12,
you correspondingly shift the 90th percentile by a factor of 12/43, i.e.,
to 53x12/43=15.

> if you add in reality that there is NO MRCA within the five most recent
> generations, i.e. P[0<=MRCA<=5] = 0. Therefore, P[MRCA<=7] - P[0<=MRCA<=5] =
> P[<=6MRCA<=7] = .5 - 0 = .5.

No. See above. When you eliminate part of the range of possibilities,
the probability is redistributed. This redistribution in particular
was discussed at length. The redistribution is quite simple: if you
eliminate generations 1-5, then you just add 5 to all the previous
generation counts. So, if the 90th percentile was at 53 generations,
it now moved to 58. This result follows from the form of the distribution.

By the way, it would be a mistake to assume that a 12/12 match will
upgrade to a 43/43 match. For example, if you know the MRCA is at
least 5 generations back, the probability of at least one mutation
cropping up in the additional 31 markers is better than even.

John Chandler

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