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Archiver > GENEALOGY-DNA > 2002-03 > 1017164990


From: "Allan S. Gleason" <>
Subject: Re: [DNA] Confidence in labs
Date: Tue, 26 Mar 2002 10:49:50 -0700
References: <JCHBN.020325.200223.RC0@CUVMB.CC.COLUMBIA.EDU>


OK John, I concede that I produced mathematical garbage - there goes my credibility
up in smoke - I admit that I'm no statistician - wasn't required in my field. I
used 'combinations' little knowing they are so restrictive - permutations would have
yielded larger numbers, but you're right, just simple exponentiation was the correct
method - just like pedigree charts and the powers of 2.

Also with exponentiation I shouldn't have been so generous with my model. The only
real way would be to take each of the twelve markers evaluate them by the observed
frequencies of each repeat value and go from there. What convinced me of my numbers
was that looking at my chart of haplotypes posted at this list that with a few
exceptions here and there all seem to be very single valued. Granted I'm sure most
of these postings are from European heritage but isn't that what we're sorting out
here? I should have left it with that argument and not tried to put in numbers.

Allan


"John F. Chandler" wrote:

> Allan wrote:
> > Lets be generous and say that with 12 markers with 4 coequal states there
> > would be about 500 combinations.
>
> I'm not sure where you got that result. The correct answer is 4 raised
> to the 12th power, i.e., over 16 million combinations. Even if you
> decide to be stingy and figure only 3 states for each marker, you still
> get over half a million combinations. With 22 markers, these numbers
> go up to 17 trillion and 31 billion in the same two "generous" and
> "stingy" cases. (These are the American/French trillions, not the
> British/German flavor.)
>
> Don't forget that most people have an assortment of close male relatives
> who would *expect* to be identical (barring non-paternity events). If
> you start with yourself and work outward through brothers, sons, fathers,
> and so on, you probably reach about 20 males before you run into the
> first mutation in a 12-marker test. However, you can't stop there
> because a certain fraction of your ever more distant cousins will still
> come through with identical haplotypes. All told, if you consider the
> descendants of your male-line ancestor back in 1600 and discount the
> fecundity since 1900, you get perhaps 10,000 living male-line descendants
> now, and perhaps 600 separate mutation events between then and now (most
> of which would simply populate the 24 adjacent states). Since we are
> being generous, lets figure the 10,000 males fall into 50 different
> haplotypes by natural variation. That means you would expect to share
> your 12-marker result with about 200 other directly related individuals
> with the same surname. That would parlay the 16 million available
> haplotypes into space for 3 billion living males, or 6 billion people
> in all. What a coincidence!
>
> The problem, of course, is that many of the possible states are empty,
> while some states are heavily overpopulated.
>
> John Chandler
>
> ==============================
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