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Archiver > GENEALOGY-DNA > 2009-02 > 1235606347


From: James Heald <>
Subject: Re: [DNA] Puzzle, resolved? (was TMRCAs for groups of haplotypes)
Date: Wed, 25 Feb 2009 23:59:07 +0000
References: <49A2D0B4.5070808@ucl.ac.uk> <49A5C9BD.5010506@ucl.ac.uk><006f01c997a0$9bcd3bd0$6400a8c0@Ken1>
In-Reply-To: <006f01c997a0$9bcd3bd0$6400a8c0@Ken1>


Ken Nordtvedt wrote:
> L(G,3) is total length of tree for 3 perfect matches, neglecting multiple
> back mutations, and G being total depth of tree
>
> We have inequality L(G,3) >= 2 G
>
> Probability of having 3 exact matches is exp[-ML(G,3)]
> So under scaling the depth of the tree, expected value of <L(G,3)> = 1/M
>
> But using our original inequality this means expected value <2G> <= 1/M
>
> So expected value of total tree depth for 3 identical matches is less than
> for 2 identical matches for any assumption of where the third guy ties into
> the V tree for two
>
> Identical twins excluded from consideration.
>

But the problem is this:

At the top of any tree with three guys is a tree with two guys. What
has caused our estimate of the TMRCA for this sub-tree with two guys to
have changed?


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