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Archiver > GENEALOGY-DNA > 2010-02 > 1266374631


From: "Ken Nordtvedt" <>
Subject: Re: [DNA] Question for John Chandler
Date: Tue, 16 Feb 2010 19:43:51 -0700
References: <mailman.4572.1266045490.2099.genealogy-dna@rootsweb.com> <A597BD8569E24290A10B37465204E6B5@anatoldesktop> <525460709C6A493EBD3D6BECD514B319@john><REME20100214190716@alum.mit.edu><000601caaeef$640b0120$2c210360$@com><REME20100216194750@alum.mit.edu><D9854FFD8A924EB9A9295845122C981C@john>


----- Original Message -----
From: "Alister John Marsh" <>


> I have been concerned about this imbalance for a long time. I wondered if
> it would impact at all on the "variance of variance' calculations to
> determine TMRCA, but I was unable to understand the maths enough to check
> myself. I had presumed that Ken and others had allowed for individual
> mutation rates of individual markers in the variance calculation, rather
> than just doing the calculations based on all markers having average
> mutation rates. Is that assumption correct? [[[ Yes, of course; the
> mixture of STR mutation rates has been taken into account. I have strived
> for over 5 years to never use the dreadful formulation or slang "average
> mutation rate". It corrupts one's frame of mind. Each STR is doing its
> own thing, and the different independent clocks are only combined when a
> best single time estimate is desired. Ken ]]]



Or does having a mixed set of
> fast and slow markers not affect the variance calculation? [[ If STRs are
> mutating in the simple text book manner, each with their own rate, each
> STR grows the expected value of its variance in proportion to its mutation
> rate. But its variance of variance grows non-linearly (faster) than in
> proportion to its mutation rate.

<Variance> = mG
Variance of Variance = mG ( 1 + 4mG)

This latter variance of variance non-linear m-dependence canalter the
optimum strength with which to combine all the STR variances, especially for
large G cases; it implies downweighting the fast STRs more and more as one's
clade is getting older (higher G)
Ken ]]


>
> In Tim's series of TMRCA calculations using variance, he consistently
> seemed
> to get different results for faster markers than slower markers. Could
> this
> be evidence that in mixed sets of fast/ slow markers, there is an effect
> from the mixture which is not being mathematically allowed for?

[[ There is growing evidence that the faster STRs are deviating from the
standard (simple) mutation rule, but instead have mutation rates, and up
versus down ratios, dependent on
repeat values, such that there repeat values tend to get confined to
sweetspots. But I don't think genealogical problems need worry much about
this. Ken]]

[[ <Variance> takes back mutations and repeated mutations in the same
direction into account automatically. No corrections are needed like GD
needs. There is no issue here if one is willing to do the necessary
corrections to <GD> versus G. These corrections are indeed dominated by the
fast markers as the correction scales as square of the STRs mutation rate.
Ken ]]



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