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Archiver > GENEALOGY-DNA > 2011-01 > 1293985511


From: "Ken Nordtvedt" <>
Subject: Re: [DNA] How old is Y-Chromosome Adam?
Date: Sun, 2 Jan 2011 09:25:11 -0700
References: <mailman.255.1293782436.1099.genealogy-dna@rootsweb.com><3203DE795D7E4D24B6A24928379E156E@anatoldesktop><AANLkTi=F+O4hFtK900wWetyKtfjzJB90r_CYi+5cc8h8@mail.gmail.com><3494E649-D554-4BFA-A206-80C054DBB9B6@vizachero.com><19954443.178870.1293883908917.JavaMail.www@wwinf2233><004001cba9d5$b0498ed0$c2482dae@Ken1><C4D1EA69-E1DC-4EB2-8F2C-E97B0E9971F3@vizachero.com><005a01cba9dc$a6a96650$c2482dae@Ken1><5E0F95F0B965408DB2815855E6B42C45@lop><AANLkTimVz4+h41_r+ZwEv+zhaWaOaVWO8Kf0xih-fV2t@mail.gmail.com><00f901cbaa01$d1a63110$c2482dae@Ken1><AANLkTimQxMy8g-wVgiqzp-4SiQ9RAVBs0PGq+BTjJbAx@mail.gmail.com><D41627AD-C565-4766-B899-2CE421596718@vizachero.com><AANLkTin92hWJUngGsmV8HqLXqC+0Gu_Uzkua0RCeWWLb@mail.gmail.com><DDD7CB70-75CD-48EF-AE59-FFAB4EF9DD5B@vizachero.com><AANLkTi=9ROdk1A2HtC3TtR2rr=nvX73bc0_TgTMm5-7D@mail.gmail.com><1AE3D85C-335B-47A8-9E00-FBE2DCA6E08C@vizachero.com>


----- Original Message -----
From: "Vincent Vizachero" <>

> Meanwhile, Ken's approach of iteratively down-weighting the fast
> markers as a function of their mutation rate and as a function of the
> TMRCA estimate itself is both our theoretical "best available" option
> and one that produces estimates that are generally sensible (i.e.
> agree with other independent lines of thought, as in the case of "out
> of Africa" and Y-Adam).
>
> VV

The downweighting factor 1/ (1+4m(i)G) is given to us by the "excessive"
growth of distribution sigmas for the STRs' variances; it is not ad-hoc to
solve the apparent problem of saturation of random walk with the fast
markers. It just by accident weights in a direction which also ameliorates
the fast marker model problem.

It is the applied math when answering the question --- how do you best
combine the age estimates of N independently mutating STRs into one best
estimate with smallest statistical sigma? --- which yields the weighting:

<G> = Sum i [ { Var(i)/2m(i) } / sigma(i)^2 ] divided by Sum i [ 1/
sigma(i)^2 ]
i summed over the STRs

and the analytic and simulation-confirmed sigma values

sigma(i)^2 = (1 + 4 m(i) G ) / 2 m(i) G

The iteration is necessary because the sigma(i) weight factors depend on G,
so differ for different applications, but reduce to the traditional weight
factors 1 in the small G limit.


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