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From:"Kenneth Nordtvedt" <>Subject:[DNA] Artificiality of Coalescence AgeDate:Mon, 6 Jun 2011 14:15:02 -0600Dinaric I2a2a and I1 are the two largest clades of haplogroup I. Suppose one had a population consisting of haplotypes from these two clades (call it Polish haplogroup I). A coalescence age could be estimated, but the problem is it would represent some age when nothing particularly interesting was happening. The branch lines eventually leading to the founders of the I2a2a population and the I1 population departed from each other 20,000 or more years ago. While the founding ages for I2a2b and I1 were about 2800 years ago and 4500 years ago, respectively.

Self-Variance = Sum over a,b of (r[i]-r[j])^2 / N^2

can be broken up into several terms involving sums of the I2a2b haplotypes “a” and the I1 haplotypes “b”

SVar = (N[A]/N)^2 Sum over a,a’ of (r[a]-r[a’])^2 /N[A]^2

+ (N[B]/N)^2 Sum over b,b’ of (r[b]-r[b’])^2 / N[B]^2

+ 2 N[A]N[B]/N^2 Sum over a,b (r[a]-r[b])^2 / N[A]N[B]

First term is estimate of coalescence age of I2a2a (less than 2800 years)

Second term is estimate of coalescence age of I1 (less than 4500 years)

Third term is estimagte of interclade node age (TMRCA) for both I2a2a + I1 (more than 20,000 years)

N[A]/N is fraction of haplotype sample population from I2a2a, etc.

So one is estimating some fractional combinations of 2800 years, 4500 years, and 20,000 years.

If you had about equal numbers of I2a2a and I1 haplotypes, your estimate would be about 12,000 years.

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**[DNA] Artificiality of Coalescence Age by "Kenneth Nordtvedt" <>**