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From: "Ken Nordtvedt" <>
Subject: [DNA] TMRCA Corrections
Date: Wed, 20 Jun 2007 07:35:09 -0600


Several days ago I outlined how information about modifications of TMRCA estimates if you had information about your pair of haplotypes being in a clade of known properties.

Here are some tables for the increase in TMRCA estimates along with their confidence intervals for the extreme case that one's pair of haplotypes have no steps of difference and are of the clade's modal haplotype. As you have seen, in the case of no mutational steps between a pair of haplotypes, the probability curve for TMRCA does not rise and then fall with increasing generations, but it basically monotonically decreases exponentially, and it is more appropriate to quote the decay rate of that probability curve, or the mean expected value of TMRCA which is the reciprocal of that curve's decay rate.

The corrections to these curves due to spreading clade distribution are approximately a decrease in curve decay rate, which means an increase in the TMRCA estimates. I calculated them for two difference choices of clade ages --- 250 generations and 400 generations, and then for a range of marker mutation rates.

G = 250 generations

m = .005 133%
m = .0025 156%
m = .001 179%
m = .0005 189%



G = 400 generations

m = .005 118%
m = .0025 138%
m = .001 168%
m = .0005 182%

For example: if you had two identical haplotypes composed of markers each having mutation rates .0025 = 1/400, and the haplotypes were from a clade estimated to be 250 generations old (7500 years), then the TMRCA estimates including confidence intervals are increased to 156 percent of the traditional size if they are equal to or very close to the modal haplotype of the clade.

Here are some more rescaling factors for a young clade of only 150 generations (4500 years)

G = 150 generations

m = .005 148%
m = .0025 169%
m = .001 186%
m = .0005 193%

Remember the reasons for these rescalings of TMRCA. Because the haplotype distribution for the clade descendants is spreading each generation, haplotypes at the center of the clade distribution will find a higher percentage of the population with haplotypes at the modal haplotype at the center of the distribution the further back in time it looks for the MRCA.. For haplotypes out at the fringes of the clade's haplotype distribution, the opposite will happen: it will find a higher percentage of haplotypes in the population which could be the MRCA the more recently in time it looks back.

Of course you can just lay back, assume your haplotypes aren't too close to the clade's modal haplotype or too far from the modal haplotype and ignore these corrections, using the traditional TMRCA curves instead.

Ken

Ken



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