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August 1999 The ages of mutations in gene trees
R. C. Griffiths, Simon Tavaré
Ann. Appl. Probab. 9(3): 567-590 (August 1999). DOI: 10.1214/aoap/1029962804


Under the infinitely many sites mutation model, the mutational history of a sample of DNA sequences can be described by a unique gene tree. We show how to find the conditional distribution of the ages of the mutations and the time to the most recent common ancestor of the sample, given this gene tree. Explicit expressions for such distributions seem impossible to find for the sample sizes of interest in practice. We resort to a Monte Carlo method to approximate these distributions. We use this method to study the effects of variable population size and variable mutation rates, the distribution of the time to the most recent common ancestor of the population and the distribution of other functionals of the underlying coalescent process, conditional on the sample gene tree.


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R. C. Griffiths. Simon Tavaré. "The ages of mutations in gene trees." Ann. Appl. Probab. 9 (3) 567 - 590, August 1999.


Published: August 1999
First available in Project Euclid: 21 August 2002

zbMATH: 0948.92016
MathSciNet: MR1722273
Digital Object Identifier: 10.1214/aoap/1029962804

Primary: 60J70 , 62M05 , 65U05 , 92D10 , 92D20

Keywords: Ages of mutations , Ancestral inference , Coalescent process , gene trees , Population genetics , samples of DNA

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.9 • No. 3 • August 1999
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