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Identifiability of a Markovian model of molecular evolution with gamma-distributed rates

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Elizabeth S. Allman ,
Cécile Ané  and
John A. Rhodes
Elizabeth S. Allman*
Affiliation:
University of Alaska Fairbanks
Cécile Ané*
Affiliation:
University of Wisconsin Madison
John A. Rhodes*
Affiliation:
University of Alaska Fairbanks
*
∗ Postal address: Department of Mathematics and Statistics, University of Alaska Fairbanks, PO Box 756660, Fairbanks, AK 99775, USA.
∗∗∗ Department of Statistics, University of Wisconsin Madison, Medical Science Center, 1300 University Avenue, Madison, WI 53706, USA. Email address: ane@stat.wisc.edu
∗ Postal address: Department of Mathematics and Statistics, University of Alaska Fairbanks, PO Box 756660, Fairbanks, AK 99775, USA.
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Abstract

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Inference of evolutionary trees and rates from biological sequences is commonly performed using continuous-time Markov models of character change. The Markov process evolves along an unknown tree while observations arise only from the tips of the tree. Rate heterogeneity is present in most real data sets and is accounted for by the use of flexible mixture models where each site is allowed its own rate. Very little has been rigorously established concerning the identifiability of the models currently in common use in data analysis, although nonidentifiability was proven for a semiparametric model and an incorrect proof of identifiability was published for a general parametric model (GTR + Γ + I). Here we prove that one of the most widely used models (GTR + Γ) is identifiable for generic parameters, and for all parameter choices in the case of four-state (DNA) models. This is the first proof of identifiability of a phylogenetic model with a continuous distribution of rates.

Keywords

Phylogeneticsidentifiability

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 92D15: Problems related to evolution 92D20: Protein sequences, DNA sequences
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 1 , March 2008 , pp. 229 - 249
Copyright
Copyright © Applied Probability Trust 2008 

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