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Identifiability of a Coalescent-Based Population Tree Model

Part of: Mathematical biology in general Stochastic processes Applications

Published online by Cambridge University Press:  30 January 2018

Arindam RoyChoudhury
Arindam RoyChoudhury*
Affiliation:
Columbia University
*
∗ Postal address: Department of Biostatistics, Columbia University, 6th Floor, 722 W. 168th Street, New York, NY 10032, USA. Email address: ar2946@columbia.edu
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Abstract

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Identifiability of evolutionary tree models has been a recent topic of discussion and some models have been shown to be nonidentifiable. A coalescent-based rooted population tree model, originally proposed by Nielsen et al. (1998), has been used by many authors in the last few years and is a simple tool to accurately model the changes in allele frequencies in the tree. However, the identifiability of this model has never been proven. Here we prove this model to be identifiable by showing that the model parameters can be expressed as functions of the probability distributions of subsamples, assuming that there are at least two (haploid) individuals sampled from each population. This a step toward proving the consistency of the maximum likelihood estimator of the population tree based on this model.

Keywords

Population treephylogenetic treeidentifiabilitycoalescent

MSC classification

Primary: 92B10: Taxonomy, cladistics, statistics
Secondary: 60G99: None of the above, but in this section 62P10: Applications to biology and medical sciences 92D15: Problems related to evolution
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 4 , December 2014 , pp. 921 - 929
Copyright
© Applied Probability Trust 

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