## Journal of Applied Probability

- J. Appl. Probab.
- Volume 51, Number 4 (2014), 921-929.

### Identifiability of a coalescent-based population tree model

#### Abstract

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.

#### Article information

**Source**

J. Appl. Probab., Volume 51, Number 4 (2014), 921-929.

**Dates**

First available in Project Euclid: 20 January 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.jap/1421763318

**Mathematical Reviews number (MathSciNet)**

MR3301279

**Zentralblatt MATH identifier**

1333.92053

**Subjects**

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

**Keywords**

Population tree phylogenetic tree identifiability coalescent

#### Citation

RoyChoudhury, Arindam. Identifiability of a coalescent-based population tree model. J. Appl. Probab. 51 (2014), no. 4, 921--929. https://projecteuclid.org/euclid.jap/1421763318