Identifiability of Large Phylogenetic Mixtures for Many Phylogenetic Model Structures

TL;DR

This paper proves the identifiability of several large phylogenetic mixture models, ensuring unique parameter recovery, which is crucial for accurate evolutionary analysis of DNA sequences.

Contribution

It extends previous theorems to establish identifiability for multiple complex phylogenetic mixture models, including Jukes-Cantor and Kimura models.

Findings

Proves identifiability for Jukes-Cantor model

Establishes identifiability for Kimura models

Extends main theorem of Rhodes and Sullivant 2012

Abstract

Identifiability of phylogenetic models is a necessary condition to ensure that the model parameters can be uniquely determined from data. Mixture models are phylogenetic models where the probability distributions in the model are convex combinations of distributions in simpler phylogenetic models. Mixture models are used to model heterogeneity in the substitution process in DNA sequences. While many basic phylogenetic models are known to be identifiable, mixture models in generality have only been shown to be identifiable in certain cases. We expand the main theorem of [Rhodes, Sullivant 2012] to prove identifiability of mixture models in equivariant phylogenetic models, specifically the Jukes-Cantor, Kimura 2-parameter model, Kimura 3-parameter model and the Strand Symmetric model.