Identifiability of 3-Class Jukes-Cantor Mixtures

TL;DR

This paper proves that the tree parameters of the 3-class Jukes-Cantor mixture model are identifiable using algebraic statistics techniques, ensuring unique inference of evolutionary trees under this model.

Contribution

It introduces a novel proof of identifiability for the 3-class Jukes-Cantor mixture model leveraging algebraic invariants and symbolic computation.

Findings

Proves identifiability of tree parameters for the model

Uses algebraic invariants to distinguish different tree varieties

Employs symbolic computation to handle complex cases

Abstract

We prove identifiability of the tree parameters of the 3-class Jukes-Cantor mixture model. The proof uses ideas from algebraic statistics, in particular: finding phylogenetic invariants that separate the varieties associated to different triples of trees; computing dimensions of the resulting phylogenetic varieties; and using the disentangling number to reduce to trees with a small number of leaves. Symbolic computation also plays a key role in handling the many different cases and finding relevant phylogenetic invariants.