Identifiability in Phylogenetics using Algebraic Matroids

TL;DR

This paper introduces a new algebraic matroid-based computational method to prove the generic identifiability of phylogenetic tree and network parameters, enhancing the reliability of evolutionary inference models.

Contribution

It presents a novel algebraic matroid approach for establishing parameter identifiability in algebraic phylogenetic models, including trees and networks.

Findings

Tree parameters are generically identifiable for 2-tree CFN and K3P mixtures.

K2P and K3P models ensure identifiability of the $k$-cycle phylogenetic network.

The method provides a systematic way to prove identifiability in algebraic phylogenetics.

Abstract

Identifiability is a crucial property for a statistical model since distributions in the model uniquely determine the parameters that produce them. In phylogenetics, the identifiability of the tree parameter is of particular interest since it means that phylogenetic models can be used to infer evolutionary histories from data. In this paper we introduce a new computational strategy for proving the identifiability of discrete parameters in algebraic statistical models that uses algebraic matroids naturally associated to the models. We then use this algorithm to prove that the tree parameters are generically identifiable for 2-tree CFN and K3P mixtures. We also show that the $k$-cycle phylogenetic network parameter is identifiable under the K2P and K3P models.