Full Reconstruction of Non-Stationary Strand-Symmetric Models on Rooted Phylogenies

TL;DR

This paper proves that the root location and full parameters of a non-stationary, strand-symmetric phylogenetic model can be uniquely identified and consistently estimated from multiple sequence alignments with at least two sequences.

Contribution

It demonstrates the identifiability and consistent estimation of the root and model parameters for a specific non-stationary phylogenetic model, extending previous work.

Findings

Root location can be identified with two or more sequences.

Full model parameters can be statistically consistently estimated.

Provides a practical approach to handle hidden state labelling in phylogenetics.

Abstract

Understanding the evolutionary relationship among species is of fundamental importance to the biological sciences. The location of the root in any phylogenetic tree is critical as it gives an order to evolutionary events. None of the popular models of nucleotide evolution used in likelihood or Bayesian methods are able to infer the location of the root without exogenous information. It is known that the most general Markov models of nucleotide substitution can also not identify the location of the root or be fitted to multiple sequence alignments with less than three sequences. We prove that the location of the root and the full model can be identified and statistically consistently estimated for a non-stationary, strand-symmetric substitution model given a multiple sequence alignment with two or more sequences. We also generalise earlier work to provide a practical means of overcoming the computationally intractable problem of labelling hidden states in a phylogenetic model.