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

Benjamin D Kaehler 

Research School of Biology, Australian National University, Canberra, Australian Capital Territory, Australia 

October 5, 2018 

## Abstract 

Understanding the evolutionary relationship among species is of funda- mental 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 informa- tion. It is known that the most general Markov models of nucleotide substi- tution can also not identify the location of the root or be fitted to multiple se- quence 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. 

