  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.
