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Understanding the evolutionary relationship among species is of fundamentalimportance to the biological sciences. The location of the root in anyphylogenetic tree is critical as it gives an order to evolutionary events. Noneof the popular models of nucleotide evolution used in likelihood or Bayesianmethods are able to infer the location of the root without exogenousinformation. It is known that the most general Markov models of nucleotidesubstitution can also not identify the location of the root or be fitted tomultiple sequence alignments with less than three sequences. We prove that thelocation of the root and the full model can be identified and statisticallyconsistently estimated for a non-stationary, strand-symmetric substitutionmodel given a multiple sequence alignment with two or more sequences. We alsogeneralise earlier work to provide a practical means of overcoming thecomputationally intractable problem of labelling hidden states in aphylogenetic model.

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