and the proportions of Gs and Cs being equal on a single strand. Strand asymmetry can also be inferred by directly comparing estimated rates of nucleotide substitu- tion, although most of the evidence seems to come from counting substitutions in ancestral state reconstructions based on maximum parsimony (eg. Wu and Maeda 1987; Bulmer 1991; Francino and Ochman 2000). 

Strand-symmetric models have been used in a maximum likelihood context, al- though rarely for the purpose of establishing whether strand symmetry is a reason- able assumption. Yap and Pachter (2004) comment that the reversible models that they fitted to real data seemed to exhibit strand symmetry. Squartini and Arndt (2008) fitted a continuous-time, non-stationary, strand-symmetric model on a known, rooted, four-taxon topology to two genome-scale data sets. They comment that their model is not identifiable on the edges incident to the root, but that it is iden- tifiable on the other two edges. This is not strictly correct. As stated in Chang (1996, Remark 2), the labelling of states at the internal nodes is not automati- cally identifiable even for a continuous-time model. Also, as the mapping from the discrete-time process considered in Chang (1996) to the continuous-time process fit- ted in Squartini and Arndt (2008) is not always unique (Higham 2008, Section 2.3), continuous-time models are not identifiable under the results in Chang (1996) with- out further constraints. 

Strand-symmetric substitution models have also been approached from a theo- retical perspective (Casanellas and Sullivant 2005; Jarvis and Sumner 2013) in the context of reversible models. Jarvis and Sumner (2013) make the observation that strand-symmetric models enjoy the property of closure ; that a model which is strand- symmetric on two adjacent phylogenetic branches is strand-symmetric across the two branches as well. It is straightforward to show that this property extends to the non-stationary processes that we consider here. 

The proofs in this work mirror those in Chang (1996), but apart from adding the assumption of strand symmetry and removing the assumption of an unrooted tree, 

