fine the sufficient conditions of Theorem 3.1. We know that a stationary process is not identifiable for a rooted topology, but that our non-stationary strand-symmetric process is. Our class of models is slightly narrower than the class of non-stationary, strand-symmetric processes, however, so it may be possible to broaden our sufficient assumptions. I am grateful to Teresa Neeman, Gavin Huttley, Von Bing Yap, Michael Roper, and John Trueman for their helpful comments. I am particularly indebted to Teresa for suggesting Corollary 3.1, which greatly simplified the proof of Theorem 3.1. This work was supported by the National Health and Medical Research Council [grant number APP1085372]. Barry, D. and J. Hartigan (1987a). Statistical analysis of hominoid molecular evo- lution. Statistical Science 2(2), 191–207. Barry, D. and J. A. Hartigan (1987b). Asynchronous distance between homologous DNA sequences. Biometrics 43(2), 261–76. Bonhomme, S., K. Jochmans, and J.-M. Robin (2014). Nonparametric spectral- based estimation of latent structures. Technical report, cemmap working paper, Centre for Microdata Methods and Practice. Bulmer, M. (1991). Strand symmetry of mutation rates in the β -globin region. Journal of Molecular Evolution 33(4), 305–310. Buneman, P. (1971). The recovery of trees from measures of dissimilarity. In D. G. 25 References Acknowledgements