The Strand Symmetric Model

Important special cases of strand symmetric Markov models are the groupbased phylogenetic models including the Jukes-Cantor model and the Kimura 2 and 3 parameter models. The general strand symmetric model or in this chapter just the strand symmetric model (SSM) has only these eight equalities of probabilities in the transition matrices and no further restriction on the transition probabilities. Thus, for each edge in the corresponding phylogenetic model, there are 6 free parameters. For the standard group-based models (i.e. Jukes-Cantor and Kimura), the transition matrices and the entire parametrization can be simultaneously diagonalized by means of the Fourier transform of the group Z2 × Z2 [2, 6]. Besides the practical uses of the Fourier transform for group based models (see for example [4]), this diagonalization of the group-based models makes it possible to compute phylogenetic invariants for these models, by reducing