Pseudo-likelihood for non-reversible nucleotide substitution models with neighbour dependent rates

In the field of molecular evolution genome substitution models with neighbour dependent substitution rates have recently received much attention. It is well-known that substitution of nucleotides does not occur independently of neighbouring nucleotides, but there has been less focus on the phenomenon that this substitution process is also not time-reversible. In this paper I construct a pseudo-likelihood type method for inference in non-reversible substitution models with neighbour dependent substitution rates. I also construct an EM-algorithm for maximising the pseudo-likelihood. For human-mouse aligned sequence data a number of different models are investigated, where I show that strand-symmetric models are appropriate, and that overlapping di-nucleotide models do not fit the data well.