Inference of higher order substitution dynamics by Markov chain lumping

We apply Markov chain lumping techniques to aggregate codons from an empirical substitution matrix. The standard genetic code as well as higher order amino acid substitution groups are identified. Since the aggregates are derived from first principles they do not rely on system dependent assumptions made beforehand, e.g. regarding criteria on what should constitute an amino acid group. We therefore argue that the acquired aggregations more accurately capture the multi-level structure of the substitution dynamics than alternative techniques.