Phylogenetic minimum description length: an optimality criterion based on algorithmic complexity

Phylogenetic minimum description length (PMDL) is proposed as an optimality criterion for phylogenetic analysis. PMDL is based on algorithmic (Kolmogorov) information and the minimum description length principle. This criterion generates natural weighting functions (i.e. not being externally specified) for a diversity of phylogenetic graph, data and model types. PMDL is a generalized criterion that converges on existing forms of inference (i.e. parsimony, likelihood, Bayesian) in specific circumstances. Furthermore, as opposed to existing criteria, PMDL includes graph complexity allowing for the competition of hypotheses with myriad types of phylogenetic graphs (e.g. trees, networks, forests). Owing to its compound nature, PMDL allows for analytical model choice along with phylogenetic graph hypothesis while avoiding over-parameterization. Although uncomputable, heuristic methods are presented for the calculation of upper bounds on the algorithmic information content of a phylogenetic hypothesis. Examples are presented demonstrating the approach.