Description languages as modelling decisions: A comment on Wheeler and Varón (2025)

Wheeler and Varón (2025) proposed phylogenetic minimum description length (PMDL) as a phylogenetic optimality criterion grounded in algorithmic (Kolmogorov) complexity. PMDL applies the minimum description length (MDL) principle to phylogenetic inference, but its claim that its graph complexity penalties arise 'naturally' and are 'not externally specified' merits careful interpretation. In MDL, description lengths are defined relative to a fixed description language, which can be interpreted as encoding domain-specific background assumptions that function analogously to implicit priors over hypotheses. In PMDL, this can be illustrated by the large graph complexity penalties assigned to phylogenetic networks, particularly the sharp increase when moving from a tree to a minimal network. These penalties reflect modelling assumptions rather than consequences determined by algorithmic complexity alone. Accordingly, PMDL's graph penalties are natural only in the conditional sense that they are not externally specified once a description language for phylogenetic graphs is fixed. The choice of that language, however, remains a substantive external modelling decision. While graph complexity provides the clearest illustration, the principle that description languages encode substantive modelling decisions also applies to PMDL's model complexity. Making this explicit clarifies the interpretation of PMDL within the MDL framework and renders its background assumptions open to evaluation.