Comparing partitioned models to mixture models: do information criteria apply?

The use of information criteria to distinguish between phylogenetic models has become ubiquitous within the field. However, the variety and complexity of available models are much greater now than when these practices were established. The literature shows an increasing trajectory of healthy skepticism with regard to the use of information theory-based model selection within phylogenetics. We add to this by analyzing the specific case of comparison between partition and mixture models. We argue from a theoretical basis that information criteria are inherently more likely to favor partition models over mixture models, and we then demonstrate this through simulation. Based on our findings, we suggest that partition and mixture models are not suitable for information-theory based model comparison.