Phylogenetic network models as graphical models
arXiv:2507.23056
The paper shows that displayed tree phylogenetic network models can be viewed as submodels of graphical models defined by directed acyclic graphs, and uses this perspective to study local modifications, identifiability issues, and rank conditions on tensor flattenings.
Abstract
The displayed tree phylogenetic network model is shown to sit as a natural submodel of the graphical model associated to a directed acyclic graph (DAG). This representation allows to derive a number of results about the displayed tree model. In particular, the concept of a local modification to a DAG model is developed and applied to the displayed tree model. As an application, some nonidentifiability issues related to the displayed tree models are highlighted as they relate to reticulation edges and stacked reticulations in the networks. We also derive rank conditions on flattenings of probability tensors for the displayed tree model, generalizing classic results for phylogenetic tree models.
24 pages, 7 figures