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Phylogenetic network models as graphical models
[Submitted on 30 Jul 2025 (v1), last revised 14 Jul 2026 (this v · 2025-07-31 · via math.ST updates on arXiv.org

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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.

Submission history

From: Seth Sullivant [view email]
[v1] Wed, 30 Jul 2025 19:34:56 UTC (41 KB)
[v2] Tue, 14 Jul 2026 06:35:46 UTC (45 KB)

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