Fence Decompositions and Cherry Covers in Non-Binary Phylogenetic Networks

Area of Science:

• Evolutionary biology
• Computational phylogenetics
• Network theory

Background:

• Phylogenetic networks model reticulate evolution, with tree-based networks representing histories with an underlying tree structure.
• Existing characterizations of tree-based networks include tree embeddings, matchings, and arc partitions.
• Two key arc partition characterizations are maximal fence decompositions and cherry covers.

Purpose of the Study:

• To establish a connection between maximal fence decompositions and cherry covers for phylogenetic networks.
• To generalize fence decompositions to non-binary networks.
• To characterize semi-binary tree-based networks and semi-binary tree-child networks using these methods.

Main Methods:

• We establish the equivalence between the number of cherry covers and support trees for semi-binary networks.
• Fence decompositions are generalized to non-binary networks.
• Forbidden structures are used to characterize semi-binary tree-based networks.
• Explicit enumeration of cherry covers is achieved by studying fence decompositions.

Main Results:

• The number of cherry covers equals the number of support trees in semi-binary networks.
• A generalized definition of fence decompositions allows characterization of semi-binary tree-based networks.
• Semi-binary tree-child networks can be characterized by their cherry cover counts.

Conclusions:

• Maximal fence decompositions and cherry covers provide equivalent insights into semi-binary network structures.
• Generalized fence decompositions offer a new tool for analyzing non-binary phylogenetic networks.
• This work unifies and extends existing characterizations of tree-based phylogenetic networks.