Counting Spinal Phylogenetic Networks

Area of Science:

• Evolutionary biology
• Computational phylogenetics
• Combinatorics

Background:

• Phylogenetic networks model complex evolutionary histories with reticulate events (hybridization, gene transfer).
• Fundamental questions about the number of such networks remain difficult to answer.
• Existing network classes include orchard, normal, tree-child, and tree-sibling networks.

Purpose of the Study:

• To introduce a novel combinatorial method for encoding and counting phylogenetic networks.
• To explore the utility of "expanding covers" for addressing fundamental counting problems in phylogenetics.
• To develop a method for counting spinal networks within familiar phylogenetic network classes.

Main Methods:

• Encoding a large class of phylogenetic networks, termed "labellable networks", using "expanding covers".
• Utilizing the combinatorial structure of expanding covers for potential counting applications.
• Developing a specific counting method for networks that are both spinal and belong to established network classes.

Main Results:

• Expanding covers provide a method to encode labellable networks, a class encompassing several familiar network types.
• The combinatorial nature of expanding covers offers a potential pathway to count networks with specific properties.
• A method is presented for counting spinal networks within more common phylogenetic network categories.

Conclusions:

• Expanding covers represent a promising combinatorial tool for tackling previously intractable counting problems in phylogenetics.
• This approach may facilitate the development of closed formulas for counting phylogenetic networks.
• Counting spinal networks within familiar classes serves as a foundational step towards analyzing more general network structures.