The Space of Tree-Based Phylogenetic Networks

Area of Science:

• Computational Biology
• Evolutionary Biology
• Phylogenetics

Background:

• Phylogenetic networks generalize trees, modeling reticulate evolution (e.g., horizontal gene transfer, hybridization) and inference uncertainty.
• Tree-based phylogenetic networks represent evolutionary patterns that broadly follow tree-like structures despite reticulations.
• Operations like nearest-neighbor interchange (NNI) are crucial for navigating the space of phylogenetic networks in data analysis.

Purpose of the Study:

• To determine if the space of unrooted tree-based phylogenetic networks is connected under the NNI operation.
• To provide a method for transforming between tree-based networks without losing the tree-based property.
• To introduce new concepts and derive bounds related to tree-based networks.

Main Methods:

• Demonstrating explicit transformations between unrooted tree-based phylogenetic networks using the NNI operation.
• Introducing and analyzing novel concepts such as "shoat networks" to understand tree-basedness.
• Deriving an upper bound for the size of the space of tree-based networks.

Main Results:

• The space of unrooted tree-based phylogenetic networks is proven to be connected under the NNI operation.
• A method is established to transition between tree-based networks while maintaining their tree-based nature.
• New theoretical insights into tree-basedness and an upper bound for the network space size are presented.

Conclusions:

• The connectivity of tree-based phylogenetic networks under NNI is established, validating their utility in evolutionary studies.
• The findings facilitate algorithmic exploration of phylogenetic network spaces, aiding in the search for optimal networks.
• This work contributes to a deeper theoretical understanding of phylogenetic network structures and their computational properties.