Bounds for phylogenetic network space metrics.

Area of Science:

• Computational Biology
• Evolutionary Biology
• Graph Theory

Background:

• Phylogenetic trees model evolutionary history, but reticulate evolution requires more complex structures like phylogenetic networks.
• A recent space of unrooted phylogenetic networks was introduced, defined by specific graph properties and leaf sets.
• This space is equipped with operations (nearest neighbor interchange and triangle) enabling transformations between networks.

Purpose of the Study:

• To derive bounds for a new metric (d) on the space of unrooted phylogenetic networks.
• To analyze a related metric ([Formula: see text]) restricted to networks with a fixed number of vertices.
• To introduce and bound two new metrics (SPR and TBR) generalizing existing tree metrics.

Main Methods:

• Defining a metric space on unrooted phylogenetic networks using graph operations.
• Deriving analytical bounds for the introduced network metrics.
• Generalizing existing phylogenetic tree metrics (NNI, SPR, TBR) to the network context.

Main Results:

• Established bounds for the metric d on the space of unrooted phylogenetic networks.
• Derived bounds for a restricted metric [Formula: see text] on networks with a fixed number of vertices.
• Introduced and provided bounds for the SPR and TBR metrics on phylogenetic networks.

Conclusions:

• The study provides novel metrics and bounds for phylogenetic networks, extending tree metrics.
• These findings offer a quantitative framework for understanding evolutionary relationships in reticulate evolution.
• The results are expected to advance the development and comprehension of network search algorithms in phylogenetics.