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Exploring spaces of semi-directed level-1 networks.

Simone Linz1, Kristina Wicke2

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Summary
This summary is machine-generated.

We introduce the cut edge transfer (CET) move, connecting semi-directed phylogenetic networks. This move ensures all level-1 networks with a fixed number of reticulations are reachable, advancing phylogenetic network reconstruction.

Keywords:
Cut edge transferLevel-1Phylogenetic networksSemi-directed networks

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Area of Science:

  • Phylogenetics
  • Computational Biology
  • Network Theory

Background:

  • Semi-directed phylogenetic networks integrate directed and undirected edges, bridging rooted and unrooted network types.
  • Existing research extensively analyzes rooted and unrooted phylogenetic networks but lacks exploration of semi-directed network spaces.
  • Understanding the structure of semi-directed phylogenetic networks is crucial for developing new reconstruction algorithms.

Purpose of the Study:

  • To introduce and analyze a novel rearrangement move, the cut edge transfer (CET), for semi-directed phylogenetic networks.
  • To establish the connectedness of the space of semi-directed level-1 networks with a fixed number of reticulations under the CET move.
  • To extend this connectedness result to the broader space of all semi-directed level-1 networks on a fixed leaf set.

Main Methods:

  • Proposed the cut edge transfer (CET) rearrangement move for semi-directed phylogenetic networks.
  • Demonstrated the connectedness of the space of semi-directed level-1 networks with k reticulations using CET.
  • Introduced additional moves (R[Formula: see text] and R[Formula: see text]) to establish connectedness for the general space of semi-directed level-1 networks.
  • Translated results to show connectedness for rooted level-1 networks under CET.

Main Results:

  • The cut edge transfer (CET) move connects the space of semi-directed level-1 networks with a fixed number of reticulations and leaf set.
  • Any semi-directed level-1 network with a specific reticulation count and leaf set is reachable from any other via CET sequences.
  • The space of all semi-directed level-1 networks on a fixed leaf set is connected through CET and additional reticulation-altering moves.
  • The space of rooted level-1 networks with a fixed number of reticulations and leaf set is also shown to be connected under CET.

Conclusions:

  • The CET move provides a fundamental tool for navigating and understanding the space of semi-directed phylogenetic networks.
  • These findings are significant for algorithms reconstructing semi-directed phylogenetic networks, particularly within the commonly used level-1 space.
  • The established connectedness facilitates broader exploration and analysis of evolutionary relationships represented by semi-directed networks.