Restricted trees: simplifying networks with bottlenecks.

Area of Science:

• Phylogenetics
• Computational Biology
• Evolutionary Biology

Background:

• Phylogenetic networks model complex evolutionary histories, including hybridizations and lateral gene transfers.
• Simplifying these networks into trees is crucial for understanding fundamental relationships.
• Existing methods for network simplification lack uniformity and clear definitions.

Purpose of the Study:

• To present a uniform and well-defined procedure for deriving a species tree from a phylogenetic network.
• To introduce the concept of a "restricted" connected surjective digraph (CSD) map for network simplification.
• To define and construct the "restricted tree" of a given phylogenetic network.

Main Methods:

• Defining a "restricted" set of vertices in a phylogenetic network as a bottleneck.
• Introducing a "restricted" connected surjective digraph (CSD) map between networks.
• Developing a uniform procedure to generate a restricted tree from any given phylogenetic network.

Main Results:

• A uniform procedure is established to yield a well-defined tree, termed the "restricted tree," from a phylogenetic network.
• A restricted CSD map is demonstrated to exist from the original network to its restricted tree.
• Key evolutionary relationships present in the tree are proven to be conserved within the original network.

Conclusions:

• The "restricted tree" provides a simplified yet accurate representation of fundamental evolutionary relationships from complex phylogenetic networks.
• The introduced methodology offers a standardized approach to phylogenetic network simplification.
• This work facilitates a clearer understanding of evolutionary histories in the presence of reticulate evolution.