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Level-1 phylogenetic networks and their balanced minimum evolution polytopes.

Cassandra Durell¹, Stefan Forcey²

¹Department of Mathematics, The University of Akron, Akron, OH, 44325-4002, USA.

Journal of Mathematical Biology

|February 13, 2020

Summary

This summary is machine-generated.

This study introduces novel polytopes for phylogenetic network reconstruction, extending the Balanced Minimum Evolution criterion. These structures enable linear programming approaches for analyzing complex evolutionary relationships.

Keywords:

Networks Phylogenetics Polytopes Trees

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Area of Science:

Computational Biology
Phylogenetics
Discrete Mathematics

Background:

Balanced Minimum Evolution (BME) is a distance-based method for phylogenetic tree reconstruction.
Current BME algorithms often involve minimizing linear functionals over polytopes.
Phylogenetic networks offer a more complex model than trees, representing reticulate evolution.

Purpose of the Study:

To develop a linear programming approach for phylogenetic network reconstruction.
To introduce and investigate a new family of polytopes related to phylogenetic networks.
To establish connections between these polytopes and existing structures like BME and Traveling Salesman Problem polytopes.

Main Methods:

Definition and analysis of a two-parameter family of polytopes derived from phylogenetic networks.
Investigation of the relationship between polytope vertices and level-1 phylogenetic networks.
Characterization of polytope facets and faces concerning phylogenetic splits and dimensions.

Main Results:

The proposed polytopes generalize BME and Traveling Salesman Problem polytopes.
Vertices of these polytopes correspond to specific level-1 phylogenetic networks.
Facets and faces of the polytopes are shown to represent phylogenetic splits and provide lower bounds.

Conclusions:

The introduced polytopes provide a framework for applying linear programming to phylogenetic network reconstruction.
This work extends distance-based criteria beyond trees to more complex phylogenetic networks.
The geometric structures offer new insights into the combinatorial properties of phylogenetic networks.