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A Practical Guide to Phylogenetics for Nonexperts
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Best Match Graphs With Binary Trees.

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    This summary is machine-generated.

    We present an algorithm to determine if a best match graph (BMG) is binary-explainable, meaning it can be represented by a fully resolved gene tree. This work also addresses the computational complexity of transforming graphs into binary-explainable BMGs.

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    Area of Science:

    • Computational Biology
    • Bioinformatics
    • Graph Theory

    Background:

    • Best match graphs (BMGs) are crucial in graph-based orthology detection, holding significant gene tree information.
    • Understanding the structure and properties of BMGs is essential for accurate phylogenetic inference.

    Purpose of the Study:

    • To develop an algorithm for determining if a BMG is binary-explainable.
    • To construct the corresponding binary gene tree if the BMG is binary-explainable.
    • To analyze the relationship between different types of trees derived from BMGs and the complexity of graph editing.

    Main Methods:

    • A near-cubic time algorithm is introduced to test for binary-explainability of BMGs.
    • The algorithm constructs a fully resolved gene tree from a binary-explainable BMG.
    • The study analyzes the unique binary-refinable tree (BRT) and the least resolved tree of a BMG.
    • NP-completeness is shown for editing arbitrary graphs to binary-explainable BMGs, with an integer linear program formulation provided.

    Main Results:

    • A near-cubic algorithm successfully determines BMG binary-explainability and constructs the associated gene tree.
    • All binary trees explaining a BMG are refinements of the unique BRT.
    • The BRT generally refines the unique least resolved tree of a BMG.
    • Editing arbitrary graphs to binary-explainable BMGs is NP-complete.

    Conclusions:

    • The developed algorithm provides an efficient method for analyzing BMGs in the context of gene tree reconstruction.
    • The findings clarify the hierarchical relationships between different tree representations of BMGs.
    • The NP-completeness result highlights the computational challenges in graph-based orthology detection and phylogenetic analysis.