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A Concoction Pipeline for Generating Molecular Operational Taxonomic Units (MOTUs) Among Riparian and Aquatic Beetles
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Tanglegrams: A Reduction Tool for Mathematical Phylogenetics.

Frederick A Matsen, Sara C Billey, Arnold Kas

    IEEE/ACM Transactions on Computational Biology and Bioinformatics
    |January 24, 2017
    PubMed
    Summary
    This summary is machine-generated.

    This study explores tanglegrams, a mathematical tool for analyzing leaf-labeled trees in phylogenetics and coevolution. Understanding tanglegrams simplifies complex tree problems and reveals underlying symmetries.

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    Area of Science:

    • Discrete Mathematics
    • Phylogenetics
    • Combinatorics
    • Coevolutionary Biology

    Background:

    • Phylogenetic and coevolutionary analyses often involve comparing leaf-labeled trees.
    • Tanglegrams provide a formal framework for these comparisons, though their combinatorial properties are underexplored.
    • Existing research has focused on planar drawings rather than the combinatorial structure of tanglegrams.

    Purpose of the Study:

    • To analyze tanglegrams as combinatorial objects.
    • To demonstrate how discrete mathematical problems on trees can be simplified by factoring through tanglegrams.
    • To investigate the structure and symmetries of tanglegrams and their variants.

    Main Methods:

    • Formalizing relative tree labelings as tanglegrams.
    • Considering unordered and unrooted versions of tanglegrams.
    • Utilizing group theory, specifically double cosets of the symmetric group, to understand tanglegram isomorphisms.
    • Investigating the automorphisms of tanglegrams.

    Main Results:

    • Many discrete mathematics problems concerning pairs of trees can be simplified by analyzing tanglegrams.
    • The isomorphism types of tanglegrams (including unordered and unrooted variants) can be characterized using double cosets of the symmetric group.
    • The study provides insights into the automorphisms of tanglegrams.

    Conclusions:

    • A deeper understanding of tanglegrams is crucial for isolating distinct problems on pairs of leaf-labeled trees.
    • Tanglegrams reveal natural symmetries in the spaces associated with these problems.
    • This work advances the combinatorial study of tanglegrams, with implications for phylogenetics and coevolutionary analysis.