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    Reconstructing gene family evolution requires inferring super gene trees. This study defines the supergenetree problem, aiming to reconcile gene trees with species trees, and proves its computational hardness.

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    Area of Science:

    • Computational Biology
    • Phylogenetics
    • Evolutionary Genomics

    Background:

    • Supertrees are crucial for inferring large phylogenetic trees from partial datasets.
    • Classical supertree methods focus on species tree reconstruction.
    • Reconstructing gene trees requires reconciliation with a known species tree.

    Purpose of the Study:

    • Define and analyze the supergenetree problem: finding a supertree of gene trees that minimizes reconciliation distance with a species tree.
    • Extend classical supertree methods to the supergenetree problem.
    • Investigate the computational complexity of the supergenetree problem and its variants.

    Main Methods:

    • Extension of exact supertree algorithms to the supergenetree problem.
    • Development of a greedy heuristic for minimizing duplication cost.
    • Complexity analysis using NP-hardness proofs for approximation and specific cases.

    Main Results:

    • Exact methods for supertrees are extended to the supergenetree problem, though they are computationally expensive.
    • A greedy heuristic is proposed for minimizing duplications.
    • The supergenetree problem and its variants are shown to be NP-hard to approximate.

    Conclusions:

    • The supergenetree problem presents significant computational challenges, even for approximation.
    • New theoretical foundations are established for supertree algorithms in gene tree reconstruction.
    • The findings open avenues for further algorithmic exploration in evolutionary biology.