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Reconstructing gene trees from Fitch’s xenology relation

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Abstract

Two genes are xenologs in the sense of Fitch if they are separated by at least one horizontal gene transfer event. Horizonal gene transfer is asymmetric in the sense that the transferred copy is distinguished from the one that remains within the ancestral lineage. Hence xenology is more precisely thought of as a non-symmetric relation: y is xenologous to x if y has been horizontally transferred at least once since it diverged from the least common ancestor of x and y. We show that xenology relations are characterized by a small set of forbidden induced subgraphs on three vertices. Furthermore, each xenology relation can be derived from a unique least-resolved edge-labeled phylogenetic tree. We provide a linear-time algorithm for the recognition of xenology relations and for the construction of its least-resolved edge-labeled phylogenetic tree. The fact that being a xenology relation is a heritable graph property, finally has far-reaching consequences on approximation problems associated with xenology relations.

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Acknowledgements

We thank Maribel Hernández Rosales and her team for stimulating discussions. This work was funded in part by the BMBF-funded project “Center for RNA-Bioinformatics” (031A538A, de.NBI-RBC) and a travel grant from DAAD PROALMEX (Proj. No. 278966).

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Authors and Affiliations

  1. Bioinformatics Group, Department of Computer Science, Leipzig University, Härtelstraße 16-18, 04107, Leipzig, Germany

    Manuela Geiß, John Anders & Peter F. Stadler

  2. Interdisciplinary Center of Bioinformatics, Leipzig University, Härtelstraße 16-18, 04107, Leipzig, Germany

    Manuela Geiß, John Anders & Peter F. Stadler

  3. German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Competence Center for Scalable Data Services and Solutions, Leipzig University, Leipzig, Germany

    Peter F. Stadler

  4. Leipzig Research Center for Civilization Diseases, Leipzig University, Leipzig, Germany

    Peter F. Stadler

  5. Department of Diagnostics, Fraunhofer Institute for Cell Therapy and Immunology – IZI, Perlickstraße 1, 04103, Leipzig, Germany

    Peter F. Stadler

  6. Max-Planck-Institute for Mathematics in the Sciences, Inselstraße 22, 04103, Leipzig, Germany

    Peter F. Stadler

  7. Inst. f. Theoretical Chemistry, University of Vienna, Währingerstraße 17, 1090, Wien, Austria

    Peter F. Stadler

  8. Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM, 87501, USA

    Peter F. Stadler

  9. Swarm Intelligence and Complex Systems Group, Department of Computer Science, Leipzig University, Augustusplatz 10, 04109, Leipzig, Germany

    Nicolas Wieseke

  10. Institute of Mathematics and Computer Science, University of Greifswald, Walther-Rathenau-Straße 47, 17487, Greifswald, Germany

    Marc Hellmuth

  11. Center for Bioinformatics, Saarland University, Building E 2.1, P.O. Box 151150, 66041, Saarbrücken, Germany

    Marc Hellmuth

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  1. Manuela Geiß
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  2. John Anders
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  3. Peter F. Stadler
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  4. Nicolas Wieseke
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  5. Marc Hellmuth
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Correspondence to Marc Hellmuth.

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Geiß, M., Anders, J., Stadler, P.F. et al. Reconstructing gene trees from Fitch’s xenology relation. J. Math. Biol. 77, 1459–1491 (2018). https://doi.org/10.1007/s00285-018-1260-8

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  • DOI: https://doi.org/10.1007/s00285-018-1260-8

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