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Gene tree reconciliation including transfers with replacement is NP-hard and FPT

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  • Damir Hasić

    (University of Sarajevo)

  • Eric Tannier

    (Inria Grenoble Rhône-Alpes
    Univ Lyon, Université Lyon 1)

Abstract

Phylogenetic trees illustrate the evolutionary history of genes and species. Although genes evolve along with the species they belong to, a species tree and gene tree are often not identical. The reasons for this are the evolutionary events at the gene level, like duplication or transfer. These differences are handled by phylogenetic reconciliation, which formally is a mapping between a gene tree nodes and a species tree nodes and branches. We investigate models of reconciliation with gene transfers replacing existing genes, which is a biologically important event, but has never been included in the reconciliation models. The problem is close to the dated version of the classical subtree prune and regraft (SPR) distance problem, where a pruned subtree has to be regrafted only on a branch closer to the root. We prove that the reconciliation problem including transfer with replacement is NP-hard, and that, if speciations and transfers with replacement are the only allowed evolutionary events, it is fixed-parameter tractable with respect to the reconciliation’s weight. We prove that the results extend to the dated SPR problem.

Suggested Citation

  • Damir Hasić & Eric Tannier, 2019. "Gene tree reconciliation including transfers with replacement is NP-hard and FPT," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 502-544, August.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:2:d:10.1007_s10878-019-00396-z
    DOI: 10.1007/s10878-019-00396-z
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    References listed on IDEAS

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    1. Bhaskar Dasgupta & Sergio Ferrarini & Uthra Gopalakrishnan & Nisha Raj Paryani, 2006. "Inapproximability results for the lateral gene transfer problem," Journal of Combinatorial Optimization, Springer, vol. 11(4), pages 387-405, June.
    2. Zhi-Zhong Chen & Ying Fan & Lusheng Wang, 2015. "Faster exact computation of rSPR distance," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 605-635, April.
    3. Feng Shi & Qilong Feng & Jie You & Jianxin Wang, 2016. "Improved approximation algorithm for maximum agreement forest of two rooted binary phylogenetic trees," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 111-143, July.
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