Polynomial-Time Algorithms for Phylogenetic Inference Problems Involving Duplication and Reticulation

Leo Van Iersel*, Remie Janssen, Mark Jones, Yukihiro Murakami, Norbert Zeh

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)
70 Downloads (Pure)


A common problem in phylogenetics is to try to infer a species phylogeny from gene trees. We consider different variants of this problem. The first variant, called Unrestricted Minimal Episodes Inference, aims at inferring a species tree based on a model with speciation and duplication where duplications are clustered in duplication episodes. The goal is to minimize the number of such episodes. The second variant, Parental Hybridization, aims at inferring a species network based on a model with speciation and reticulation. The goal is to minimize the number of reticulation events. It is a variant of the well-studied Hybridization Number problem with a more generous view on which gene trees are consistent with a given species network. We show that these seemingly different problems are in fact closely related and can, surprisingly, both be solved in polynomial time, using a structure we call 'beaded trees'. However, we also show that methods based on these problems have to be used with care because the optimal species phylogenies always have a restricted form. To mitigate this problem, we introduce a new variant of Unrestricted Minimal Episodes Inference that minimizes the duplication episode depth. We prove that this new variant of the problem can also be solved in polynomial time.

Original languageEnglish
Article number8798653
Pages (from-to)14-26
Number of pages13
JournalIEEE/ACM Transactions on Computational Biology and Bioinformatics
Issue number1
Publication statusPublished - 2020

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • duplication
  • gene trees
  • Hybridization Number problem
  • inference
  • Phylogenetics
  • polynomial-time algorithm


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