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Inferring phylogenetic trees from the knowledge of rare evolutionary events

Abstract

Rare events have played an increasing role in molecular phylogenetics as potentially homoplasy-poor characters. In this contribution we analyze the phylogenetic information content from a combinatorial point of view by considering the binary relation on the set of taxa defined by the existence of a single event separating two taxa. We show that the graph-representation of this relation must be a tree. Moreover, we characterize completely the relationship between the tree of such relations and the underlying phylogenetic tree. With directed operations such as tandem-duplication-random-loss events in mind we demonstrate how non-symmetric information constrains the position of the root in the partially reconstructed phylogeny.

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Acknowledgements

We thank the anonymous reviewers for the example in Fig. 2 and numerous valuable comments that helped us to streamline the presentation and to shorten the proofs. This work was funded by the German Research Foundation (DFG) (Proj. No. MI439/14-1 to PFS). YJL acknowledges support of National Natural Science Foundation of China (No. 11671258) and Postdoctoral Science Foundation of China (No. 2016M601576)

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Correspondence to Yangjing Long.

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Hellmuth, M., Hernandez-Rosales, M., Long, Y. et al. Inferring phylogenetic trees from the knowledge of rare evolutionary events. J. Math. Biol. 76, 1623–1653 (2018). https://doi.org/10.1007/s00285-017-1194-6

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Keywords

  • Phylogenetic combinatorics
  • Rare events
  • Binary relations

Mathematics Subject Classification

  • 05C90
  • 05C05
  • 68R05
  • 68R10
  • 92D15