Bulletin of Mathematical Biology

, Volume 80, Issue 3, pp 493–518 | Cite as

New Gromov-Inspired Metrics on Phylogenetic Tree Space

  • Volkmar LiebscherEmail author
Original Article


We present a new class of metrics for unrooted phylogenetic X-trees inspired by the Gromov–Hausdorff distance for (compact) metric spaces. These metrics can be efficiently computed by linear or quadratic programming. They are robust under NNI operations, too. The local behaviour of the metrics shows that they are different from any previously introduced metrics. The performance of the metrics is briefly analysed on random weighted and unweighted trees as well as random caterpillars.


Tree space Phylogenetic distance Caterpillars Gromov–Hausdorff metric Mathematical programming 



First of all, I have to thank Mareike Fischer for introducing me to the world of phylogenetic distances. She helped also a lot for getting a clear notation. Second, I’m very grateful to Jürgen Eichhorn who unconsciously draw my attention to metrics between metric spaces. Third, I’d like to thank Michelle Kendall for her inspiring talk at the Portobello conference 2015 and additional discussion later. Fourth, I thank Mike Steel for many interesting discussions, useful hints, his kind hospitality during my stay in Christchurch 2010, and for the organisation of the amazing 2015 workshop in Kaikoura with an inspiring and open atmosphere. Further, Miroslav Bačak, Andrew Francis, Alexander Gavryushkin, Stefan Grünewald, Marc Hellmuth and Giulio dalla Riva gave useful hints and inspiration in many discussions. The questions and hints of five anonymous referees regarding previous versions of this manuscript helped to improve it substantially.


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Copyright information

© Society for Mathematical Biology 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of GreifswaldGreifswaldGermany

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