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Computing phylogenetic diversity for split systems

Thursday 6th September 2007 - 11:50 to 12:10
INI Seminar Room 1

In conservation biology, it is important to measure, predict, and preserve biodiversity as many species are facing extinction. In 1992, Faith proposed measuring the diversity of a collection of species in terms of their relationship on a phylogenetic tree, and using this information to identify collections of species with high diversity. Here we are interested in some variants of the resulting optimisation problem that arise when considering species whose evolution is better represented by a network rather than a tree. More specifically, we consider the problem of computing phylogenetic diversity relative to split systems. We show that for general split systems, this problem is NP-hard. In addition we provide some efficient algorithms for some special classes of split systems, in particular presenting an optimal O(n) time algorithm for phylogenetic trees and an O(n log n + nk) time algorithm for circular split systems.

Keywords: Phylogenetic tree, Phylogenetic network, Phylogenetic diversity, Biodiversity conservation, Split systems

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons