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Computing phylogenetic diversity for split systems

<28>In conservation biology, a central problem is to measure, predict, and preserve biodiversity as species face extinction. A common measure of biodiversity, called phylogenetic diversity, is based on evolutionary trees. We present novel variants of this measure that arise when studying species whose evolution is better represented by a network rather than a tree. This results in novel optimization problems involving split systems, structures that generalise phylogenetic trees. Hardness results are derived, as well as novel efficient algorithms for special cases. These approaches have been adapted and implemented in software to prioritize populations for conservation (e.g. New Zealand Tuatara populations).