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Optimizing Phylogenetic Diversity with Ecological Constraints
Beáta Faller1, Charles Semple2, and Dominic Welsh2
1Institute of Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary
faller@cs.elte.hu
2Biomathematics Research Centre, Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand
c.semple@math.canterbury.ac.nz
3Merton College, University of Oxford, Merton Street, Oxford OX1 4JD, United Kingdom
dwelsh@maths.ox.ac.uk
Annals of Combinatorics 15 (2) pp.255-266 April, 2011
AMS Subject Classification: 05C05; 92D15
Abstract:
Given an edge-weighted tree T with leaf set X, define the weight of a subset S of X as the sum of the edge-weights of the minimal subtree of T connecting the elements in S. It is known that the problem of selecting subsets of X of a given size to maximize this weight can be solved using a greedy algorithm. This optimization problem arises in conservation biology where the weight is referred to as the phylogenetic diversity of a taxa set S. Here, we consider the extension of this problem whereby we are only interested in selecting subsets of the taxa set that are ecologically “viable”. Such subsets are specified by an acyclic digraph which represents, for example, a food web. This additional constraint makes the problem computationally hard. In this paper, we analyze the complexity of different variations of the
extended problem.
Keywords: phylogenetic tree, phylogenetic diversity, food web

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