Budgeted Nature Reserve Selection with diversity feature loss and arbitrary split systems

Arising in the context of biodiversity conservation, the Budgeted Nature Reserve Selection (BNRS) problem is to select, subject to budgetary constraints, a set of regions to conserve so that the phylogenetic diversity (PD) of the set of species contained within those regions is maximized. Here PD is...

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Vydáno v:Journal of mathematical biology Ročník 64; číslo 1-2; s. 69 - 85
Hlavní autoři: Bordewich, Magnus, Semple, Charles
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer-Verlag 01.01.2012
Springer Nature B.V
Témata:
Algorithms
Applications of Mathematics
Biodiversity
Budgets
Conservation of Natural Resources - economics
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Models, Statistical
Phylogeny
Biodiversity conservation
Combinatorial algorithms
Submodular functions
92D15
Split systems
Phylogenetic diversity
05C05
ISSN:0303-6812, 1432-1416, 1432-1416
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Shrnutí:Arising in the context of biodiversity conservation, the Budgeted Nature Reserve Selection (BNRS) problem is to select, subject to budgetary constraints, a set of regions to conserve so that the phylogenetic diversity (PD) of the set of species contained within those regions is maximized. Here PD is measured across either a single rooted tree or a single unrooted tree. Nevertheless, in both settings, this problem is NP-hard. However, it was recently shown that, for each setting, there is a polynomial-time -approximation algorithm for it and that this algorithm is tight. In the first part of the paper, we consider two extensions of BNRS. In the rooted setting we additionally allow for the disappearance of features, for varying survival probabilities across species, and for PD to be measured across multiple trees. In the unrooted setting, we extend to arbitrary split systems. We show that, despite these additional allowances, there remains a polynomial-time -approximation algorithm for each extension. In the second part of the paper, we resolve a complexity problem on computing PD across an arbitrary split system left open by Spillner et al.
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ISSN:0303-6812
1432-1416
1432-1416
DOI:10.1007/s00285-011-0405-9