Optimizing phylogenetic diversity under constraints

Moulton, Vincent; Semple, Charles; Steel, Mike

doi:10.1016/j.jtbi.2006.12.021

Cited by 40 publications

(41 citation statements)

References 17 publications

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“…Given a fixed budget B, the task is to find a subset of regions in R to be preserved which maximizes the PD score of the species contained within at least one preserved region while keeping within budget. This problem is called the Budgeted Nature Reserve Selection (BNRS) and generalizes the analogous unit cost problems described in Moulton et al (2007), Pardi and Goldman (2007), Rodrigues and Gaston (2002), and Rodrigues et al (2005). The applications to conservation planning mentioned above are BNRS with unit costs.…”

Section: The Problem Considered In Bordewich and Semple (2008) Is Thementioning

confidence: 99%

“…Regardless of the setting (whether T is rooted or unrooted), it follows from a result in Moulton et al (2007) that BNRS is NP-hard. Nevertheless, it is shown in Bordewich and Semple (2008) that, for each setting, there is a polynomial-time 1 − 1 e -approximation algorithm for it and that this algorithm is tight.…”

Section: The Problem Considered In Bordewich and Semple (2008) Is Thementioning

confidence: 99%

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

Bordewich

Semple

2011

J. Math. Biol.

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Abstract. 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`1 − 1 e´-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-timè 1 − 1 e´-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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Section: The Problem Considered In Bordewich and Semple (2008) Is Thementioning

confidence: 99%

Section: The Problem Considered In Bordewich and Semple (2008) Is Thementioning

confidence: 99%

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

Bordewich

Semple

2011

J. Math. Biol.

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“…As stated, this problem has been considered by Moulton et al [10] and Spillner et al [17]. The first paper was interested in the problem in the context of greedoids and greedy algorithms, while the second paper noted without proof that the problem was NP-complete.…”

Section: Given a Phylogenetic X-tree T And A Fixed Integer K The Pd mentioning

confidence: 99%

“…Greedy algorithms have been regularly considered as approaches for solving problems that optimize some measure of diversity (for example, [1,2,11,7,10,18]). There are a variety of reasons for this consideration.…”

Section: Improving Greedy Solutions Is Hardmentioning

confidence: 99%

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Optimizing Phylogenetic Diversity with Ecological Constraints

2011

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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.

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Split Diversity: Measuring and Optimizing Biodiversity Using Phylogenetic Split Networks

Chernomor

Klaere

Haeseler

et al. 2016

Biodiversity Conservation and Phylogenetic Systematics

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About 20 years ago the concepts of phylogenetic diversity and phylogenetic split networks were separately introduced in conservation biology and evolutionary biology, respectively. While it has been widely recognized that biodiversity assessment should better take into account the phylogenetic tree of life, it has also been widely acknowledged that phylogenetic networks are more appropriate for phylogenetic analysis in the presence of hybridization, horizontal gene transfer, or contradicting trees among genomic loci. Here, we aim to combine phylogenetic diversity and networks into one concept, split diversity (SD), which properly measures biodiversity for conflicting phylogenetic signals. Moreover, we reformulate well-known conservation questions under the SD framework and present computational methods to solve these, in general, computationally intractable questions. Notably, integer programming, a technique widely used to solve many real-life problems, serves as a general and efficient strategy that delivers optimal solutions to many biodiversity optimization problems. We finally discuss future directions for the new concept.

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Optimizing phylogenetic diversity under constraints

Cited by 40 publications

References 17 publications

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

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

Optimizing Phylogenetic Diversity with Ecological Constraints

Split Diversity: Measuring and Optimizing Biodiversity Using Phylogenetic Split Networks

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