On the optimality of the neighbor-joining algorithm

Eickmeyer, Kord; Huggins, Peter; Pachter, Lior; Yoshida, Ruriko

doi:10.1186/1748-7188-3-5

Cited by 40 publications

(73 citation statements)

References 17 publications

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“…There are several equivalent formulations of the BME length (Eickmeyer et al 2008), although we prefer (1) because of its polyhedral interpretation.…”

Section: Remark 22mentioning

confidence: 99%

“…We now introduce the BME polytope, first investigated by Eickmeyer et al (2008). A polytope in R m is the convex hull of a finite number of points in R m .…”

Section: Remark 22mentioning

confidence: 99%

“…Some of its combinatorial properties have been studied for small number of taxa, although several questions remain open for n ≥ 6. We investigate some of its features below, as described by Eickmeyer et al (2008).…”

Section: Remark 23mentioning

confidence: 99%

“…= (2n − 5) · (2n − 3) · · · 3 · 1. In addition, the vector ω s ij associated with the star tree s (the tree with a single internal node) lies in the interior of the polytope, whereas all other points ω t lie on its boundary (Eickmeyer et al 2008, Lemma 2.1).…”

Section: Remark 23mentioning

confidence: 99%

“…Another motivation for studying BME is the close relationship between BME and the very popular Neighbor-Joining (NJ) algorithm (Saitou and Nei 1987). Specifically, NJ has been shown to be a heuristic BME minimizer (Desper and Gascuel 2005); the relationship between the two algorithms has been investigated by Eickmeyer et al (2008).…”

Section: Introductionmentioning

confidence: 99%

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Polyhedral Geometry of Phylogenetic Rogue Taxa

Cueto

Matsen

2010

Bull Math Biol

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It is well known among phylogeneticists that adding an extra taxon (e.g. species) to a data set can alter the structure of the optimal phylogenetic tree in surprising ways. However, little is known about this "rogue taxon" effect. In this paper we characterize the behavior of balanced minimum evolution (BME) phylogenetics on data sets of this type using tools from polyhedral geometry. First we show that for any distance matrix there exist distances to a "rogue taxon" such that the BME-optimal tree for the data set with the new taxon does not contain any nontrivial splits (bipartitions) of the optimal tree for the original data. Second, we prove a theorem which restricts the topology of BME-optimal trees for data sets of this type, thus showing that a rogue taxon cannot have an arbitrary effect on the optimal tree. Third, we computationally construct polyhedral cones that give complete answers for BME rogue taxon behavior when our original data fits a tree on four, five, and six taxa. We use these cones to derive sufficient conditions for rogue taxon behavior for four taxa, and to understand the frequency of the rogue taxon effect via simulation.

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“…There are several equivalent formulations of the BME length (Eickmeyer et al 2008), although we prefer (1) because of its polyhedral interpretation.…”

Section: Remark 22mentioning

confidence: 99%

“…We now introduce the BME polytope, first investigated by Eickmeyer et al (2008). A polytope in R m is the convex hull of a finite number of points in R m .…”

Section: Remark 22mentioning

confidence: 99%

Section: Remark 23mentioning

confidence: 99%

Section: Remark 23mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Polyhedral Geometry of Phylogenetic Rogue Taxa

Cueto

Matsen

2010

Bull Math Biol

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The Geometry of the Neighbor-Joining Algorithm for Small Trees

Eickmeyer

Yoshida

Algebraic Biology

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Abstract. In 2007, Eickmeyer et al. showed that the tree topologies outputted by the Neighbor-Joining (NJ) algorithm and the balanced minimum evolution (BME) method for phylogenetic reconstruction are each determined by a polyhedral subdivision of the space of dissimilarity maps R ( n 2 ) , where n is the number of taxa. In this paper, we will analyze the behavior of the Neighbor-Joining algorithm on five and six taxa and study the geometry and combinatorics of the polyhedral subdivision of the space of dissimilarity maps for six taxa as well as hyperplane representations of each polyhedral subdivision. We also study simulations for one of the questions stated by Eickmeyer et al., that is, the robustness of the NJ algorithm to small perturbations of tree metrics, with tree models which are known to be hard to be reconstructed via the NJ algorithm.

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An algebraic view of bacterial genome evolution

Francis

2013

J. Math. Biol.

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Rearrangements of bacterial chromosomes can be studied mathematically at several levels, most prominently at a local, or sequence level, as well as at a topological level. The biological changes involved locally are inversions, deletions, and transpositions, while topologically they are knotting and catenation. These two modelling approaches share some surprising algebraic features related to braid groups and Coxeter groups. The structural approach that is at the core of algebra has long found applications in sciences such as physics and analytical chemistry, but only in a small number of ways so far in biology. And yet there are examples where an algebraic viewpoint may capture a deeper structure behind biological phenomena. This article discusses a family of biological problems in bacterial genome evolution for which this may be the case, and raises the prospect that the tools developed by algebraists over the last century might provide insight to this area of evolutionary biology.

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On the optimality of the neighbor-joining algorithm

Cited by 40 publications

References 17 publications

Polyhedral Geometry of Phylogenetic Rogue Taxa

Polyhedral Geometry of Phylogenetic Rogue Taxa

The Geometry of the Neighbor-Joining Algorithm for Small Trees

An algebraic view of bacterial genome evolution

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