# The Geometry of the Neighbor-Joining Algorithm for Small Trees

@inproceedings{Eickmeyer2008TheGO, title={The Geometry of the Neighbor-Joining Algorithm for Small Trees}, author={Kord Eickmeyer and Ruriko Yoshida}, booktitle={Algebraic Biology}, year={2008} }

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 ${\mathbb R}^{n \choose 2}$, where nis 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…

## 6 Citations

### Combinatorial and Computational Investigations of Neighbor-Joining Bias

- 2020

Computer Science

Frontiers in Genetics

The Neighbor-Joining algorithm is a popular distance-based phylogenetic method that computes a tree metric from a dissimilarity map arising from biological data that partitions the input space into polyhedral regions indexed by the combinatorial type of the trees returned.

### Optimality of the Neighbor Joining Algorithm and Faces of the Balanced Minimum Evolution Polytope

- 2011

Computer Science

Bulletin of mathematical biology

It is proved that any subtree-prune-regraft move from a binary tree to another binary tree corresponds to an edge of the BME polytope, and an entire family of faces parameterized by disjoint clades are described, showing that these clade-faces are smaller dimensional BMEpolytopes themselves.

### Stochastic safety radius on Neighbor-Joining method and Balanced Minimal Evolution on small trees

- 2015

Computer Science, Mathematics

Stochastic safety radii for the neighbor-joining (NJ) method and balanced minimal evolution (BME) method for n = 5 are investigated.

### On the optimality of the neighbor-joining algorithm

- 2007

Mathematics

Algorithms for Molecular Biology

The l2 radius for neighbor-joining for n = 5 is obtained and the ability of the neighbor- joining algorithm to recover the BME tree depends on the diameter of the B ME tree.

### Bayes estimators for phylogenetic reconstruction

- 2011

Computer Science

Systematic biology

In this work, a unified framework of BE trees is discussed, focusing especially on tree distances that are expressible as squared euclidean distances, and it is shown that BEs can be estimated in practice by hill-climbing and tends to be closer to the true tree compared with ML and neighbor joining.

### Mathematical and Simulation-Based Analysis of the Behavior of Admixed Taxa in the Neighbor-Joining Algorithm

- 2018

Computer Science

Bulletin of Mathematical Biology

The neighbor-joining algorithm for phylogenetic inference has been seen to have three specific properties when applied to distance matrices that contain an admixed taxon, but it is observed that these properties are sometimes violated by distanceMatrices that include an admixture.

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