# Why Neighbor-Joining Works

@article{Mihaescu2007WhyNW, title={Why Neighbor-Joining Works}, author={Radu Mihaescu and D. Levy and L. Pachter}, journal={Algorithmica}, year={2007}, volume={54}, pages={1-24} }

Abstract
We show that the neighbor-joining algorithm is a robust quartet method for constructing trees from distances. This leads to a new performance guarantee that contains Atteson’s optimal radius bound as a special case and explains many cases where neighbor-joining is successful even when Atteson’s criterion is not satisfied. We also provide a proof for Atteson’s conjecture on the optimal edge radius of the neighbor-joining algorithm. The strong performance guarantees we provide also hold… Expand

#### 96 Citations

Neighbor Joining Algorithms for Inferring Phylogenies via LCA Distances

- Mathematics, Medicine
- J. Comput. Biol.
- 2007

These algorithms are shown to reconstruct a refinement of the Buneman tree, which implies optimal robustness to noise under criteria defined by Atteson, and outperform many popular algorithms such as Saitou and Nei's NJ. Expand

Fast neighbor joining

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2009

An algorithm called Fast Neighbor Joining (FNJ) with optimal reconstruction radius and optimal run time complexity O(n^2) is presented and a greatly simplified proof for the correctness of NJ is presented. Expand

The neighbor-net algorithm

- Computer Science, Mathematics
- Adv. Appl. Math.
- 2011

This work describes the output of neighbor-net in terms of the tessellation of M@?"0^n(R) by associahedra and shows that neighbor-nets is a greedy algorithm for finding circular split systems of minimal balanced length. Expand

Quartet consistency count method for reconstructing phylogenetic trees

- Biology, Mathematics
- 2006

A new algorithm which counts the number of consistent quartets for cherry picking with tie breaking is proposed and it is shown that the success rate of the new algorithm is almost equal to that of neighbor-joining. Expand

Accuracy Guarantees for Phylogeny Reconstruction Algorithms Based on Balanced Minimum Evolution

- Biology, Medicine
- IEEE/ACM Transactions on Computational Biology and Bioinformatics
- 2013

Examination of two distance-based algorithms based on the principle of minimizing the balanced minimum evolution score of the output tree in relation to the given estimated distance matrix shows that GREEDYBME and FASTME both reconstruct the entire correct tree if the input data are quartet consistent. Expand

The Geometry of the Neighbor-Joining Algorithm for Small Trees

- Computer Science, Mathematics
- AB
- 2008

This paper analyzes 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 sixTaxa as well as hyperplane representations of eachpolyhedral subdivision. Expand

A fast neighbor joining method.

- Computer Science, Medicine
- Genetics and molecular research : GMR
- 2015

Experimental results show that FastNJ yields a significant increase in speed compared to RNJ and conventional neighbor joining with a minimal loss of accuracy. Expand

On the optimality of the neighbor-joining algorithm

- Mathematics, Medicine
- Algorithms for Molecular Biology
- 2007

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. Expand

Analysis on Algorithms for Constructing Phylogenetic Trees From Distances

- Computer Science
- IEEE Access
- 2019

A new improved algorithm, called RandomNJ, is introduced, which is an efficient method for constructing phylogenetic trees from distances, and the INJ which is a web-based server for on-line constructing the phylogenetics trees using the improved algorithms and NJ is designed. Expand

Accuracy Guarantees for Phylogeny Reconstruction Algorithms Based on Balanced Minimum Evolution

- Mathematics, Computer Science
- WABI
- 2010

This paper examines two distance based algorithms (GREEDYBME and FASTME) which are based on the principle of trying to minimise the balanced minimum evolution (BME) score of the output tree in relation to the given estimated distance matrix and shows that these algorithms will both reconstruct the correct tree if the input data is quartet consistent. Expand

#### References

SHOWING 1-10 OF 44 REFERENCES

Beyond pairwise distances: neighbor-joining with phylogenetic diversity estimates.

- Biology, Medicine
- Molecular biology and evolution
- 2006

A generalization of the neighbor- joining transformation is presented, which uses estimates of phylogenetic diversity rather than pairwise distances in the tree, which leads to an improved neighbor-joining algorithm whose total running time is still polynomial in the number of taxa. Expand

Fast Neighbor Joining

- Computer Science
- ICALP
- 2005

Initial experiments show that FNJ in practice has almost the same accuracy as NJ, indicating that the property of optimal reconstruction radius has great importance to their good performance. Expand

The Performance of Neighbor-Joining Methods of Phylogenetic Reconstruction

- Computer Science
- Algorithmica
- 1999

An upper bound on the amount of data necessary to reconstruct the topology with high confidence is demonstrated by finding conditions under which these methods will determine the correct tree topology and showing that these perform as well as possible in a certain sense. Expand

On the Uniqueness of the Selection Criterion in Neighbor-Joining

- Mathematics, Computer Science
- J. Classif.
- 2005

It is shown that any selection criterion that is linear, permutation equivariant, statistically consistent and based solely on distance data will give the same trees as those created by NJ. Expand

The neighbor-joining method: a new method for reconstructing phylogenetic trees.

- Biology, Medicine
- Molecular biology and evolution
- 1987

The neighbor-joining method and Sattath and Tversky's method are shown to be generally better than the other methods for reconstructing phylogenetic trees from evolutionary distance data. Expand

Neighbor-joining revealed.

- Biology, Medicine
- Molecular biology and evolution
- 2006

A rigorous answer to this question has recently been provided by further mathematical investigation, and the purpose of this note is to highlight these results and their significance for interpreting NJ. Expand

NJML: a hybrid algorithm for the neighbor-joining and maximum-likelihood methods.

- Biology, Medicine
- Molecular biology and evolution
- 2000

A "divide-and-conquer" heuristic algorithm in which an initial neighbor-joining (NJ) tree is divided into subtrees at internal branches having bootstrap values higher than a threshold, which is suitable for reconstructing relatively large molecular phylogenetic trees. Expand

Performance study of phylogenetic methods: (unweighted) quartet methods and neighbor-joining

- Mathematics, Computer Science
- SODA '01
- 2001

The experimental results and theoretical results suggest that quartet-cleaning methods are unlikely to yield accurate trees with less than exponentially long sequences, and suggest that a proposed reconstruction method should first be compared to the neighbor-joining method and further studied only if it offers a demonstrable practical advantage. Expand

On the edge linfinitf radius of Saitou and Nei's method for phylogenetic reconstruction

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2006

The performance of Saitou and Nei's neighbor-joining method for phylogenetic reconstruction is studied to show that the edge l∞ radius of the method is 1/4, which improves an result by Atteson and Xu. Expand

A lower bound on the edge linfinitely radius of Saitou and Nei's method for phylogenetic reconstruction

- Mathematics, Computer Science
- Inf. Process. Lett.
- 2005

The performance of Saitou and Nei's neighbor-joining method for phylogenetic reconstruction is studied to show that the edge linfin; radius of the method is at least 1/6. Expand