Combinatorial and Computational Investigations of Neighbor-Joining Bias

Frontiers in Genetics
Ruth Davidson, Abraham Martín Del Campo

Abstract

The Neighbor-Joining algorithm is a popular distance-based phylogenetic method that computes a tree metric from a dissimilarity map arising from biological data. Realizing dissimilarity maps as points in Euclidean space, the algorithm partitions the input space into polyhedral regions indexed by the combinatorial type of the trees returned. A full combinatorial description of these regions has not been found yet; different sequences of Neighbor-Joining agglomeration events can produce the same combinatorial tree, therefore associating multiple geometric regions to the same algorithmic output. We resolve this confusion by defining agglomeration orders on trees, leading to a bijection between distinct regions of the output space and weighted Motzkin paths. As a result, we give a formula for the number of polyhedral regions depending only on the number of taxa. We conclude with a computational comparison between these polyhedral regions, to unveil biases introduced in any implementation of the algorithm.

References

Aug 1, 2006·Molecular Biology and Evolution·Olivier Gascuel, Mike Steel
May 2, 2008·Algorithms for Molecular Biology : AMB·Kord EickmeyerRuriko Yoshida
Mar 31, 2011·Systematic Biology·Liang Liu, Lili Yu
Feb 12, 2013·Mathematical Biosciences·Filippo Disanto, Thomas Wiehe
Feb 28, 2014·BMC Genomics·Tae-Ho LeeAndrew H Paterson
Mar 1, 2014·IEEE/ACM Transactions on Computational Biology and Bioinformatics·Ruth Davidson, Seth Sullivant
May 18, 2018·BMC Bioinformatics·Guilherme P TellesNalvo F Almeida
Nov 17, 2020·Frontiers in Genetics·Ruth Davidson, Abraham Martín Del Campo

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Citations

Nov 17, 2020·Frontiers in Genetics·Ruth Davidson, Abraham Martín Del Campo
Aug 21, 2021·Frontiers in Veterinary Science·Ahmad Nadzri Nur-FarahiyahSiti Nazrina Camalxaman

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