title: Phylogenetic trees and Euclidean embeddings.
abstract: It was recently observed by de Vienne et al. (Syst Biol 60(6):826-832, 2011) that a simple square root transformation of distances between taxa on a phylogenetic tree allowed for an embedding of the taxa into Euclidean space. While the justification for this was based on a diffusion model of continuous character evolution along the tree, here we give a direct and elementary explanation for it that provides substantial additional insight. We use this embedding to reinterpret the differences between the NJ and BIONJ tree building algorithms, providing one illustration of how this embedding reflects tree structures in data.
authors.affiliation: Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK, 99775, USA.
authors.forename: Mark
authors.initials: M
authors.lastname: Layer
authors.affiliation: Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK, 99775, USA. j.rhodes@alaska.edu.
authors.forename: John A
authors.initials: JA
authors.lastname: Rhodes
mesh_terms: D000465:Algorithms; D002965:Classification / Q000379:methods*; D008957:Models, Genetic; D010802:Phylogeny
keywords: Distance methods; Multidimensional scaling; Neighbor joining; Phylogenetic trees