Geometry of the Space of Phylogenetic Trees

By Louis J. Billera, Susan P. Holmes, Karen Vogtmann. Advances in Applied Mathematics, 2001

707 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Nature and Landscape Conservation

View Paper: https://www.semanticscholar.org/paper/3519d16aa6cc859dd77824b8195ff1ccd9ae5f92

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Citations in the corpus

Equations for Chow and Hilbert quotients (2007, background): “This fan is the well-studied space of phylogenetic trees (see, for example, [SS04, Section 4], or [Bun74], [Vog90], [ BHV01 ]).”
Poset Topology: Tools and Applications (2006, background): “The d= 1 case of the tree poset T 2 mod d nd+2 has arisen in various areas such as algebraic geometry, homotopy theory, geometric group theory, mathematical physics and mathematical biology; see eg., [46, 195, 146, 209, 145, 1, 18, 136] and the references contained therein. Vogtmann [195] showed tha”
A smeary central limit theorem for manifolds with application to high-dimensional spheres (2018, background): “Billera et al. (2001); Moulton and Steel (2004), for varying geometries).”
Rayleigh processes, real trees, and root growth with re-grafting (2004, background): “The rst construction of codes for labeled trees without edge-length goes back to 1918: Pr ufer [Pr u18] sets up a bijection between labeled trees of size n and the points of f1; 2;:::;ng n 2 . Phylogenetic trees are identied with points in matching polytopes in [DH98], and [ BHV01 ] equips the spa”
Persistent Homology Analysis of Brain Artery Trees (2014, background): “An approach to overcoming this problem is based on the concept of phylogenetic tree from evolutionary biology; see [19] for a good introduction to this area, and [8] for an insightful mathematical treatment.”
The Bergman complex of a matroid and phylogenetic trees (2003, methodology): “This leads us to consider the space of trees Tn of [3].”
Sensitivity and correlation of hypervariable regions in 16S rRNA genes in phylogenetic analysis (2016, background): “The topological similarity between phylogenetic trees may be estimated by a geodesic algorithm that can project the node structure of a tree into a multi-dimensional model [21].”
Tropical curves, their Jacobians and Theta functions (2006, background): “e same information as the so-called metric graph. Recall that the edges adjacent to one-valent vertices of a graph are called leaves. Other (non-leaf) edges are called inner. A metric graph (cf. e.g. [BHV01]) is a graph equipped with ﬁnite positive length for all its inner edges. The leaves of a met”
The tropical Grassmannian (2003, methodology): “This property is crucial for the existence of unique geodesics in [5].”
Convergence rates for the generalized Fréchet mean via the quadruple inequality (2018, methodology): “ shows algorithms for calculating the Fr´echet mean in Hadamard spaces with cost function d2a for a= 1 2 and a= 1. An important application of Hadamard spaces in Bioinformatics are phylogenetic trees [BHV01]. See also [Bac18, section 6.3] for a quick overview. Another application of Hadamard spaces ”
MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY (2014, background): “The latter is the fan over the Petersen graph with 10 rays vi j , i 6= j ⊂ [5] and 15 cones spanned by v{i, j} and v{k,l} if {i, j} ∩ {k, l} = ∅.”
Sticky central limit theorems on open books (2012, background): “); and • tree spaces, representing metric phylogenetic trees on fixed sets of taxa (see [7, 16, 17], e.”