Browse by author
Lookup NU author(s): Dr Tom Nye
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
© 2024 The Authors. Journal of the London Mathematical Society is copyright © London Mathematical Society.Evolutionary relationships between species are represented by phylogenetic trees, but these relationships are subject to uncertainty due to the random nature of evolution. A geometry for the space of phylogenetic trees is necessary in order to properly quantify this uncertainty during the statistical analysis of collections of possible evolutionary trees inferred from biological data. Recently, the wald space has been introduced: a length space for trees which is a certain subset of the manifold of symmetric positive definite matrices. In this work, the wald space is introduced formally and its topology and structure is studied in detail. In particular, we show that wald space has the topology of a disjoint union of open cubes, it is contractible, and by careful characterisation of cube boundaries, we demonstrate that wald space is a Whitney stratified space of type (A). Imposing the metric induced by the affine invariant metric on symmetric positive definite matrices, we prove that wald space is a geodesic Riemann stratified space. A new numerical method is proposed and investigated for construction of geodesics, computation of Fréchet means and calculation of curvature in wald space. This work is intended to serve as a mathematical foundation for further geometric and statistical research on this space.
Author(s): Lueg J, Garba MK, Nye TMW, Huckemann SF
Publication type: Article
Publication status: Published
Journal: Journal of the London Mathematical Society
Year: 2024
Volume: 109
Issue: 5
Online publication date: 16/04/2024
Acceptance date: 01/03/2024
Date deposited: 30/04/2024
ISSN (print): 0024-6107
ISSN (electronic): 1469-7750
Publisher: John Wiley and Sons Ltd
URL: https://doi.org/10.1112/jlms.12893
DOI: 10.1112/jlms.12893
Altmetrics provided by Altmetric
