Probability and Real Trees

École d'Été de Probabilités de Saint-Flour XXXV - 2005

verfasst von: Steven Neil Evans

Verlag: Springer Berlin Heidelberg

Buchreihe : Lecture Notes in Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Einloggen, um Zugang zu erhalten

Über dieses Buch

Random trees and tree-valued stochastic processes are of particular importance in combinatorics, computer science, phylogenetics, and mathematical population genetics. Using the framework of abstract "tree-like" metric spaces (so-called real trees) and ideas from metric geometry such as the Gromov-Hausdorff distance, Evans and his collaborators have recently pioneered an approach to studying the asymptotic behaviour of such objects when the number of vertices goes to infinity. These notes survey the relevant mathematical background and present some selected applications of the theory.

Inhaltsverzeichnis

Frontmatter

1. Introduction

The Oxford English Dictionary provides the following two related definitions of the word phylogeny: 1. The pattern of historical relationships between species or other groups resulting from divergence during evolution. 2. A diagram or theoretical model of the sequence of evolutionary divergence of species or other groups of organisms from their common ancestors.

2. Around the Continuum Random Tree

3. R-Trees and 0-Hyperbolic Spaces

4. Hausdorff and Gromov–Hausdorff Distance

5. Root Growth with Re-Grafting

6. The Wild Chain and other Bipartite Chains

7. Diffusions on a R-Tree without Leaves: Snakes and Spiders

8. R–Trees from Coalescing Particle Systems

9. Subtree Prune and Re-Graft

As we mentioned in Chapter 1, Markov chains that move through a space of finite trees are an important ingredient in several algorithms in phylogenetic analysis, and one standard set of moves that is implemented in several phylogenetic software packages is the set of subtree prune and re-graft (SPR) moves.

Backmatter

Titel: Probability and Real Trees
verfasst von: Steven Neil Evans
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-540-74798-7
Print ISBN: 978-3-540-74797-0
DOI: https://doi.org/10.1007/978-3-540-74798-7