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Table of Contents
Intro
Forewords
Foreword by Professor Mike Steel (University of Canterbury)
Foreword by Professor Arne Mooers (Simon Fraser University)
Preface
Acknowledgements
Contents
Part I Introduction
Chapter 1 Opening remarks
Organization of this book.
Using this book as a reference guide.
Using this book as a textbook for a university seminar.
Chapter 2 Preliminaries
2.1 General notation and concepts
2.2 Rooted trees and related concepts
Rooted (binary) trees.
Ancestors, descendants, and cherries.
Depth, height, and width.
Cophenetic value and nodal distance.
Pending subtrees and decomposition of rooted trees.
Rooted quartets.
Symmetry nodes, balance values, and values.
Special trees.
2.3 Ordering and enumerating rooted (binary) trees
Furnas ranking scheme.
Number of rooted (binary) trees.
2.4 Probabilistic models of phylogenetic trees
Phylogenetic trees.
The Aldous' -splitting model of binary phylogenetic trees.
The Yule model
a special case of Aldous' -splitting model.
The uniform model
a special case of Aldous' -splitting model.
Chapter 3 A brief sketch on the relevance and history of tree balance
The relevance and history of tree balance and related concepts in evolutionary biology.
Probabilistic models for phylogenetic trees and their link to tree balance.
Discriminating the evolutionary dynamics of RNA viruses by means of tree balance.
Chapter 4 Concepts of tree balance and imbalance
4.1 Definition of tree balance and imbalance
Less established tree shape statistics that are (im)balance indices.
4.2 General, combinatorial and statistical properties
Part II Tree balance and imbalance indices
Chapter 5 Sackin index
Chapter 6 Average leaf depth
Chapter 7 Variance of leaf depths
Chapter 8 Total cophenetic index
Chapter 9 ?-shape statistic
Chapter 10 B1 index
Chapter 11 B2 index
Chapter 12 Colless index
Chapter 13 Corrected Colless index
Chapter 14 Corrected Colless index / I2 index
Chapter 15 Quadratic Colless index
Chapter 16 Colless-like indices
Chapter 17 I-based indices
Chapter 18 Symmetry nodes index
Chapter 19 Rogers J index
Chapter 20 Rooted quartet index
Chapter 21 Col?n-Plazzotta rank
Chapter 22 Furnas rank
Chapter 23 Less established tree shape statistics that are (im)balance indices
23.1 Total internal path length
23.2 Total path length
23.3 Average (vertex) depth
23.4 Maximum depth
23.5 Maximum width
23.6 Modified maximum difference in widths
23.7 Maximum width over maximum depth
23.8 stairs1
23.9 stairs2
Chapter 24 Related tree shape statistics that are not (im)balance indices
24.1 Diameter, area per pair index, and the Wiener index
24.2 Farness and betweenness centrality
24.3 Degree of root imbalance, I value, and the mean I'10 index
24.4 D index
Forewords
Foreword by Professor Mike Steel (University of Canterbury)
Foreword by Professor Arne Mooers (Simon Fraser University)
Preface
Acknowledgements
Contents
Part I Introduction
Chapter 1 Opening remarks
Organization of this book.
Using this book as a reference guide.
Using this book as a textbook for a university seminar.
Chapter 2 Preliminaries
2.1 General notation and concepts
2.2 Rooted trees and related concepts
Rooted (binary) trees.
Ancestors, descendants, and cherries.
Depth, height, and width.
Cophenetic value and nodal distance.
Pending subtrees and decomposition of rooted trees.
Rooted quartets.
Symmetry nodes, balance values, and values.
Special trees.
2.3 Ordering and enumerating rooted (binary) trees
Furnas ranking scheme.
Number of rooted (binary) trees.
2.4 Probabilistic models of phylogenetic trees
Phylogenetic trees.
The Aldous' -splitting model of binary phylogenetic trees.
The Yule model
a special case of Aldous' -splitting model.
The uniform model
a special case of Aldous' -splitting model.
Chapter 3 A brief sketch on the relevance and history of tree balance
The relevance and history of tree balance and related concepts in evolutionary biology.
Probabilistic models for phylogenetic trees and their link to tree balance.
Discriminating the evolutionary dynamics of RNA viruses by means of tree balance.
Chapter 4 Concepts of tree balance and imbalance
4.1 Definition of tree balance and imbalance
Less established tree shape statistics that are (im)balance indices.
4.2 General, combinatorial and statistical properties
Part II Tree balance and imbalance indices
Chapter 5 Sackin index
Chapter 6 Average leaf depth
Chapter 7 Variance of leaf depths
Chapter 8 Total cophenetic index
Chapter 9 ?-shape statistic
Chapter 10 B1 index
Chapter 11 B2 index
Chapter 12 Colless index
Chapter 13 Corrected Colless index
Chapter 14 Corrected Colless index / I2 index
Chapter 15 Quadratic Colless index
Chapter 16 Colless-like indices
Chapter 17 I-based indices
Chapter 18 Symmetry nodes index
Chapter 19 Rogers J index
Chapter 20 Rooted quartet index
Chapter 21 Col?n-Plazzotta rank
Chapter 22 Furnas rank
Chapter 23 Less established tree shape statistics that are (im)balance indices
23.1 Total internal path length
23.2 Total path length
23.3 Average (vertex) depth
23.4 Maximum depth
23.5 Maximum width
23.6 Modified maximum difference in widths
23.7 Maximum width over maximum depth
23.8 stairs1
23.9 stairs2
Chapter 24 Related tree shape statistics that are not (im)balance indices
24.1 Diameter, area per pair index, and the Wiener index
24.2 Farness and betweenness centrality
24.3 Degree of root imbalance, I value, and the mean I'10 index
24.4 D index