Tree Balance Indices

Mareike Fischer (), Lina Herbst (), Sophie Kersting (), Annemarie Luise Kühn () and Kristina Wicke ()
Additional contact information
Mareike Fischer: University of Greifswald, Institute of Mathematics and Computer Science
Lina Herbst: Max Planck Institute of Geoanthropology (formerly MPI for the Science of Human History) Transmission, Infection, Diversification and Evolution Group, Department of English and American Studies, Friedrich Schiller University Jena, Jena, Germany
Sophie Kersting: University of Greifswald, Institute of Mathematics and Computer Science
Annemarie Luise Kühn: University Medicine Greifswald, Institute of Mathematics and Computer Science, University of Greifswald, Greifswald, Germany, Department of Psychiatry and Psychotherapy
Kristina Wicke: New Jersey Institute of Technology, Department of Mathematical Sciences

in Springer Books from Springer

Date: 2023
ISBN: 978-3-031-39800-1
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Chapters in this book:

Ch Chapter 1 Opening remarks

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 10 𝑩1 index

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 11 𝑩2 index

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 12 Colless index

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 13 Corrected Colless index

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 14 Equal weights Colless index / 𝑰2 index

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 15 Quadratic Colless index

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 16 Colless-like indices

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 17 𝑰-based indices

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 18 Symmetry nodes index

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 19 Rogers 𝑱 index

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 2 Preliminaries

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 20 Rooted quartet index

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 21 Colijn-Plazzotta rank

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 22 Furnas rank

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 23 Less established tree shape statistics that are (im)balance indices

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 24 Related tree shape statistics that are not (im)balance indices

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 25 Extension of tree balance and imbalance indices and alternative ways of measuring tree balance

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 26 Software

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 27 Applications

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 28 Discussion and outlook

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 3 A brief sketch on the relevance and history of tree balance

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 4 Concepts of tree balance and imbalance

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 5 Sackin index

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 6 Average leaf depth

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 7 Variance of leaf depths

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 8 Total cophenetic index

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

Ch Chapter 9 $$ \widehat{s} $$ -shape statistic

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke

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DOI: 10.1007/978-3-031-39800-1

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