Tree Balance Indices : A Comprehensive Survey / by Mareike Fischer, Lina Herbst, Sophie Kersting, Annemarie Luise Kühn, Kristina Wicke.

Format:

Book

Author/Creator:

Fischer, Mareike.

Contributor:

Herbst, Lina.

Kersting, Sophie.

Kühn, Annemarie Luise.

Wicke, Kristina.

Mooers, Arne.

Steel, Mike.

Language:

English

Subjects (All):

Graph theory.

Phylogeny.

Evolution (Biology).

Graph Theory.

Phylogenetics.

Evolutionary Biology.

Local Subjects:

Graph Theory.

Phylogenetics.

Evolutionary Biology.

Physical Description:

1 online resource (398 pages)

Edition:

1st ed. 2023.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2023.

Summary:

Whether you are looking for an introduction to the field of tree balance, a reference work on the multitude of available balance indices or inspiration for your future research, this book offers all three. It delves into the significance of tree balance in phylogenetics and other research domains, where numerous indices have been introduced over the years. While the variations in definitions and underlying principles among these indices have long remained a challenge, this survey addresses the problem by presenting formal definitions of balance and imbalance indices and establishing desirable properties. The book is comprehensive both in the inclusion of a variety of indices and in the information provided on them: the authors meticulously analyze and categorize established indices, shedding light on their general, statistical and combinatorial properties. They reveal that, while some known balance indices fail to meet the most basic criteria, certain tree shape statistics from other contexts prove to be effective balance measures. The collected properties are neatly presented, numerous new results are established, open research questions are highlighted, and possible applications are discussed. Reviewing over twenty (im)balance indices, a wealth of mathematical insights is provided, accompanied by real-world examples showcasing the importance of tree balance in diverse research areas. Catering to researchers, students, mathematicians, and biologists, the book can be used as a textbook for university seminars, a reference on tree balance, and as a source of inspiration for future research. It is accompanied by the free R package 'treebalance', a powerful tool to further explore and apply the discussed concepts, and a website allowing quick access to the main information and the latest developments in the field.

Contents:

Part I: Introduction

1 Opening Remarks

2 Preliminaries

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

4 Concepts of tree balance and imbalance

Part II: Tree balance and imbalance indices

5 Sackin index

6 Average leaf depth

7 Variance of leaf depths

8 Total cophenetic index

9 s-shape statistic

10 B1 index

11 B2 index

12 Colless index

13 Corrected Colless index

14 Equal weights Colless index / I2 index

15 Quadratic Colless index

16 Colless-like indices

17 I-based indices

18 Symmetry nodes index

19 Rogers J index

20 Rooted quartet index

21 Colijn-Plazzotta rank

22 Furnas rank

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

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

25 Extended and alternative measures of tree balance

Part III: Applications and outlook

26 Software

27 Applications

28 Discussion and outlook

Appendix A: Lookup Tables.

Other Format:

Print version: Fischer, Mareike Tree Balance Indices

ISBN:

9783031398001

3031398009

OCLC:

1407315678