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

In: Tree Balance Indices

Author

Listed:
  • Mareike Fischer

    (University of Greifswald, Institute of Mathematics and Computer Science)

  • Lina Herbst

    (Department of English and American Studies Friedrich Schiller University Jena
    Max Planck Institute of Geoanthropology (formerly MPI for the Science of Human History) Transmission, Infection, Diversification and Evolution Group)

  • Sophie Johanna Kersting

    (University of Greifswald, Institute of Mathematics and Computer Science)

  • Annemarie Luise Kühn

    (University of Greifswald, Institute of Mathematics and Computer Science
    University Medicine Greifswald, Department of Psychiatry and Psychotherapy)

  • Kristina Wicke

    (New Jersey Institute of Technology, Department of Mathematical Sciences)

Abstract

In this chapter, we consider nine tree shape statistics, namely the total internal path length, the total path length and its normalized version the average vertex depth, the maximum depth, the maximum width, the modified maximum difference in widths, and the maximum width over maximum depth, as well as the tree shape statistics known as stairs1 and stairs2. These have occurred in different contexts, e.g., in the identification of disease transmission patterns [25] and the study of the evolutionary history of viral populations [109], but so far have not been considered as (im)balance indices. Since they have not been thoroughly studied yet, we now briefly explore some of their properties. Most importantly, we show that all nine of them fulfill our definition of a balance or imbalance index, results that – to the best of our knowledge – are new to the literature. An in-depth analysis of these tree shape statistics is beyond the scope of this book, but we anticipate and hope that the short fact sheets we present on these indices will inspire new research.

Suggested Citation

  • Mareike Fischer & Lina Herbst & Sophie Johanna Kersting & Annemarie Luise Kühn & Kristina Wicke, 2023. "Less established tree shape statistics that are (im)balance indices," Springer Books, in: Tree Balance Indices, chapter 0, pages 269-320, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-39800-1_23
    DOI: 10.1007/978-3-031-39800-1_23
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