Rao's Entropy and Diversity Measures

Volume 56
Erscheinungsjahr 2027
ISBN: 978-0-443-52010-5
Verlag: Elsevier Science

Buch, Englisch, 420 Seiten, Format (B × H): 152 mm x 229 mm

Rao’s entropy, also known as Rao’s quadratic entropy or Rao’s diversity index, is attributed to C.R. Rao. Along with his formula to help understand diversity, he also introduced the acronym ANODIV (Analysis of Diversity). In addition to Rao’s other well-known contributions, such as Rao distances, the Cramer-Rao inequality, and the Rao-Blackwell Theorem, his diversity measures have gained popularity among statisticians, particularly those focused on ecology and biodiversity.

This volume of the "Handbook of Statistics" series is dedicated to presenting the latest methodologies and applications not only related to Rao’s entropy, but also in general diversity measures. The book aims to provide a comprehensive overview of the theories, models, and methods that are foundational in this field. Our goal is to serve a wide audience interested in statistics, statistical applications in ecology, biomathematics, and related areas.

The chapters in this volume have been meticulously curated to offer detailed and educational content, moving away from conventional journal-style articles. Contributors include leading experts in the field, ensuring high-quality content that combines theoretical rigor with practical insights. Through this comprehensive compilation, we aim to enhance the understanding and application of diversity measures, thereby making significant contributions to the broader fields of statistics, biomathematics and ecology.

Autoren/Hrsg.

Weitere Mitwirkende

Pavoine, Sandrine

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

1. Rao’s quadratic diversity as a general model for functional alpha and beta diversity decomposition: An overview
2. An information-geometric framework for mapping maximum potential biodiversity
3. Finding the Right Diversity Metric: Using Spectral Analysis to Navigate Evolutionarily Informed Measures
4. Weighted Measures of Biodiversity with Applications to Island Biogeography
5. TBD
6. Phylogeny-based metrics of biodiversity: theory and practice
7. Geometric variability and proximity function in distance-based multivariate analysis
8. Unifying spatially-explicit Rao’s entropy, spatial concentration, and accumulation curves: the different aspects of local biodiversity
9. Rao’s quadratic entropy as a tool for describing multilingualism
10. TBD
11. Correspondences between ecological and population-genetic diversity measures

Über Autor(innen)

Pavoine, Sandrine
Sandrine Pavoine is a professor of statistical ecology at the National Museum of Natural History (Muséum national d'Histoire naturelle, MNHN) in Paris, France, affiliated with the Center for Ecology and Conservation Sciences (CESCO). She holds a PhD in statistical ecology from Lyon 1 University (2005) and has served as a research associate in the Mathematical Ecology Research Group at the University of Oxford. Her work sits at the intersection of applied mathematics, community ecology, evolutionary biology, and conservation science. Honored with the prestigious CNRS Bronze Medal in 2016 for her contributions to ecological modeling, her research focuses on developing mathematical frameworks, statistical metrics, and specialized open-source tools to measure diverse facets of biodiversity, particularly functional and phylogenetic diversity. A fundamental pillar of Sandrine Pavoine’s research centers on expanding and refining Rao’s quadratic entropy, a key mathematical index used to measure diversity by incorporating both species' relative abundances and pairwise distances (functional or phylogenetic). In seminal papers, Pavoine rigorously explored the mathematical behavior and limitations of quadratic entropy. She pioneered new frameworks for partitioning quadratic entropy across ecological scales. Her work transformed Rao’s quadratic entropy from a theoretical concept into a versatile, widely adopted tool for quantitative conservation and community ecology.