Rao's Entropy and Diversity Measures

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.

Arni S.R. Srinivasa Rao works in pure mathematics, applied mathematics, probability, artificial intelligence and applications in medicine. He developed the concept of “Exact Deep Learning Machines”, which can provide designs for accurate predictions without any uncertainty. He had edited these handbooks jointly with renowned statistician Dr. C. R. Rao. He is a Professor at the Medical College of Georgia, Augusta University, U.S.A., and the Director of the Laboratory for Theory and Mathematical Modeling housed within the Division of Infectious Diseases, Medical College of Georgia, Augusta, U.S.A. Previously, Dr. Rao conducted research and/or taught at the Mathematical Institute, University of Oxford (2003, 2005-07), Indian Statistical Institute (1998-2002, 2006-2012), Indian Institute of Science (2002-04), University of Guelph (2004-06). Until 2012, Dr. Rao held a permanent faculty position at the Indian Statistical Institute. He has won the Heiwa-Nakajima Award (Japan) and Fast Track Young Scientists Fellowship in Mathematical Sciences (DST, New Delhi). Dr. Rao also proved a major theorem in stationary population models, such as, Rao’s Partition Theorem inPopulations, Rao-Carey Theorem in stationary populations, and developed mathematical modeling-based policies for the spread of diseases like HIV, H5N1, COVID-19, etc. He developed a new set of network models for understanding avian pathogen biology on grid graphs (these were called chicken walk models), AI Models for COVID-19, and received wide coverage in the science media. Dr. Rao is an elected Fellow of ISMMACS (Indian Society for Mathematical Modeling and Computer Simulation), and ISPS (Indian Society for Probability and Statistics). He developed concepts such as “Multilevel Contours within a bundle of Complex Number Planes”.