Entropy and Diversity - The Axiomatic Approach

The biodiversity crisis is one of our most urgent problems. This book develops the mathematics behind the measurement of diversity, spanning a great breadth of subjects: from geometry to logic, from algebra to probability theory. The mathematical prerequisites are few, accessible to mathematicians and biologists with a mathematical background.

List of contents

Introduction; 1. Fundamental functional equations; 2. Shannon entropy; 3. Relative entropy; 4. Deformations of Shannon entropy; 5. Means; 6. Species similarity and magnitude; 7. Value; 8. Mutual information and metacommunities; 9. Probabilistic methods; 10. Information loss; 11. Entropy modulo a prime; 12. The categorical origins of entropy; Appendix A. Proofs of background facts; Appendix B. Summary of conditions; References; Index of notation; Subject index.

About the author

Tom Leinster is Professor of Category Theory at the University of Edinburgh, a member of the University of Glasgow's Boyd Orr Centre for Population and Ecosystem Health, and co-author of a highly-cited Ecology article on measuring biodiversity. He was awarded the 2019 Chauvenet Prize for mathematical writing.

Product details

• Authors: Tom Leinster, Tom (University of Edinburgh) Leinster, Leinster Tom
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 30.04.2021
• EAN: 9781108832700
• ISBN: 978-1-108-83270-0
• No. of pages: 456
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Basic principles; Social sciences, law, business > Media, communication > Book trade, library system; SCIENCE / Life Sciences / Biological Diversity, COMPUTERS / Information Theory, MATHEMATICS / Applied, MATHEMATICS / Set Theory, Biodiversity, Information theory, Mathematical modelling, Set theory