Entropy and Diversity - Leinster, Tom

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Résumé :
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.

Biographie:
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.

Sommaire:
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.