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  1. Home
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  3. Entropy and Diversity
  • Cited by 36
Publisher:
Cambridge University Press
Online publication date:
April 2021
Print publication year:
2021
Online ISBN:
9781108963558
DOI:
https://doi.org/10.1017/9781108963558
Subjects:
Mathematics, Life Sciences, Logic, Categories and Sets, Quantitative Biology, Biostatistics and Mathematical Modeling
Information

Book description

The global biodiversity crisis is one of humanity's most urgent problems, but even quantifying biological diversity is a difficult mathematical and conceptual challenge. This book brings new mathematical rigour to the ongoing debate. It was born of research in category theory, is given strength by information theory, and is fed by the ancient field of functional equations. It applies the power of the axiomatic method to a biological problem of pressing concern, but it also presents new theorems that stand up as mathematics in their own right, independently of any application. The question 'what is diversity?' has surprising mathematical depth, and this book covers a wide breadth of mathematics, from functional equations to geometric measure theory, from probability theory to number theory. Despite this range, the mathematical prerequisites are few: the main narrative thread of this book requires no more than an undergraduate course in analysis.

Reviews

‘The book shows that the theory of diversity measurement is fertile soil for new mathematics, just as much as the neighboring but far more thoroughly worked field of information theory.’

Hirokazu Nishimura Source: ZB Math Reviews

‘Each new mathematical concept is introduced from fundamental principles, in a lucid, engaging style, keeping the core biological application in the foreground … Leinster provides us with the tools to clearly assess what we are losing, so that we may focus better on what we can save.'

Benjamin Allen Source: The Quarterly Review of Biology

‘The book is a welcome addition to the theory of biodiversity in that it covers the topics of entropy and diversity in a mathematically rigorous yet fairly accessible way … Recommended.’

M. Bona Source: Choice Magazine

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