Entropy and Diversity: The Axiomatic Approach

TL;DR

This book develops a rigorous mathematical framework for quantifying biological diversity using axiomatic methods, integrating diverse mathematical fields to deepen understanding of what constitutes diversity.

Contribution

It introduces a novel axiomatic approach to measure biological diversity, connecting concepts from information theory, probability, and advanced mathematics.

Findings

New axiomatic measures of diversity

Mathematical theorems characterizing diversity measures

Bridging biology and advanced mathematics

Abstract

This book brings new mathematical rigour to the ongoing vigorous debate on how to quantify biological diversity. The question "what is diversity?" has surprising mathematical depth, and breadth too: this book involves parts of mathematics ranging from information theory, functional equations and probability theory to category theory, geometric measure theory and number theory. It applies the power of the axiomatic method to a biological problem of pressing concern, but the new concepts and theorems are also motivated from a purely mathematical perspective. The main narrative thread requires no more than an undergraduate course in analysis. No familiarity with entropy or diversity is assumed.