A maximum entropy theorem with applications to the measurement of biodiversity

Abstract

This is a preliminary article stating and proving a new maximum entropy theorem. The entropies that we consider can be used as measures of biodiversity. In that context, the question is: for a given collection of species, which frequency distribution(s) maximize the diversity? The theorem provides the answer. The chief surprise is that although we are dealing with not just a single entropy, but a one-parameter family of entropies, there is a single distribution maximizing all of them simultaneously.

arXiv comment26 pages. v4: references added, and other minor edits

References in corpus (2)

• On the asymptotic magnitude of subsets of Euclidean space
• Infinite paths and cliques in random graphs

Cited by in corpus (7)

• The magnitude of metric spaces
• On the asymptotic magnitude of subsets of Euclidean space
• The magnitude of a metric space: from category theory to geometric measure theory
• Maximizing diversity in biology and beyond
• On the magnitude of spheres, surfaces and other homogeneous spaces
• Entropy and Diversity: The Axiomatic Approach
• Spread: a measure of the size of metric spaces