A maximum entropy theorem with applications to the measurement of biodiversity
Information Theory
2011-01-14 v4 math.IT
Populations and Evolution
Quantitative Methods
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.
Keywords
Cite
@article{arxiv.0910.0906,
title = {A maximum entropy theorem with applications to the measurement of biodiversity},
author = {Tom Leinster},
journal= {arXiv preprint arXiv:0910.0906},
year = {2011}
}
Comments
26 pages. v4: references added, and other minor edits