A maximum entropy theorem with applications to the measurement of biodiversity

Tom Leinster

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arXiv · 0910.0906

A maximum entropy theorem with applications to the measurement of biodiversity

Tom Leinster

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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.

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Tom Leinster. 2009-10-06. A maximum entropy theorem with applications to the measurement of biodiversity. https://arxiv.org/abs/0910.0906

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