A maximum entropy theorem with applications to the measurement of biodiversity

Computer Science – Information Theory

Scientific paper

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26 pages. v4: references added, and other minor edits

Scientific paper

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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