  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.
