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Comparative analysis of nonhuman animal communication systems and their complexity, particularly in comparison to human language, has been generally hampered by both a lack of sufficiently extensive data sets and appropriate analytic tools. Information theory measures provide an important quantitative tool for examining and comparing communication systems across species. In this paper we use the original application of information theory, that of statistical examination of a communication system’s structure and organization. As an example of the utility of information theory to the analysis of animal communication systems, we applied a series of information theory statistics to a statistically categorized set of bottlenose dolphinTursiops truncatus, whistle vocalizations. First, we use the first-order entropic relation in a Zipf-type diagram (Zipf 1949Human Behavior and the Principle of Least Effort) to illustrate the …