ANIMAL BEHAVIOUR, 1999, 57, 409–419 Article No. anbe.1998.1000, available online at http://www.idealibrary.com on Quantitative tools for comparing animal communication systems: information theory applied to bottlenose dolphin whistle repertoires BRENDA McCOWAN*†, SEAN F. HANSER† & LAURANCE R. DOYLE‡ *California Regional Primate Research Center, University of California at Davis †Marine World Foundation ‡SETI Institute, NASA Ames Research Center (Received 29 August 1997; initial acceptance 10 December 1997; final acceptance 21 July 1998; MS. number: A8015) 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 dolphin, Tursiops truncatus, whistle vocalizations. First, we use the first-order entropic relation in a Zipf-type diagram (Zipf 1949, Human Behavior and the Principle of Least Effort) to illustrate the application of temporal statistics as comparative indicators of repertoire complexity, and as possible predictive indicators of acquisition/learning in animal vocal repertoires. Second, we illustrate the need for more extensive temporal data sets when examining the higher entropic orders, indicative of higher levels of internal informational structure, of such vocalizations, which could begin to allow the statistical reconstruction of repertoire organization. Third, we propose using ‘communication capacity’ as a measure of the degree of temporal structure and complexity of statistical correlation, represented by the values of entropic order, as an objective tool for interspecies comparison of communication complexity. In doing so, we introduce a new comparative measure, the slope of Shannon entropies, and illustrate how it potentially can be used to compare the organizational complexity of vocal repertoires across a diversity of species. Finally, we illustrate the nature and predictive application of these higher-order entropies using a preliminary sample of dolphin whistle vocalizations. The purpose of this preliminary report is to re-examine the original application of information theory to the field of animal communication, illustrate its potential utility as a comparative tool for examining the internal informational structure of animal vocal repertoires and their development, and discuss its relationship to behavioural ecology and evolutionary theory.  1999 The Association for the Study of Animal Behaviour The comparative analysis of animal communication sys- tems and their complexity, particularly in comparison to human language, has been generally limited by both a lack of sufficiently extensive data sets and appropriate analytic tools. Information theory measures, in their original application (Shannon 1948; Shannon & Weaver 1949), provide important quantitative tools for examin- ing and comparing communication systems across species. These measures represent statistical information that is imperative for analysing communicative reper- toires objectively, and for elucidating repertoires of unknown structure or function (Pea 1979). This statistical characterization is independent of the kind of communi- cation system of interest and thus allows a comparative examination of the complexity of vocal repertoires and their organization, both with respect to human language (Zipf 1949, 1968) and, more generally, in relationship to behavioural ecology and evolutionary theory. Correspondence: B. McCowan, Behavioral and Neurobiology Unit, California Regional Primate Research Center, University of California, Davis, CA, 95616, U.S.A. (email: bjmccowan@ucdavis.edu). S. Hanser is at the Marine World Foundation, Vallejo, CA, 94589, U.S.A. L. Doyle is at the SETI Institute, NASA Ames Research Center, Moffett Field, CA, 94035, U.S.A. 0003–3472/99/020409+11 $30.00/0  1999 The Association for the Study of Animal Behaviour 409