Using Shannon Entropy On Measuring The Individual Variability In The Rafous-bellied Thrush Turdus Rufiventris Vocal Communication

We applied the information theory concepts to notes repertoire characteristics combined with temporal parameters of the Rufous-bellied thrush Turdus rufiventris song, using this particular case to test a new method of analysing quantitatively complex animal communication systems. Like most Turdus thrushes, Rufous-bellied thrushes are remarkable for their long, varied and melodious songs. For the analysis of the species repertoire, we used recordings of 44 individuals from 24 localities covering its full geographical range. We measured the repertoire size, note duration and rhythm (frequency of note utterance), and combined these parameters with the Shannon entropy values calculated for each individual. Although individuals maintain species-specific recognition capacity, we find a large variation between their song parameters and show that the information theory can be useful to analyse large and varied animal vocal repertoires. We are introducing two new parameters, temporal average entropy (E(t)) and utterance frequency average entropy (E(f)), for measuring such communication systems. (C) 2000 Academic Press.20715764Baker, M.C., Cunningham, M.A., The biology of bird-song dialects (1985) Behav. Brain Sci., 8, pp. 85-133Blumenfeld, L.A., (1981) Problems of Biological Physics, , Berlin: Springer-VerlagCanady, R.A., Kroodsma, D.E., Nottebohm, F., Population differences in complexity of a learned skill are correlated with the brain space involved (1984) Proc. Natl. Acad. Sci. U.S.A., 81, pp. 6232-6234Culmann, G., Denis-Papin, M.Y., Kaufmann, A., (1967) Elementos de Calculo Informacional, , Bilbao, Spain: UrmoDa Silva, M.L., (1997) Descricao do repertorio vocal do Sabia-laranjeira Turdus rufiventris (Aves, Passeriformes, Turdinae), , Unpublished M.Sc. Dissertation, Sao Paulo University, Sao Paulo, BrazilGuiassu, S., Theodorescu, R., (1968) La Theorie mathematique de l'Information, , Paris, France: DunodKhinchin, A.I., (1957) Mathematical Foundations of Information Theory, , New York, U.S.A.: Dover Publications IncKroodsma, D.E., Song learning and its consequences (1982), pp. 315-326. , Acoustic Communication in Birds (Kroodsma, D. E. and Miller, E. H., eds). New York: Academic PressKroodsma, D.E., Ecology of Passerine song development (1996), pp. 3-19. , Ecology and Evolution of Acoustic Communication in Birds (Kroodsma, D. E. and Miller, E. H., eds), Ithaca: Cornell University PressKugler, P.N., Turvey, M.T., (1987) Information, Natural Law, and the Self assembly of Rhythmic Movement, , Hillsdale, NJ: Lawrence Erbaun Associated PublishersMarler, P., Three models of song learning: Evidence from behavior (1997) J. Neurobiol., 33, pp. 501-516McCowan, B., Hanser, S.F., Doyle, L.R., Quantitative tools for comparing animal communication systems: Information theory applied to bottlenose dolphin whistle repertoires (1999) Anim. Behav., 57, pp. 409-419Mundinger, P.C., Microgeographic and macrogeographic variation in the acquired vocalizations of birds (1982), pp. 147-208. , Acoustic Communication in Birds (Kroodsma, D. E. and Miller, E. H., eds). New York: Academic PressPiqueira, J.R.C., Structural and functional complexity: An informational approach (1994) Proceedings of IEEE Conference on Systems, Man and Cybernetics, pp. 1974-1978. , TX, USA.: San AntonioShannon, C., Weaver, W., (1949) The Mathematical Theory of Communication, , Chicago, USA.: University of Illinois PressSick, H., (1993) Birds in Brazil, a natural History, , Princeton, NJ: Princeton University Press. (translated by William Belton.)Todt, D., Hultsch, H., Acquisition and performance of song repertoires: Ways of coping with diversity and versatility (1996), pp. 79-96. , Ecology and Evolution of Acoustic Communication in Birds (Kroodsma, D. E. and Miller, E. H., eds). Ithaca: Cornell University PressVielliard, J.M.E., Uso da bioacustica na observacao das aves (1987), pp. 98-121. , II Encontro Nac. Anilhad. Aves. Rio de JaneiroWeber, B.H., Depew, D.J., Smith, J.D., (1988) Entropy, Information and Evolution, , Cambridge, MA, USA.: MIT Pres