Bradbury, J. W. & Vehrencamp, S. L. Principles of Animal Communicationvol. 132 (Sinauer Associates, 1998).
Brenowitz, E. A., Margoliash, D. & Nordeen, K. W. An introduction to birdsong and the avian song system. J. Neurobiol. 33 (5), 495–500 (1997).
Demartsev, V. et al. The progression pattern of male hyrax songs and the role of climactic ending. Sci. Rep. 7, 2794 (2017).
Bohn, K. M., Schmidt-French, B., Schwartz, C., Smotherman, M. & Pollak, G. D. Versatility and stereotypy of Free-Tailed Bat songs. PLoS One. 4, e6746 (2009).
Haraway, M. M. & Maples, E. G. Flexibility in the species-typical songs of Gibbons. Primates 39, 1 (1998).
Clarke, E., Reichard, U. H. & Zuberbühler, K. The syntax and meaning of wild Gibbon songs. PLoS One. 1, e73 (2006).
Holy, T. E. & Guo, Z. Ultrasonic songs of male mice. PLoS Biol. 3, e386 (2005).
Allen, J. A., Garland, E. C., Dunlop, R. A. & Noad, M. J. Cultural revolutions reduce complexity in the songs of humpback whales. Proceedings of the Royal Society B: Biological Sciences 285, 20182088 (2018).
Payne, R. S. & McVay, S. Songs of humpback whales. Sci. (1979). 173, 585–597 (1971).
Lameira, A. R. et al. Predator guild does not influence orangutan alarm call rates and combinations. Behav. Ecol. Sociobiol. 67, 519–528 (2013).
McCowan, B., Doyle, L. R. & Hanser, S. F. Using information theory to assess the diversity, complexity, and development of communicative repertoires. J. Comp. Psychol. 116, 166–172 (2002).
Sharma, P. et al. Contextual and combinatorial structure in sperm Whale vocalisations. Nat. Commun. 15, 3617 (2024).
Watkins, W. A. & Schevill, W. E. Sperm Whale Codas. J. Acoust. Soc. Am. 62, 1485–1490 (1977).
Riesch, R., Ford, J. K. B. & Thomsen, F. Whistle sequences in wild killer whales (Orcinus orca). J. Acoust. Soc. Am. 124, 1822–1829 (2008).
Selbmann, A., Miller, P. J. O., Wensveen, P. J., Svavarsson, J. & Samarra, F. I. P. Call combination patterns in Icelandic killer whales (Orcinus orca). Sci. Rep. 13, 21771 (2023).
Sayigh, L., Quick, N., Hastie, G. & Tyack, P. Repeated call types in short-finned pilot whales, Globicephala macrorhynchus. Mar. Mamm. Sci. 29, 312–324 (2013).
McCowan, B., Hanser, S. F. & Doyle, L. R. Quantitative tools for comparing animal communication systems: information theory applied to bottlenose Dolphin whistle repertoires. Anim. Behav. 57, 409–419 (1999).
LuÃs, A. R., Alves, I. S., Sobreira, F. V., Couchinho, M. N. & dos Santos, M. E. Brays and bits: information theory applied to acoustic communication sequences of bottlenose dolphins. Bioacoustics 28, 286–296 (2019).
Rogers, T. L., Cato, D. H. & Bryden, M. M. Behavioral significance of underwater vocalizations of captive Leopard seals, Hydrurga leptonyx. Mar. Mamm. Sci. 12, 414–427 (1996).
Stirling, I. & Siniff, D. Underwater vocalizations of Leopard seals (Hydrurga leptonyx) and crabeater seals (Lobodon carcinophagus) near the South Shetland islands, Antarctica. Can. J. Zool. 57, 1244–1248 (1979).
Thomas, J. A. & DeMaster, D. P. An acoustic technique for determining diurnal activities in Leopard (Hydrurga leptonyx) and crabeater (Lobodon carcinophagus) seal. Can. J. Zool. 60, 2028–2031 (1982).
Rogers, T. L. Source levels of the underwater calls of a male Leopard seal. J. Acoust. Soc. Am. 136, 1495–1498 (2014).
Rogers, T. L. Factors influencing the acoustic behaviour of male phocid seals. Aquat. Mamm. 29, 247–260 (2003).
Shabangu, F. W. & Rogers, T. L. Summer circumpolar acoustic occurrence and call rates of ross, Ommatophoca rossii, and leopard, Hydrurga leptonyx, seals in the Southern ocean. Polar Biol. 44, 433–450 (2021).
Borsa, P. Seasonal occurrence of the Leopard seal, Hydrurga leptonyx, in the kerguelen Islands. Can. J. Zool. 68, 405–408 (1990).
Meade, J. et al. Spatial patterns in activity of Leopard seals Hydrurga leptonyx in relation to sea ice. Mar. Ecol. Prog Ser. 521, 265–275 (2015).
Rogers, T. & Bryden, M. M. Predation of adélie Penguins (Pygoscelis adeliae) by Leopard seals (Hydrurga leptonyx) in Prydz bay, Antarctica. Can. J. Zool. 73, 1001–1004 (1995).
Rogers, T. L. Calling underwater is a costly signal: size-related differences in the call rates of Antarctic Leopard seals. Curr. Zool. 63, 433–443 (2017).
Rogers, T. L. & Bryden, M. M. Density and haul-out behaviour of Leopard seals (Hydrurga leptonyx) in Prydz bay, Antarctica. Mar. Mamm. Sci. 13, 293–302 (1997).
Rogers, T., Cato, D. H. & Bryden, M. M. Underwater vocal repertoire of the Leopard seal (Hydrurga leptonyx) in Prydz bay, Antarctica. in Sensory Abilities of Aquatic Animals (ed Kastelein, R. A. et al.) 223–236 (DeSpil., Amsterdam, 1995).
Rogers, T. & Cato, D. Individual variation in the acoustic behaviour of the adult male Leopard seal, Hydrurga leptonyx. Behaviour 139, 1267–1286 (2002).
Arnon, I. et al. Whale song shows language-like statistical structure. Sci. (1979). 387, 649–653 (2025).
Youngblood, M. Language-like efficiency in Whale communication. Sci. Adv. 11, eads6014 (2025).
Hersh, T. A., Ravignani, A. & Whitehead, H. Cetaceans are the next frontier for vocal rhythm research. Proceedings of the National Academy of Sciences 121, (2024).
Fitch, W. T. The evolution of music in comparative perspective. Ann. N Y Acad. Sci. 1060, 29–49 (2005).
Rohrmeier, M., Zuidema, W., Wiggins, G. A. & Scharff, C. Principles of structure Building in music, Language and animal song. Philosophical Trans. Royal Soc. B: Biol. Sci. 370, 20140097 (2015).
Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948).
Cover, T. M. & Thomas, J. A. Elements of Information Theory (John Wiley & Sons, Inc., 2006).
Kershenbaum, A. Entropy rate as a measure of animal vocal complexity. Bioacoustics 23, 195–208 (2014).
Ames, C. The Markov process as a compositional model: A survey and tutorial. MIT Press. 22, 175–187 (1989).
Manzara, L. C., Witten, I. H. & James, M. On the entropy of music: an experiment with Bach chorale melodies. Leonardo Music J. 2, 81 (1992).
Margulis, E. H. & Beatty, A. P. Musical style, psychoaesthetics, and prospects for entropy as an analytic tool. Comput. Music J. 32, 64–78 (2008).
Gündüz, G. Entropy, energy, and instability in music. Phys. A: Stat. Mech. Its Appl. 609, 128365 (2023).
Moore, J. M., Corrêa, D. C. & Small, M. Is bach’s brain a Markov chain? Recurrence quantification to assess Markov order for short, symbolic, musical compositions. Chaos: Interdisc. J. Nonlinear Sci. 28, 085715 (2018).
Knopoff, L. & Hutchinson, W. Entropy as a measure of style: the influence of sample length. J. Music Ther. 27, 75–97 (1983).
Pollastri, E. & Simoncelli, G. Classification of melodies by composer with hidden Markov models. in Proceedings First International Conference on WEB Delivering of Music. WEDELMUSIC 88–95 (IEEE Comput. Soc, 2001). 88–95 (IEEE Comput. Soc, 2001). (2001). https://doi.org/10.1109/WDM.2001.990162
Hedges, S. A. Dice music in the eighteenth century. Music Lett. 59, 180–187 (1978).
Collins, T., Laney, R., Willis, A., Garthwaite, P. H. & Chopin Mazurkas Markov Significance 8, 154–159 (2011).
Kershenbaum, A. et al. Animal vocal sequences: not the Markov chains we thought they were. Proc. Royal Soc. B: Biol. Sci. 281, 20141370 (2014).
Wyner, A. D. & Ziv, J. The sliding-window Lempel-Ziv algorithm is asymptotically optimal. Proc. IEEE. 82, 872–877 (1994).
Wyner, A. D., Ziv, J. & Wyner, A. J. On the role of pattern matching in information theory. IEEE Trans. Inf. Theory. 44, 2045–2056 (1998).
Ziv, J. & Lempel, A. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory. 23, 337–343 (1977).
Suzuki, R., Buck, J. R. & Tyack, P. L. Information entropy of humpback Whale songs. J. Acoust. Soc. Am. 119, 1849–1866 (2006).
Pinkerton, R. Information theory and melody. Sci. Am. 194, 77–87 (1956).
Youngblood, J. E. Style as information. J. Music Theory. 2, 24 (1958).
Miksis-Olds, J. L., Buck, J. R., Noad, M. J. & Cato, D. H. Dale stokes, M. Information theory analysis of Australian humpback Whale song. J. Acoust. Soc. Am. 124, 2385–2393 (2008).
Lamoni, L. et al. Variability in humpback Whale songs reveals how individuals can be distinctive when sharing a complex vocal display. J. Acoust. Soc. Am. 153, 2238–2250 (2023).
Parsons, E. C. M., Wright, A. J. & Gore, M. A. The nature of humpback Whale (Megaptera novaeangliae) song. J. Mar. Anim. Ecol. 1, 22–31 (2008).
Kershenbaum, A. et al. Acoustic sequences in non-human animals: a tutorial review and prospectus. Biol. Rev. 91, 13–52 (2016).
Stirling, I. & Thomas, J. A. Relationships between underwater vocalizations and mating systems in phocid seals. Aquat. Mamm. 29, 227–246 (2003).
Oliveira, C. et al. Sperm Whale Codas May encode individuality as well as clan identity. J. Acoust. Soc. Am. 139, 2860–2869 (2016).
Antunes, R. et al. Individually distinctive acoustic features in sperm Whale Codas. Anim. Behav. 81, 723–730 (2011).
Gero, S., Whitehead, H. & Rendell, L. Individual, unit and vocal clan level identity cues in sperm Whale Codas. R Soc. Open. Sci. 3, 150372 (2016).
Wyner, A. D. & Ziv, J. Some asymptotic properties of the entropy of a stationary ergodic data source with applications to data compression. IEEE Trans. Inf. Theory. 35, 1250–1258 (1989).
Basharin, G. P. On a statistical estimate for the entropy of a sequence of independent random variables. Theory Probab. Its Appl. 4, 333–336 (1959).
Payne, K., Tyack, P. & Payne, R. Progressive changes in the songs of humpback whales (Megaptera novaeangliae): A detailed analysis of two seasons in Hawaii. in Communication and Behavior of Whales, AAAS Selected Symposium 76 (ed. Payne, R.) 9–58Westview, Boulder, CO, (1983).