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@article{Stepanov2025a,

title = {Bottlenose Dolphins’ Clicks Comply with Three Laws of Efficient Communication},

author = {Arthur Stepanov and Hristo Zhivomirov and Ivaylo Nedelchev and Todor Ganchev and Penka Stateva},

doi = {10.3390/a18070392},

year  = {2025},

date = {2025-01-01},

journal = {Algorithms},

volume = {18},

number = {7},

abstract = {Bottlenose dolphins’ broadband click vocalisations are well-studied in the literature concerning their echolocation function. Their potential use for communication among conspecifics has long been speculated but has yet to be conclusively established. In this study, we first categorised dolphins’ click production based on their amplitude contour and then analysed the distribution of individual clicks and click sequences against their duration and length. The results show that the repertoire and composition of clicks and click sequences adhere to the three essential linguistic laws of efficient communication: Zipf’s rank\textendashfrequency law, the law of brevity, and the Menzerath\textendashAltmann law. Conforming to the rank\textendashfrequency law suggests that clicks may form a linguistic code subject to selective pressures for unification, on the one hand, and diversification, on the other. Conforming to the other two laws also implies that dolphins use clicks according to the compression criterion or minimisation of code length without losing information. Such conformity of dolphin clicks might indicate that these linguistic laws are more general, which produces an exciting research perspective on animal communication.},

keywords = {Menzerath-Altmann law, Zipf\'s law for word frequencies, Zipf\'s law of abbreviation},

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1126/science.adq7055,

title = {Whale song shows language-like statistical structure},

author = {Inbal Arnon and Simon Kirby and Jenny A. Allen and Claire Garrigue and Emma L. Carroll and Ellen C. Garland},

url = {https://www.science.org/doi/abs/10.1126/science.adq7055},

doi = {10.1126/science.adq7055},

year  = {2025},

date = {2025-01-01},

journal = {Science},

volume = {387},

number = {6734},

pages = {649-653},

abstract = {Humpback whale song is a culturally transmitted behavior. Human language, which is also culturally transmitted, has statistically coherent parts whose frequency distribution follows a power law. These properties facilitate learning and may therefore arise because of their contribution to the faithful transmission of language over multiple cultural generations. If so, we would expect to find them in other culturally transmitted systems. In this study, we applied methods based on infant speech segmentation to 8 years of humpback recordings, uncovering in whale song the same statistical structure that is a hallmark of human language. This commonality, in two evolutionarily distant species, points to the role of learning and cultural transmission in the emergence of properties thought to be unique to human language. All human languages follow a particular distribution of words known as the Zipf distribution. This distribution pertains to the frequency of relative word use and is believed to reflect cultural transmission of language. This pattern has also been found in infants during the beginnings of language production. The approach used to study these preverbal patterns allows for the study of songs and calls in other species. Arnon et al. used this approach to study humpback whale song collected over 8 years (see the Perspective by Whiten and Youngblood). They found clear evidence of a Zipf distribution in this song, as well as other hallmarks of human language such as statistical coherence and brevity of subsequences. \textemdashSacha Vignieri},

keywords = {Zipf\'s law for word frequencies, Zipf\'s law of abbreviation},

pubstate = {published},

tppubtype = {article}

}

@article{Youngblood2024a,

title = {Language-like efficiency and structure in house finch song},

author = {Mason Youngblood},

doi = {10.1098/rspb.2024.0250},

year  = {2024},

date = {2024-01-01},

journal = {Proceedings of the Royal Society B: Biological Sciences},

volume = {291},

number = {2020},

publisher = {The Royal Society},

abstract = {Vocal communication systems in humans and other animals experience selection for efficiency\textemdashoptimizing the benefits they convey relative to the costs of producing them. Two hallmarks of efficiency, Menzerath’s law and Zipf’s law of abbreviation, predict that longer sequences will consist of shorter elements and more frequent elements will be shorter, respectively. Here, we assessed the evidence for both laws in cetaceans by analyzing vocal sequences from 16 baleen and toothed whale species and comparing them to 51 human languages. Eleven whale species exhibit Menzerath’s law, sometimes with greater effect sizes than human speech. Two of the five whale species with categorized element types exhibit Zipf’s law of abbreviation. On average, whales also tend to shorten elements and intervals toward the end of sequences, although this varies by species. Overall, the results of this study suggest that the vocalizations of many cetacean species have undergone compression for increased efficiency in time.},

keywords = {Menzerath-Altmann law, Zipf\'s law for word frequencies, Zipf\'s law of abbreviation},

pubstate = {published},

tppubtype = {article}

}

@article{Ferrer2022a,

title = {Parallels of human language in the behavior of bottlenose dolphins},

author = {R. Ferrer-i-Cancho and D. Lusseau and B. McCowan},

url = {https://arxiv.org/abs/1605.01661},

doi = {10.2478/lf-2022-0002},

year  = {2022},

date = {2022-01-01},

journal = {Linguistic Frontiers},

volume = {5},

number = {1},

pages = {5-11},

abstract = {Dolphins exhibit striking similarities with humans. Here we review them with the help of quantitative linguistics and information theory. Various statistical laws of language that are well-known in quantitative linguistics, i.e. Zipf’s law for word frequencies, the law of meaning distribution, the law of abbreviation and Menzerath’s law, have been found in dolphin vocal or gestural behavior. The information theory of these laws suggests that humans and dolphins share cost-cutting principles of organization.},

keywords = {Law of meaning distribution, Meaning-frequency law, Menzerath-Altmann law, theory construction, Zipf\'s law for word frequencies, Zipf\'s law of abbreviation},

pubstate = {published},

tppubtype = {article}

}

@article{Semple2021a,

title = {Linguistic laws in biology},

author = {S. Semple and R. Ferrer-i-Cancho and M. Gustison},

doi = {10.1016/j.tree.2021.08.012},

year  = {2022},

date = {2022-01-01},

journal = {Trends in Ecology and Evolution},

volume = {37},

number = {1},

pages = {53-66},

abstract = {Linguistic laws, the common statistical patterns of human language, have been investigated by quantitative linguists for nearly a century. Recently, biologists from a range of disciplines have started to explore the prevalence of these laws beyond language, finding patterns consistent with linguistic laws across multiple levels of biological organisation - from molecular (genomes, genes and proteins) to organismal (animal behaviour) to ecological (populations and ecosystems). We propose a new conceptual framework for the study of linguistic laws in biology, comprising and integrating distinct levels of analysis - from description to prediction to theory building. Adopting this framework will provide critical new insights into the fundamental rules of organization underpinning natural systems, unifying linguistic laws and core theory in biology.},

keywords = {Law of meaning distribution, Meaning-frequency law, Menzerath-Altmann law, Zipf\'s law for word frequencies, Zipf\'s law of abbreviation},

pubstate = {published},

tppubtype = {article}

}

@article{10.3389/fmicb.2021.655990,

title = {The compressed vocabulary of microbial life},

author = {Gustavo Caetano-Anoll\'{e}s},

url = {https://www.frontiersin.org/article/10.3389/fmicb.2021.655990},

doi = {10.3389/fmicb.2021.655990},

issn = {1664-302X},

year  = {2021},

date = {2021-01-01},

journal = {Frontiers in Microbiology},

volume = {12},

pages = {1273},

abstract = {Communication is an undisputed central activity of life that requires an evolving molecular language. It conveys meaning through messages and vocabularies. Here, I explore the existence of a growing vocabulary in the molecules and molecular functions of the microbial world. There are clear correspondences between the lexicon, syntax, semantics, and pragmatics of language organization and the module, structure, function, and fitness paradigms of molecular biology. These correspondences are constrained by universal laws and engineering principles. Macromolecular structure, for example, follows quantitative linguistic patterns arising from statistical laws that are likely universal, including the Zipf’s law, a special case of the scale-free distribution, the Heaps’ law describing sublinear growth typical of economies of scales, and the Menzerath\textendashAltmann’s law, which imposes size-dependent patterns of decreasing returns. Trade-off solutions between principles of economy, flexibility, and robustness define a “triangle of persistence” describing the impact of the environment on a biological system. The pragmatic landscape of the triangle interfaces with the syntax and semantics of molecular languages, which together with comparative and evolutionary genomic data can explain global patterns of diversification of cellular life. The vocabularies of proteins (proteomes) and functions (functionomes) revealed a significant universal lexical core supporting a universal common ancestor, an ancestral evolutionary link between Bacteria and Eukarya, and distinct reductive evolutionary strategies of language compression in Archaea and Bacteria. A “causal” word cloud strategy inspired by the dependency grammar paradigm used in catenae unfolded the evolution of lexical units associated with Gene Ontology terms at different levels of ontological abstraction. While Archaea holds the smallest, oldest, and most homogeneous vocabulary of all superkingdoms, Bacteria heterogeneously apportions a more complex vocabulary, and Eukarya pushes functional innovation through mechanisms of flexibility and robustness.},

keywords = {Herdan\'s law, Menzerath-Altmann law, Zipf\'s law for word frequencies, Zipf\'s law of abbreviation},

pubstate = {published},

tppubtype = {article}

}

@article{Gultekineabf2938,

title = {High plasticity in marmoset monkey vocal development from infancy to adulthood},

author = {Yasemin B. Gultekin and David G. C. Hildebrand and Kurt Hammerschmidt and Steffen R. Hage},

url = {https://advances.sciencemag.org/content/7/27/eabf2938},

doi = {10.1126/sciadv.abf2938},

year  = {2021},

date = {2021-01-01},

journal = {Science Advances},

volume = {7},

number = {27},

publisher = {American Association for the Advancement of Science},

abstract = {The vocal behavior of human infants undergoes marked changes across their first year while becoming increasingly speech-like. Conversely, vocal development in nonhuman primates has been assumed to be largely predetermined and completed within the first postnatal months. Contradicting this assumption, we found a dichotomy between the development of call features and vocal sequences in marmoset monkeys, suggestive of a role for experience. While changes in call features were related to physical maturation, sequences of and transitions between calls remained flexible until adulthood. As in humans, marmoset vocal behavior developed in stages correlated with motor and social development stages. These findings are evidence for a prolonged phase of plasticity during marmoset vocal development, a crucial primate evolutionary preadaptation for the emergence of vocal learning and speech.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{Allen2019a,

title = {Network analysis reveals underlying syntactic features in a vocally learnt mammalian display, humpback whale song},

author = {Jenny A. Allen and Ellen C. Garland and Rebecca A. Dunlop and Michael J. Noad},

doi = {10.1098/rspb.2019.2014},

year  = {2019},

date = {2019-01-01},

journal = {Proceedings of the Royal Society B: Biological Sciences},

volume = {286},

number = {1917},

pages = {20192014},

abstract = {Vocal communication systems have a set of rules that govern the arrangement of acoustic signals, broadly defined as ‘syntax’. However, there is a limited understanding of potentially shared or analogous rules across vocal displays in different taxa. Recent work on songbirds has investigated syntax using network-based modelling. This technique quantifies features such as connectivity (adjacent signals in a sequence) and recurring patterns. Here, we apply network-based modelling to the complex, hierarchically structured songs of humpback whales (Megaptera novaeangliae) from east Australia. Given the song's annual evolving pattern and the cultural conformity of males within a population, network modelling captured the patterns of multiple song types over 13 consecutive years. Song arrangements in each year displayed clear ‘small-world’ network structure, characterized by clusters of highly connected sounds. Transitions between these connected sounds further suggested a combination of both structural stability and variability. Small-world network structure within humpback songs may facilitate the characteristic and persistent vocal learning observed. Similar small-world structures and transition patterns are found in several birdsong displays, indicating common syntactic patterns among vocal learning in multiple taxa. Understanding the syntactic rules governing vocal displays in multiple, independently evolving lineages may indicate what rules or structural features are important to the evolution of complex communication, including human language.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1002/anie.201403708,

title = {Organic Chemistry as a Language and the Implications of Chemical Linguistics for Structural and Retrosynthetic Analyses},

author = {Andrea Cadeddu and Elizabeth K. Wylie and Janusz Jurczak and Matthew Wampler-Doty and Bartosz A. Grzybowski},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.201403708},

doi = {10.1002/anie.201403708},

year  = {2014},

date = {2014-01-01},

journal = {Angewandte Chemie International Edition},

volume = {53},

number = {31},

pages = {8108-8112},

abstract = {Abstract Methods of computational linguistics are used to demonstrate that a natural language such as English and organic chemistry have the same structure in terms of the frequency of, respectively, text fragments and molecular fragments. This quantitative correspondence suggests that it is possible to extend the methods of computational corpus linguistics to the analysis of organic molecules. It is shown that within organic molecules bonds that have highest information content are the ones that 1) define repeat/symmetry subunits and 2) in asymmetric molecules, define the loci of potential retrosynthetic disconnections. Linguistics-based analysis appears well-suited to the analysis of complex structural and reactivity patterns within organic molecules.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{Ferrer_i_Cancho_2012,

title = {The span of correlations in dolphin whistle sequences},

author = {Ramon Ferrer-i-Cancho and Brenda McCowan},

url = {https://doi.org/10.1088%2F1742-5468%2F2012%2F06%2Fp06002},

doi = {10.1088/1742-5468/2012/06/p06002},

year  = {2012},

date = {2012-06-01},

journal = {Journal of Statistical Mechanics: Theory and Experiment},

volume = {2012},

number = {06},

pages = {P06002},

publisher = {IOP Publishing},

abstract = {Long-range correlations are found in symbolic sequences from human language, music and 

DNA. Determining the span of correlations in dolphin whistle sequences is crucial for shedding 

light on their communicative complexity. Dolphin whistles share various statistical properties 

with human words, i.e. Zipf’s law for word frequencies (namely that the probability of the 

ith most frequent word of a text is about i−α) and a parallel of the tendency of more frequent words to have more meanings. The finding 

of Zipf’s law for word frequencies in dolphin whistles has been the topic of an intense 

debate on its implications. One of the major arguments against the relevance of Zipf’s law 

in dolphin whistles is that it is not possible to distinguish the outcome of a die-rolling 

experiment from that of a linguistic or communicative source producing Zipf’s law for word 

frequencies. Here we show that statistically significant whistle\textendashwhistle correlations extend 

back to the second previous whistle in the sequence, using a global randomization test, and 

to the fourth previous whistle, using a local randomization test. None of these correlations 

are expected by a die-rolling experiment and other simple explanations of Zipf’s law for 

word frequencies, such as Simon’s model, that produce sequences of unpredictable 

elements.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{Freeberg2012a,

title = {Information theoretical approaches to chick-a-dee calls of Carolina chickadees (Poecile carolinensis)},

author = {T. M. Freeberg and J. R. Lucas},

doi = {10.1037/a0024906},

year  = {2012},

date = {2012-01-01},

journal = {Journal of Comparative Psychology},

volume = {126},

issue = {1},

pages = {68\textendash81},

abstract = {One aim of this study was to apply information theoretical analyses to understanding the structural complexity of chick-a-dee calls of Carolina chickadees, Poecile carolinensis. A second aim of this study was to compare this structural complexity to that of the calls of black-capped chickadees, P. atricapillus, described in an earlier published report (Hailman, Ficken, \& Ficken, 1985). Chick-a-dee calls were recorded from Carolina chickadees in a naturalistic observation study in eastern Tennessee. Calls were analyzed using approaches from information theory, including transition probability matrices, Zipf's rules, entropies, and information coding capacities of calls and notes of calls. As described for black-capped chickadees, calls of Carolina chickadees exhibited considerable structural complexity. Most results suggested that the call of Carolina chickadees is more structurally complex than that of black-capped chickadees. These findings add support to the growing literature on the complexity of this call system in Paridae species. Furthermore, these results point to the feasibility of detailed cross-species comparative analyses that may allow strong testing of hypotheses regarding signal evolution.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{DOYLE2011406,

title = {Information theory, animal communication, and the search for extraterrestrial intelligence},

author = {Laurance R. Doyle and Brenda McCowan and Simon Johnston and Sean F. Hanser},

url = {http://www.sciencedirect.com/science/article/pii/S0094576509005682},

doi = {https://doi.org/10.1016/j.actaastro.2009.11.018},

issn = {0094-5765},

year  = {2011},

date = {2011-01-01},

journal = {Acta Astronautica},

volume = {68},

number = {3},

pages = {406 - 417},

abstract = {We present ongoing research in the application of information theory to animal communication systems with the goal of developing additional detectors and estimators for possible extraterrestrial intelligent signals. Regardless of the species, for intelligence (i.e., complex knowledge) to be transmitted certain rules of information theory must still be obeyed. We demonstrate some preliminary results of applying information theory to socially complex marine mammal species (bottlenose dolphins and humpback whales) as well as arboreal squirrel monkeys, because they almost exclusively rely on vocal signals for their communications, producing signals which can be readily characterized by signal analysis. Metrics such as Zipf's Law and higher-order information-entropic structure are emerging as indicators of the communicative complexity characteristic of an “intelligent message” content within these animals’ signals, perhaps not surprising given these species’ social complexity. In addition to human languages, for comparison we also apply these metrics to pulsar signals-perhaps (arguably) the most “organized” of stellar systems-as an example of astrophysical systems that would have to be distinguished from an extraterrestrial intelligence message by such information theoretic filters. We also look at a message transmitted from Earth (Arecibo Observatory) that contains a lot of meaning but little information in the mathematical sense we define it here. We conclude that the study of non-human communication systems on our own planet can make a valuable contribution to the detection of extraterrestrial intelligence by providing quantitative general measures of communicative complexity. Studying the complex communication systems of other intelligent species on our own planet may also be one of the best ways to deprovincialize our thinking about extraterrestrial communication systems in general.},

note = {SETI Special Edition},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{Genty2010,

title = {Why do gorillas make sequences of gestures?},

author = {Emilie Genty and Richard W. Byrne},

url = {https://doi.org/10.1007/s10071-009-0266-4},

doi = {10.1007/s10071-009-0266-4},

issn = {1435-9456},

year  = {2010},

date = {2010-01-01},

journal = {Animal Cognition},

volume = {13},

number = {2},

pages = {287-301},

abstract = {Great ape gestures have attracted considerable research interest in recent years, prompted by their flexible and intentional pattern of use; but almost all studies have focused on single gestures. Here, we report the first quantitative analysis of sequential gesture use in western gorillas (Gorilla gorilla gorilla), using data from three captive groups and one African study site. We found no evidence that gesture sequences were given for reasons of increased communicative efficiency over single gestures. Longer sequences of repeated gestures did not increase the likelihood of response, and using a sequence was seldom in reaction to communicative failure. Sequential combination of two gestures with similar meanings did not generally increase effectiveness, and sometimes reduced it. Gesture sequences were closely associated with play contexts. Markov transition analysis showed two networks of frequently co-occurring gestures, both consisting of gestures used to regulate play. One network comprised only tactile gestures, the other a mix of silent, audible and tactile gestures; apparently, these clusters resulted from gesture use in play with proximal or distal contact, respectively. No evidence was found for syntactic effects of sequential combination: meanings changed little or not at all. Semantically, many gestures overlapped massively with others in their core information (i.e. message), and gesture messages spanned relatively few functions. We suggest that the underlying semantics of gorilla gestures is highly simplified compared to that of human words. Gesture sequences allow continual adjustment of the tempo and nature of social interactions, rather than generally conveying semantically referential information or syntactic structures.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{MCCOWAN2005F1,

title = {The appropriate use of Zipf's law in animal communication studies},

author = {B. McCowan and L. R. Doyle and J. M. Jenkins and S. F. Hanser},

url = {http://www.sciencedirect.com/science/article/pii/S000334720400346X},

doi = {https://doi.org/10.1016/j.anbehav.2004.09.002},

issn = {0003-3472},

year  = {2005},

date = {2005-01-01},

journal = {Animal Behaviour},

volume = {69},

number = {1},

pages = {F1 - F7},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{SUZUKI2005F9,

title = {The use of Zipf's law in animal communication analysis},

author = {Ryuji Suzuki and John R. Buck and Peter L. Tyack},

url = {http://www.sciencedirect.com/science/article/pii/S0003347204003471},

doi = {https://doi.org/10.1016/j.anbehav.2004.08.004},

issn = {0003-3472},

year  = {2005},

date = {2005-01-01},

journal = {Animal Behaviour},

volume = {69},

number = {1},

pages = {F9 - F17},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{Furusawa2003,

title = {Zipf's law in gene expression},

author = {Chikara Furusawa and Kunihiko Kaneko},

doi = {10.1103/PhysRevLett.90.088102},

year  = {2003},

date = {2003-01-01},

journal = {Physical Review Letters},

volume = {90},

pages = {088102},

abstract = {Using data from gene expression databases on various organisms and tissues, including yeast, nematodes, human normal and cancer tissues, and embryonic stem cells, we found that the abundances of expressed genes exhibit a power-law distribution with an exponent close to -1; i.e., they obey Zipf's law. Furthermore, by simulations of a simple model with an intracellular reaction network, we found that Zipf's law of chemical abundance is a universal feature of cells where such a network optimizes the efficiency and faithfulness of self-reproduction. These findings provide novel insights into the nature of the organization of reaction dynamics in living cells.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{McCowan2002,

title = {Using information theory to assess the diversity, complexity and development of communicative repertoires},

author = {B. McCowan and L. R. Doyle and S. F. Hanser},

doi = {10.1037/0735-7036.116.2.166},

year  = {2002},

date = {2002-01-01},

journal = {Journal of Comparative Psychology},

volume = {116},

pages = {166-172},

abstract = {The application of quantitative and comparative measures from information theory on animal communication can provide novel insights into the ecological, environmental, social, and contextual properties that shape the structure, organization, and function of signal repertoires. Using 2 phylogenetically different mammalian species that share similar ecological and social constraints as examples, the authors quantitatively examined the internal structure and development of a subsystem of these species' vocal repertoires in comparison with that of human language and illustrated that these species exhibit convergent developmental processes. The authors also discussed how predictions on the structure and organization of animal communication systems can be made from this new application of information theoretic measures with respect to behavioral ecology.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{Searls2002,

title = {The language of genes},

author = {David B. Searls},

url = {https://doi.org/10.1038/nature01255},

doi = {10.1038/nature01255},

issn = {1476-4687},

year  = {2002},

date = {2002-01-01},

journal = {Nature},

volume = {420},

number = {6912},

pages = {211-217},

abstract = {Linguistic metaphors have been woven into the fabric of molecular biology since its inception. The determination of the human genome sequence has brought these metaphors to the forefront of the popular imagination, with the natural extension of the notion of DNA as language to that of the genome as the 'book of life'. But do these analogies go deeper and, if so, can the methods developed for analysing languages be applied to molecular biology? In fact, many techniques used in bioinformatics, even if developed independently, may be seen to be grounded in linguistics. Further interweaving of these fields will be instrumental in extending our understanding of the language of life.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{MCCOWAN1999409,

title = {Quantitative tools for comparing animal communication systems: information theory applied to bottlenose dolphin whistle repertoires},

author = {Brenda McCowan and Sean F. Hanser and Laurance R. Doyle},

url = {http://www.sciencedirect.com/science/article/pii/S0003347298910004},

doi = {https://doi.org/10.1006/anbe.1998.1000},

issn = {0003-3472},

year  = {1999},

date = {1999-01-01},

journal = {Animal Behaviour},

volume = {57},

number = {2},

pages = {409 - 419},

abstract = {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 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.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{BURGOS1996227,

title = {Zipf-scaling behavior in the immune system},

author = {Javier D. Burgos and Pedro Moreno-Tovar},

url = {http://www.sciencedirect.com/science/article/pii/0303264796016188},

doi = {https://doi.org/10.1016/0303-2647(96)01618-8},

issn = {0303-2647},

year  = {1996},

date = {1996-01-01},

journal = {Biosystems},

volume = {39},

number = {3},

pages = {227 - 232},

abstract = {The Zipf law, an approach to analyzing linguistic texts, was applied to study the Cytotoxic T Lymphocytes (CTL) repertoire, one of the major components of the immune system. A Zipf-scaling behavior was observed in those CTL repertoires obtained in normal or conventional mice. In contrast, CTL repertoires from irradiated chimeric animals, showed a non-scaling statistical behavior when tested by the Zipf analysis,suggesting that normal repertoires work like a structured biological language. The fractal dimension (D) was derived from the Zipf plots, and correlates well with the nature of the repertoires: high, D \> 0.8, in conventional mice. Non-fractal, D \> 1, in chimeric animals, and low, D \< 0.3, in athymic mice. Then, D seems to be an useful tool to characterize the current status of the immune system.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{BURGOS199619,

title = {Fractal representation of the immune B cell repertoire},

author = {Javier D. Burgos},

url = {http://www.sciencedirect.com/science/article/pii/0303264795015744},

doi = {10.1016/0303-2647(95)01574-4},

issn = {0303-2647},

year  = {1996},

date = {1996-01-01},

journal = {Biosystems},

volume = {39},

number = {1},

pages = {19\textendash24},

abstract = {The immune repertoire is characterized by a complex and dynamic organization. Here I suggest, based on the presence of well-defined immune reactivity patterns (RP) analyzed using a linguistic analogy, that the B cell repertoires could possess a fractal structure. A simple estimation method of the fractal dimension (D) for a given immune B repertoire was developed, and D demonstrated to be an useful tool to define what complexity is regarding the immune repertoire, and to evaluate the complexity level of the immune B repertoire among age-structured groups of mice sensitized with the hemagglutinin (HA) molecule of influenza virus. Also, since a fractal-linguistic point of view, considerations are made about the ontogeny, connectivity, chaotic regimes, and size of the immune repertoire. Fractal analysis indicates that the immune repertoire shows a Zipf-like scaling behavior, a statistical property of natural languages. This result suggests that immune repertoire is structured like a powerful language.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{Ficken1994,

title = {The chick-a-dee call system of the Mexican chickadee},

author = {M. S. Ficken and E. D. Hailman and J. P. Hailman},

doi = {10.2307/1369065},

year  = {1994},

date = {1994-01-01},

journal = {Condor},

volume = {96},

pages = {70-82},

abstract = {Chick-a-dee calls of the Mexican Chickadee (Parus sclateri) are composed of combinations of three common note types (A, C and D) and one very rare type (B). Calls have the invariant sequence of notes A-B-C-D, where any note type may be omitted, given once or repeated a variable number of times before transiting to the next type. The B and C notes are phonologically similar to the B and C notes of chick-a-dee calls of the Black-capped Chickadee (P. atricapillus), but the A note is markedly different and the D note somewhat different from equivalent notes of the congener. A total of 2,071 calls recorded yielded 60 different call types, and Zipf-Mandelbrot plots show that the call system is "open"; as the sample size is increased new call types will be found without demonstrable bound. In relatively undisturbed contexts (with mate on territory, in fall flocks, alone in fall) birds gave mainly [A][D] calls with lesser numbers of [A] and [C] calls, where brackets indicate variable repetition of note types. In disturbed contexts (mobbing plastic Great Horned Owl, mobbing speaker playing calls of the Northern Pygmy-Owl, observer sitting under the nest cavity) the birds gave more [C] calls with [A][C] as well. In the longest mobbing session to owl calls, birds gave mainly [A] calls when approaching, switched to [C] calls while flying about the speaker, and then resumed [A] calls and moved off when the playback was stopped. Outside of human language, this is the second truly combinatorial system of vocal communication found in animals, the first being chick-a-dee calls of the Black-capped Chickadee. This study provides the first data substantiating quantitative differences in calls from different contexts, an important step toward understanding what kinds of information combinatorial chick-a-dee calls encode.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{Hailman1994,

title = {Constrained permutation in 'chick-a-dee' like calls of a black-lored tit em Parus em Xanthogenys},

author = {J. P. Hailman},

doi = {10.1080/09524622.1994.9753270},

year  = {1994},

date = {1994-01-01},

journal = {Bioacoustics},

volume = {6},

pages = {33-50},

abstract = {Examined the vocalizations of 2 wild-caught black-lored tits. It was found that the Ss gave chick-a-dee-like calls in response to a stuffed owl. The tit used combinations of 4 note types to create 65 different call types. The repertoire of call types had the language-like property of openness to formation of new call types without limit. Calling under constant stimulus conditions changed unidirectionally during the course of mobbing, with the 4 note types replacing each other in calls, as time progressed. Thus, the tit had a constrained type of permuted order of note types, which enlarged the potential for call variety and closely resembled properties of language.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{10.2307/2742889,

title = {The genetic code and Zipf's Law},

author = {M. L. Bender and Pritmohinder Gill},

url = {http://www.jstor.org/stable/2742889},

issn = {00113204, 15375382},

year  = {1986},

date = {1986-01-01},

journal = {Current Anthropology},

volume = {27},

number = {3},

pages = {280\textendash283},

publisher = {University of Chicago Press, Wenner-Gren Foundation for Anthropological Research},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}

@article{10.1121/1.1908584,

title = {Linguistic considerations of porpoise sounds},

author = {John J. Dreher},

doi = {10.1121/1.1908584},

year  = {1961},

date = {1961-01-01},

journal = {The Journal of the Acoustical Society of America},

volume = {33},

number = {12},

pages = {1799-1800},

abstract = {A brief comparison of intonation and tone languages is given, with criteria of the latter applied to observed whistle contours appearing in underwater recordings of Tursiops truncatus and Langenorhynchus obliquidens.},

note = {The author actually reports evidence of an exponential-like distribution, rather than the power-law like distribution of Zipf's law for word frequencies.},

keywords = {Zipf\'s law for word frequencies},

pubstate = {published},

tppubtype = {article}

}