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@article{Youngblood2026a,

title = {Zebra finches transform manipulated songs with shuffled syllables to exhibit linguistic laws},

author = {Mason Youngblood},

url = {http://dx.doi.org/10.1007/s10071-026-02058-0},

doi = {10.1007/s10071-026-02058-0},

year  = {2026},

date = {2026-01-01},

journal = {Animal Cognition},

abstract = {Linguistic laws are increasingly used as markers of efficiency in non-human communication, but it remains unclear how rapidly these patterns can emerge. In this re-analysis of experimental data from James and Sakata (James and Sakata 2017), I assessed whether zebra finches tutored with songs with shuffled syllables, where each syllable type is equally common and songs have equal length, transform them to exhibit three linguistic laws associated with efficiency in human language. Menzerath's law and Zipf's rank-frequency law are present in the learned songs to a similar extent as in human language, while there is only weak support for Zipf's law of abbreviation. These results suggest that some measures of language-like efficiency can emerge extremely rapidly, while others may require iterated social learning.},

keywords = {Menzerath-Altmann law, Zipf\'s law of abbreviation, Zipf\'s rank-frequency law},

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{doi:10.1126/sciadv.ads6014,

title = {Language-like efficiency in whale communication},

author = {Mason Youngblood},

url = {https://www.science.org/doi/abs/10.1126/sciadv.ads6014},

doi = {10.1126/sciadv.ads6014},

year  = {2025},

date = {2025-01-01},

journal = {Science Advances},

volume = {11},

number = {6},

pages = {eads6014},

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. Whale vocalizations follow efficiency rules seen in human language, revealing striking similarities in communication systems.},

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

pubstate = {published},

tppubtype = {article}

}

@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{Tucker2025a,

title = {Does Zipf’s law of abbreviation shape birdsong?},

author = {R. Tucker Gilman and CD Durrant and Lucy Malpas and Rebecca N. Lewis},

doi = {10.1371/journal.pcbi.1013228},

year  = {2025},

date = {2025-01-01},

journal = {PLOS Computational Biology},

volume = {21},

number = {8},

pages = {1-17},

publisher = {Public Library of Science},

abstract = {In human languages, words that are used more frequently tend to be shorter than words that are used less frequently. This pattern is known as Zipf’s law of abbreviation. It has been attributed to the principle of least effort \textendash communication is more efficient when words that are used more frequently are easier to produce. Zipf’s law of abbreviation appears to hold in all human languages, and recently attention has turned to whether it also holds in animal communication. In birdsong, which has been used as a model for human language learning and development, researchers have focused on whether more frequently used notes or phrases are shorter than those that are used less frequently. Because birdsong can be highly stereotyped, have high interindividual variation, and have phrase repertoires that are small relative to human language lexicons, studying Zipf’s law of abbreviation in birdsong presents challenges that do not arise when studying human languages. In this paper, we describe a new method for assessing evidence for Zipf’s law of abbreviation in birdsong, and we introduce the R package ZLAvian to implement this method. We used ZLAvian to study Zipf’s law of abbreviation in the songs of 11 bird populations archived in the open-access repository Bird-DB. We did not find strong evidence for Zipf’s law of abbreviation in any population when studied alone, but we found evidence for Zipf’s law in a synthetic analysis across all populations. Overall, the negative concordance between phrase length and frequency of use in birdsong was several times weaker than the negative concordance between word length and frequency of use in written human languages. The method and the results we present here offer a new foundation for researchers studying if or how the principle of least effort shapes animal communication.},

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

pubstate = {published},

tppubtype = {article}

}

@article{Deng2024a,

title = {Hainan frilled treefrogs' calls partially conform to Menzerath\textendashAltmann's law, but oppose Zipf's law of abbreviation},

author = {Ke Deng and Yu-Xiao He and Xiao-Ping Wang and Tong-Liang Wang and Ji-Chao Wang and You-Hua Chen and Jian-Guo Cui},

doi = {10.1016/j.anbehav.2024.04.011},

year  = {2024},

date = {2024-01-01},

journal = {Animal Behaviour},

volume = {213},

pages = {51-59},

abstract = {Information compression is widely regarded as a fundamental principle that applies to human language. Zipf's law of abbreviation and Menzerath\textendashAltmann's law are two linguistic laws related to information compression and have been demonstrated in human language and other communication systems. Female choice and male-male competition in anurans (frogs and toads) depend heavily on vocal communication. However, it remains unclear whether the laws reflecting information compression apply to vocal communication in anurans. Hainan frilled treefrogs, Kurixalus hainanus, are suitable anuran species to test Zipf's law of abbreviation and Menzerath\textendashAltmann's law as male K. hainanus can emit either monosyllabic or multisyllabic calls with three types of notes (i.e. A, B and C notes). In the present study, we mathematically examined whether the vocalizations of K. hainanus conform to these laws. We found that the note type duration was positively correlated with its frequency of occurrence, which was the opposite finding to that predicted by Zipf's law of abbreviation. We also found that the note duration was negatively correlated with call size (the number of notes in a call), but only A notes exhibited patterns consistent with Menzerath\textendashAltmann's law when analysed separately. These results may be caused by the different physical characteristics or different functions and selection pressures of different note types. Further linear mixed model analysis showed that the duration of A notes was significantly negatively correlated with note position in a call, which suggests that the conformity to Menzerath\textendashAltmann's law in A note is caused by energetic or breathing constraints on vocal production. Lastly, we observed a negative correlation between internote interval duration and call size. Our findings support the existence of information compression in vocal communication systems in anurans, among other communication principles, and contribute to increasing our understanding of universal patterns in communication systems.},

keywords = {Menzerath-Altmann law, 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{Zhang2024a,

title = {Do bats’ social vocalizations conform to Zipf’s law and the Menzerath-Altmann law?},

author = {Chunmian Zhang and Ziqi Zheng and Jeffrey R. Lucas and Yicheng Wang and Xin Fan and Xin Zhao and Jiang Feng and Congnan Sun and Tinglei Jiang},

doi = {10.1016/j.isci.2024.110401},

year  = {2024},

date = {2024-01-01},

journal = {iScience},

volume = {27},

number = {7},

pages = {110401},

abstract = {The study of vocal communication in non-human animals can uncover the roots of human languages. Recent studies of language have focused on two linguistic laws: Zipf’s law and the Menzerath-Altmann law. However, whether bats’ social vocalizations follow these linguistic laws, especially Menzerath’s law, has largely been unexplored. Here, we used Asian particolored bats, Vespertilio sinensis, to examine whether aggressive vocalizations conform to Zipf’s and Menzerath’s laws. Aggressive vocalizations of V. sinensis adhere to Zipf’s law, with the most frequent syllables being the shortest in duration. There was a negative association between the syllable number within a call and the average syllable duration, in agreement with Menzerath’s law. A decrease in the proportion of some long syllables and a decrease in the duration of several syllable types in long-duration calls explain the occurrence of this law. Our results indicate that a general compression principle organizes aspects of bat vocal communication systems.},

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

pubstate = {published},

tppubtype = {article}

}

@article{RisuenoSegovia2023,

title = {Linguistic law-like compression strategies emerge to maximize coding efficiency in marmoset vocal communication},

author = {Cristina Risueno-Segovia and Deniz Dohmen and Yasemin B. Gultekin and Thomas Pomberger and Steffen R. Hage},

doi = {10.1098/rspb.2023.1503},

year  = {2023},

date = {2023-01-01},

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

volume = {290},

number = {2007},

abstract = {Human language follows statistical regularities or linguistic laws. For instance, Zipf's law of brevity states that the more frequently a word is used, the shorter it tends to be. All human languages adhere to this word structure. However, it is unclear whether Zipf's law emerged de novo in humans or whether it also exists in the non-linguistic vocal systems of our primate ancestors. Using a vocal conditioning paradigm, we examined the capacity of marmoset monkeys to efficiently encode vocalizations. We observed that marmosets adopted vocal compression strategies at three levels: (i) increasing call rate, (ii) decreasing call duration and (iii) increasing the proportion of short calls. Our results demonstrate that marmosets, when able to freely choose what to vocalize, exhibit vocal statistical regularities consistent with Zipf's law of brevity that go beyond their context-specific natural vocal behaviour. This suggests that linguistic laws emerged in non-linguistic vocal systems in the primate lineage.},

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

pubstate = {published},

tppubtype = {article}

}

@article{Safryghin2022a,

title = {Variable expression of linguistic laws in ape gesture: a case study from chimpanzee sexual solicitation},

author = {A. Safryghin and C. Cross and B. Fallon and R. Heesen and R. Ferrer-i-Cancho and C. Hobaiter},

doi = {10.1098/rsos.220849},

year  = {2022},

date = {2022-01-01},

journal = {Royal Society Open Science},

volume = {9},

pages = {9220849},

abstract = {Two language laws have been identified as consistent patterns shaping animal behaviour, both acting on the organizational level of communicative systems. Zipf's law of brevity describes a negative relationship between behavioural length and frequency. Menzerath's law defines a negative correlation between the number of behaviours in a sequence and average length of the behaviour composing it. Both laws have been linked with the information-theoretic principle of compression, which tends to minimize code length. We investigated their presence in a case study of male chimpanzee sexual solicitation gesture. We failed to find evidence supporting Zipf's law of brevity, but solicitation gestures followed Menzerath's law: longer sequences had shorter average gesture duration. Our results extend previous findings suggesting gesturing may be limited by individual energetic constraints. However, such patterns may only emerge in sufficiently large datasets. Chimpanzee gestural repertoires do not appear to manifest a consistent principle of compression previously described in many other close-range systems of communication. Importantly, the same signallers and signals were previously shown to adhere to these laws in subsets of the repertoire when used in play; highlighting that, in addition to selection on the signal repertoire, ape gestural expression appears shaped by factors in the immediate socio-ecological context.},

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

pubstate = {published},

tppubtype = {article}

}

@article{Hernandez2022a,

title = {Compression principle and Zipf’s Law of brevity in infochemical communication},

author = {Antoni Hern\'{a}ndez-Fern\'{a}ndez and Iv\'{a}n G. Torre},

doi = {10.1098/rsbl.2022.0162},

year  = {2022},

date = {2022-01-01},

journal = {Biology Letters},

volume = {18},

pages = {20220162},

abstract = {Compression has been presented as a general principle of animal communication. Zipf’s Law of brevity is a manifestation of this postulate and can be generalized as the tendency of more frequent communicative elements to be shorter. Previous works supported this claim, showing evidence of Zipf’s Law of brevity in animal acoustical communication and human language. However, a significant part of the communicative effort in biological systems is carried out in other transmission channels, such as those based on infochemicals. To fill this gap, we seek, for the first time, evidence of this principle in infochemical communication by analysing the statistical tendency of more frequent infochemicals to be chemically shorter and lighter. We analyse data from the largest and most comprehensive open-access infochemical database known as Pherobase, recovering Zipf’s Law of brevity in interspecific communication (allelochemicals) but not in intraspecific communication (pheromones). Moreover, these results are robust even when addressing different magnitudes of study or mathematical approaches. Therefore, different dynamics from the compression principle would dominate intraspecific chemical communication, defying the universality of Zipf’s Law of brevity. To conclude, we discuss the exception found for pheromones in the light of other potential communicative paradigms such as pressures on successful communication or the Handicap principle.},

keywords = {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{Valente2021,

title = {Linguistic laws of brevity: conformity in Indri indri},

author = {Daria Valente and Chiara De Gregorio and Livio Favaro and Olivier Friard and Longondraza Miaretsoa and Teresa Raimondi and Jonah Ratsimbazafy and Valeria Torti and Anna Zanoli and Cristina Giacoma and Marco Gamba},

url = {https://doi.org/10.1007/s10071-021-01495-3},

doi = {10.1007/s10071-021-01495-3},

issn = {1435-9456},

year  = {2021},

date = {2021-03-08},

journal = {Animal Cognition},

abstract = {Vocal and gestural sequences of several primates have been found to conform to two general principles of information compression: the compensation between the duration of a construct and that of its components (Menzerath\textendashAltmann law) and an inverse relationship between signal duration and its occurrence (Zipf's law of abbreviation). Even though Zipf's law of brevity has been proposed as a universal in animal communication, evidence on non-human primate vocal behavior conformity to linguistic laws is still debated, and information on strepsirrhine primates is lacking. We analyzed the vocal behavior of the unique singing lemur species (Indri indri) to assess whether the song of the species shows evidence for compression. As roars have a chaotic structure that impedes the recognition of each individual utterance, and long notes are usually given by males, we focused on the core part of the song (i.e., the descending phrases, composed of two\textendashsix units). Our results indicate that indris' songs conform to Zipf's and Menzerath\textendashAltmann linguistic laws. Indeed, shorter phrases are more likely to be included in the song, and units' duration decrease at the increase of the size of the phrases. We also found that, despite a sexual dimorphism in the duration of both units and phrases, these laws characterize sequences of both males and females. Overall, we provide the first evidence for a trade-off between signal duration and occurrence in the vocal behavior of a strepsirrhine species, suggesting that selective pressures for vocal compression are more ancestral than previously assumed within primates.},

keywords = {Menzerath-Altmann law, 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{doi:10.1098/rsbl.2019.0589,

title = {Do penguins' vocal sequences conform to linguistic laws?},

author = {Livio Favaro and Marco Gamba and Eleonora Cresta and Elena Fumagalli and Francesca Bandoli and Cristina Pilenga and Valentina Isaja and Nicolas Mathevon and David Reby},

url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsbl.2019.0589},

doi = {10.1098/rsbl.2019.0589},

year  = {2020},

date = {2020-01-01},

journal = {Biology Letters},

volume = {16},

number = {2},

pages = {20190589},

abstract = {Information compression is a general principle of human language: the most frequent words are shorter in length (Zipf's Law of Brevity) and the duration of constituents decreases as the size of the linguistic construct increases (Menzerath\textendashAltmann Law). Vocal sequences of non-human primates have been shown to conform to both these laws, suggesting information compression might be a more general principle. Here, we investigated whether display songs of the African penguin, which mediate recognition, intersexual mate choice and territorial defence, conform with these laws. Display songs are long, loud sequences combining three types of syllables. We found that the shortest type of syllable was the most frequent (with the shortest syllable being repeated stereotypically, potentially favouring signal redundancy in crowded environments). We also found that the average duration of the song's constituents was negatively correlated with the size of the song (a consequence of increasing the relative number of the shortest syllable type, rather than reducing the duration across all syllable types, thus preserving the communication of size-related information in the duration of the longest syllable type). Our results provide the first evidence for conformity to Zipf's and Menzerath\textendashAltmann Laws in the vocal sequences of a non-primate species, indicating that these laws can coexist with selection pressures specific to the species' ecology.},

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

pubstate = {published},

tppubtype = {article}

}

@article{Clink2020a,

title = {Brevity is not a universal in animal communication: evidence for compression depends on the unit of analysis in small ape vocalizations},

author = {Abdul Hamid Ahmad Dena J. Clink and Holger Klinck},

url = {https://royalsocietypublishing.org/doi/full/10.1098/rsos.200151},

doi = {10.1098/rsos.200151},

year  = {2020},

date = {2020-01-01},

journal = {Royal Society Open Science},

pages = {7200151},

abstract = {Evidence for compression, or minimization of code length, has been found across biological systems from genomes to human language and music. Two linguistic laws-Menzerath's Law (which states that longer sequences consist of shorter constituents) and Zipf's Law of abbreviation (a negative relationship between signal length and frequency of use)-are predictions of compression. It has been proposed that compression is a universal in animal communication, but there have been mixed results, particularly in reference to Zipf's Law of abbreviation. Like songbirds, male gibbons (Hylobates muelleri) engage in long solo bouts with unique combinations of notes which combine into phrases. We found strong support for Menzerath's Law as the longer a phrase, the shorter the notes. To identify phrase types, we used state-of-the-art affinity propagation clustering, and were able to predict phrase types using support vector machines with a mean accuracy of 74%. Based on unsupervised phrase type classification, we did not find support for Zipf's Law of abbreviation. Our results indicate that adherence to linguistic laws in male gibbon solos depends on the unit of analysis. We conclude that principles of compression are applicable outside of human language, but may act differently across levels of organization in biological systems.},

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

pubstate = {published},

tppubtype = {article}

}

@article{HUANG2020145,

title = {Male gibbon loud morning calls conform to Zipf's law of brevity and Menzerath's law: insights into the origin of human language},

author = {Mingpan Huang and Haigang Ma and Changyong Ma and Paul A. Garber and Pengfei Fan},

url = {http://www.sciencedirect.com/science/article/pii/S000334721930377X},

doi = {https://doi.org/10.1016/j.anbehav.2019.11.017},

issn = {0003-3472},

year  = {2020},

date = {2020-01-01},

journal = {Animal Behaviour},

volume = {160},

pages = {145 - 155},

abstract = {The study of vocal communication in nonhuman primates, especially apes, offers critical insight into the origins of human language. Although human language represents a highly derived and complex form of communication, researchers have found that the organization of language follows a series of common statistical patterns, known as ‘linguistic laws’. Zipf's law of brevity and Menzerath's law are pervasive across human languages, and these laws have been identified in the communication of a small number of primate species. What remains less clear is whether these two laws also affect long-distance vocal communication in primates. Here, we provide evidence that the long-distance morning calls of male gibbons (cao vit gibbon, Nomascus nasutus, and western black-crested gibbon, Nomascus concolor) follow both Zipf's law of brevity and Menzerath's law. We found that notes of male gibbon calls conform to Zipf's law of brevity, with the most common notes being shortest in duration. Similarly, longer sequences are made up of shorter calls on average, consistent with Menzerath's law; we also found a shortening of specific note type duration and an increase in proportion of shorter call types in longer sequences, which may underpin the emergence of this law. Our findings support the generality of these two linguistic laws beyond human language and provide evidence for compression at two levels of organizations (how frequently different note types are used, and how vocal sequences are constructed) in a long-range communication system.},

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

pubstate = {published},

tppubtype = {article}

}

@article{https://doi.org/10.1002/evl3.147,

title = {The “Law of Brevity” in animal communication: Sex-specific signaling optimization is determined by call amplitude rather than duration},

author = {Vlad Demartsev and Naomi Gordon and Adi Barocas and Einat Bar-Ziv and Tchia Ilany and Yael Goll and Amiyaal Ilany and Eli Geffen},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/evl3.147},

doi = {https://doi.org/10.1002/evl3.147},

year  = {2019},

date = {2019-01-01},

journal = {Evolution Letters},

volume = {3},

number = {6},

pages = {623-634},

abstract = {Abstract The efficiency of informational transfer is one of the key aspects of any communication system. The informational coding economy of human languages is often demonstrated by their almost universal fit to Zipf's “Law of Brevity,” expressing negative relationship between word length and its usage frequency. Animal vocal systems, however, provided mixed results in their adherence to this relationship, potentially due to conflicting evolutionary pressures related to differences in signaling range and communicational needs. To examine this potential parallel between human and animal vocal communication, and also to explore how divergent, sex-specific, communicational settings affect signaling efficiency within a species, we examined the complete vocal repertoire of rock hyraxes (Procavia capensis). As male and female hyraxes differ in their sociality levels and male hyraxes vocal repertoire is dominated by sexual advertisement songs, we hypothesized that sex-specific vocal repertoires could be subjected to different signaling optimization pressures. Our results show that the sexes differ in repertoire size, call usage, and adherence to coding efficiency principles. Interestingly, the classic call length/call usage relationship is not consistently found in rock hyraxes. Rather, a negative relationship between call amplitude and call usage is found, suggesting that the efficiency of the vocal repertoire is driven by call amplitude rather than duration. We hypothesize that, in contrast to human speech that is mainly intended for short distance, the need for frequent long-range signaling shapes an animal's vocal repertoire efficiency according to the cost of call amplitude rather than call length. However, call duration may be a secondary factor affecting signaling efficiency, in cases where amplitude is under specific selection pressures, such as sexual selection.},

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

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1098/rspb.2018.2900,

title = {Linguistic laws in chimpanzee gestural communication},

author = {Raphaela Heesen and Catherine Hobaiter and Ramon Ferrer-i-Cancho and Stuart Semple},

url = {https://royalsocietypublishing.org/doi/abs/10.1098/rspb.2018.2900},

doi = {10.1098/rspb.2018.2900},

year  = {2019},

date = {2019-01-01},

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

volume = {286},

number = {1896},

pages = {20182900},

abstract = {Studies testing linguistic laws outside language have provided important insights into the organization of biological systems. For example, patterns consistent with Zipf's law of abbreviation (which predicts a negative relationship between word length and frequency of use) have been found in the vocal and non-vocal behaviour of a range of animals, and patterns consistent with Menzerath's law (according to which longer sequences are made up of shorter constituents) have been found in primate vocal sequences, and in genes, proteins and genomes. Both laws have been linked to compression-the information theoretic principle of minimizing code length. Here, we present the first test of these laws in animal gestural communication. We initially did not find the negative relationship between gesture duration and frequency of use predicted by Zipf's law of abbreviation, but this relationship was seen in specific subsets of the repertoire. Furthermore, a pattern opposite to that predicted was seen in one subset of gestures-whole body signals. We found a negative correlation between number and mean duration of gestures in sequences, in line with Menzerath's law. These results provide the first evidence that compression underpins animal gestural communication, and highlight an important commonality between primate gesturing and language.},

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

pubstate = {published},

tppubtype = {article}

}

@article{Ferrer2012a,

title = {The failure of the law of brevity in two New World primates. Statistical caveats},

author = {R. Ferrer-i-Cancho and A. Hern\'{a}ndez-Fern\'{a}ndez},

doi = {10.1524/glot.2013.0004},

year  = {2013},

date = {2013-01-01},

journal = {Glottotheory},

volume = {4},

number = {1},

abstract = {Parallels of Zipf’s law of brevity, the tendency of more frequent words to be shorter, have been found in bottlenose dolphins and Formosan macaques. Although these findings suggest that behavioral repertoires are shaped by a general principle of compression, common marmosets and golden-backed uakaris do not exhibit the law. However, we argue that the law may be impossible or difficult to detect statistically in a given species if the repertoire is too small, a problem that could be affecting golden backed uakaris, and show that the law is present in a subset of the repertoire of common marmosets. We suggest that the visibility of the law will depend on the subset of the repertoire under consideration or the repertoire size.},

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

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1111/cogs.12061,

title = {Compression as a Universal Principle of Animal Behavior},

author = {Ramon Ferrer-i-Cancho and Antoni Hern\'{a}ndez-Fern\'{a}ndez and David Lusseau and Govindasamy Agoramoorthy and Minna J. Hsu and Stuart Semple},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/cogs.12061},

doi = {10.1111/cogs.12061},

year  = {2013},

date = {2013-01-01},

journal = {Cognitive Science},

volume = {37},

number = {8},

pages = {1565-1578},

abstract = {Abstract A key aim in biology and psychology is to identify fundamental principles underpinning the behavior of animals, including humans. Analyses of human language and the behavior of a range of non-human animal species have provided evidence for a common pattern underlying diverse behavioral phenomena: Words follow Zipf's law of brevity (the tendency of more frequently used words to be shorter), and conformity to this general pattern has been seen in the behavior of a number of other animals. It has been argued that the presence of this law is a sign of efficient coding in the information theoretic sense. However, no strong direct connection has been demonstrated between the law and compression, the information theoretic principle of minimizing the expected length of a code. Here, we show that minimizing the expected code length implies that the length of a word cannot increase as its frequency increases. Furthermore, we show that the mean code length or duration is significantly small in human language, and also in the behavior of other species in all cases where agreement with the law of brevity has been found. We argue that compression is a general principle of animal behavior that reflects selection for efficiency of coding.},

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

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1080/09296174.2013.799917,

title = {The Law of Brevity in Macaque Vocal Communication is not an Artefact of Analysing Mean Call Durations},

author = {Stuart Semple and Minna J. Hsu and Govindasamy Agoramoorthy and Ramon Ferrer-i-Cancho},

url = {https://doi.org/10.1080/09296174.2013.799917},

doi = {10.1080/09296174.2013.799917},

year  = {2013},

date = {2013-01-01},

journal = {Journal of Quantitative Linguistics},

volume = {20},

number = {3},

pages = {209-217},

publisher = {Routledge},

abstract = {ABSTRACT Words follow the law of brevity, i.e. more frequent words tend to be shorter. From a statistical point of view, this qualitative definition of the law states that word length and word frequency are negatively correlated. Here the recent finding of patterning consistent with the law of brevity in Formosan macaque vocal communication (Semple, Hsu, \& Agoramoorthy, 2010) is revisited. It is shown that the negative correlation between mean duration and frequency of use in the vocalizations of Formosan macaques is not an artefact of the use of a mean duration for each call type instead of the customary ‘word’ length of studies of the law in human language. The key point demonstrated is that the total duration of calls of a particular type increases with the number of calls of that type. The finding of the law of brevity in the vocalizations of these macaques therefore defies a trivial explanation.},

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

pubstate = {published},

tppubtype = {article}

}

@article{Luo2013a,

title = {Brevity is prevalent in bat short-range communication},

author = {B. Luo and T. Jiang and Y. Liu and J. Wang and A. Lin and X. Wei and J. Feng},

year  = {2013},

date = {2013-01-01},

journal = {Journal of Comparative Physiology A},

volume = {199},

issue = {4},

pages = {325-333},

abstract = {Animal communication follows many coding schemes. Less is known about the coding strategy for signal length and rates of use in animal vocal communication. A generalized brevity (negative relation between signal length and frequency of use) is innovatively explored but remains controversial in animal vocal communication. We tested brevity for short-range social and distress sounds from four echolocating bats: adult black-bearded tomb bat Taphozous melanopogon, Mexican free-tailed bat Tadarida brasiliensis, adult greater horseshoe bat Rhinolophus ferrumequinum, and adult least horseshoe bat Rhinolophus pusillus. There was a negative association between duration and number of social but not distress calls emitted. The most frequently emitted social calls were brief, while most distress calls were long. Brevity or lengthiness was consistently selected in vocal communications for each species. Echolocating bats seem to have convergent coding strategy for communication calls. The results provide the evidence of efficient coding in bat social vocalizations, and lay the basis of future researches on the convergence for neural control on bats’ communication calls.},

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

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1098/rsbl.2010.0455,

title = {Brevity is not always a virtue in primate communication},

author = {Bruna M. Bezerra and Antonio S. Souto and Andrew N. Radford and Gareth Jones},

url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsbl.2010.0455},

doi = {10.1098/rsbl.2010.0455},

year  = {2011},

date = {2011-01-01},

journal = {Biology Letters},

volume = {7},

number = {1},

pages = {23-25},

abstract = {Semple et al. (Semple et al. in press, Biol. Lett. (doi:10.1098/rsbl.2009.1062)) argued that the ‘law of brevity’ (an inverse relationship between word length and frequency of use) applies not only to human language but also to vocal signalling in non-human primates, because coding efficiency is paramount in both situations. We analysed the frequency of use of signals of different duration in the vocal repertoires of two Neotropical primate species studied in the wild-the common marmoset (Callithrix jacchus) and the golden-backed uakari (Cacajao melanocephalus). The key prediction of the law of brevity was not supported in either species: although the most frequently emitted calls were relatively brief, they were not the shortest signals in the repertoire. The costs and benefits associated with signals of different duration must be appreciated to understand properly their frequency of use. Although relatively brief vocal signals may be favoured by natural selection in order to minimize energetic costs, the very briefest signals may be ambiguous, contain reduced information or be difficult to detect or locate, and may therefore be selected against. Analogies between human language and vocal communication in animals can be misleading as a basis for understanding frequency of use, because coding efficiency is not the only factor of importance in animal communication, and the costs and benefits associated with different signal durations will vary in a species-specific manner.},

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

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1098/rsbl.2009.1062,

title = {Efficiency of coding in macaque vocal communication},

author = {Stuart Semple and Minna J. Hsu and Govindasamy Agoramoorthy},

url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsbl.2009.1062},

doi = {10.1098/rsbl.2009.1062},

year  = {2010},

date = {2010-01-01},

journal = {Biology Letters},

volume = {6},

number = {4},

pages = {469-471},

abstract = {A key characteristic of human language efficiency is that more frequently used words tend to be shorter in length-the ‘law of brevity’. To date, no test of this relationship between frequency of use and length has been carried out on non-human animal vocal communication. We show here that the vocal repertoire of the Formosan macaque (Macaca cyclopis) conforms to the pattern predicted by the law of brevity, with an inverse relationship found between call duration and rate of utterance. This finding provides evidence for coding efficiency in the vocal communication system of this species, and indicates commonality in the basic structure of the coding system between human language and vocal communication in this non-human primate.},

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

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1002/cplx.20266,

title = {Efficient coding in dolphin surface behavioral patterns},

author = {Ramon Ferrer-i-Cancho and David Lusseau},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cplx.20266},

doi = {10.1002/cplx.20266},

year  = {2009},

date = {2009-01-01},

journal = {Complexity},

volume = {14},

number = {5},

pages = {23-25},

abstract = {Abstract We show that the law of brevity, i.e. the tendency of words to shorten as their frequency increases, is also found in dolphin surface behavioral patterns. As far as we know, this is the first evidence of the law in another species, suggesting that coding efficiency is not unique to humans.},

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

pubstate = {published},

tppubtype = {article}

}

@article{Hailman1987a,

title = {Constraints on the structure of combinatorial "chick-a-dee" calls},

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

doi = {10.1111/j.1439-0310.1987.tb00642.x},

year  = {1987},

date = {1987-01-01},

journal = {Ethology},

volume = {75},

pages = {62-80},

abstract = {Chickadee calls include 4 note types (A, B, C, and D) that occur in fixed sequence. Quantitative analyses determining the nature of departures from 1st-order transitional probabilities between successive notes in calls of the blackcapped chickadee found that (1) some constraint limited the length of calls (i.e., shortening of repetition strings, omitting of note types) and (2) there was an opposing tendency to include at least 1 D-note at the end of a call. The 2nd feature suggests semantic properties of D-notes. A chicakadee call is thought to resemble a natural sentence of spoken human language.},

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

pubstate = {published},

tppubtype = {article}

}

@article{Hailman1985,

title = {The 'chick-a-dee' calls of em Parus em atricapillus: a recombinant system of animal communication compared with written English},

author = {J. P. Hailman and M. S. Ficken and R. W. Ficken},

doi = {10.1515/semi.1985.56.3-4.191},

year  = {1985},

date = {1985-01-01},

journal = {Semiotica},

volume = {56},

pages = {121-224},

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

pubstate = {published},

tppubtype = {article}

}

@article{FICKEN1978630,

title = {A model of repetitive behaviour illustrated by chickadee calling},

author = {Millicent S. Ficken and Jack P. Hailman and Robert W. Ficken},

url = {http://www.sciencedirect.com/science/article/pii/0003347278900751},

doi = {10.1016/0003-3472(78)90075-1},

issn = {0003-3472},

year  = {1978},

date = {1978-01-01},

journal = {Animal Behaviour},

volume = {26},

pages = {630 - 631},

abstract = {If the probability of an animal's continuing (or repeating) a given behavioral pattern is independent of the elapsed time (or number of previous acts), the data conform to the exponential distribution generated by a Poisson process. The number of chickadee calls/bout was recorded for 1,524 bouts. Results show a negative linear relation between the number of calls/bout and the cumulative frequency of bouts when plotted on logarithmic axes.},

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

pubstate = {published},

tppubtype = {article}

}