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@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{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{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{Watson2024a,

title = {Inter-call intervals, but not call durations, adhere to Menzerath’s Law in the submissive vocal bouts of meerkats},

author = {Stuart Kyle Watson and Mara Zali and Nikola Falk and Paul Widmer and Marta B Manser},

doi = {10.1098/rsos.241351},

year  = {2024},

date = {2024-01-01},

journal = {Royal Society Open Science},

volume = {11},

number = {12},

abstract = {Diverse information encoding systems, including human language, the vocal and gestural systems of non-human animals and the structure of DNA and proteins, have been found to conform to ‘Menzerath’s Law’\textemdasha negative relationship between the number of units composing a sequence, and the size of those units. Here, we test for the presence of Menzerath’s Law in the vocal bouts produced in a submissive context by meerkats (Suricata suricatta). Using a suite of Bayesian mixed effects models, we examined 1676 vocal bouts produced by 89 wild meerkats, ranging from 1 to 590 calls in length, to determine whether the number of calls composing each bout had a negative relationship with the duration of those calls or their inter-call intervals. In contradiction to Menzerath’s Law, we found that the duration of vocalizations had a positive relationship with the number of calls in a bout. However, the duration of intervals between calls did have a negative relationship with bout size. Moreover, both calls and intervals had longer durations the closer they were positioned to the end of the bout. These findings highlight the multi-faceted ways in which efficiency trade-offs can occur in the vocal repertoires of non-human animals, shaping variability in the production of signal forms.},

keywords = {Menzerath-Altmann law},

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{James2021a,

title = {Phylogeny and mechanisms of shared hierarchical patterns in birdsong},

author = {Logan S. James and Chihiro Mori and Kazuhiro Wada and Jon T. Sakata},

doi = {10.1016/j.cub.2021.04.015},

year  = {2021},

date = {2021-01-01},

journal = {Current Biology},

volume = {31},

number = {13},

pages = {2796\textendash2808.e9},

abstract = {Organizational patterns can be shared across biological systems, and revealing the factors shaping common patterns can provide insight into fundamental biological mechanisms. The behavioral pattern that elements 

with more constituents tend to consist of shorter constituents (Menzerath’s law [ML]) was described first in speech and language (e.g., words with more syllables consist of shorter syllables) and subsequently in music and animal communication. Menzerath’s law is hypothesized to reflect efficiency in information transfer, but biases and constraints in motor production can also lead to this pattern. We investigated the evolutionary breadth of ML and the contribution of production mechanisms to ML in the songs of 15 songbird species. Negative relationships between the number and duration of constituents (e.g., syllables in phrases) were observed in all 15 species. However, negative relationships were also observed in null models in which constituents were randomly allocated into observed element durations, and the observed negative relationship for numerous species did not differ from the null model; consequently, ML in these species could simply reflect production constraints and not communicative efficiency. By contrast, ML was significantly different from the null model for more than half the cases, suggesting additional organizational rules are imposed onto birdsongs. Production mechanisms are also underscored by the finding that canaries and zebra finches reared without auditory experiences that guide vocal development produced songs with nearly identical ML patterning as typically reared birds. These analyses highlight the breadth with which production mechanisms contribute to this prevalent organizational pattern in behavior.},

keywords = {Menzerath-Altmann law},

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{life11060489,

title = {Menzerath\textendashAltmann’s law of syntax in RNA accretion history},

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

url = {https://www.mdpi.com/2075-1729/11/6/489},

doi = {10.3390/life11060489},

issn = {2075-1729},

year  = {2021},

date = {2021-01-01},

journal = {Life},

volume = {11},

number = {6},

pages = {489},

abstract = {RNA evolves by adding substructural parts to growing molecules. Molecular accretion history can be dissected with phylogenetic methods that exploit structural and functional evidence. Here, we explore the statistical behaviors of lengths of double-stranded and single-stranded segments of growing tRNA, 5S rRNA, RNase P RNA, and rRNA molecules. The reconstruction of character state changes along branches of phylogenetic trees of molecules and trees of substructures revealed strong pushes towards an economy of scale. In addition, statistically significant negative correlations and strong associations between the average lengths of helical double-stranded stems and their time of origin (age) were identified with the Pearson’s correlation and Spearman’s rho methods. The ages of substructures were derived directly from published rooted trees of substructures. A similar negative correlation was detected in unpaired segments of rRNA but not for the other molecules studied. These results suggest a principle of diminishing returns in RNA accretion history. We show this principle follows a tendency of substructural parts to decrease their size when molecular systems enlarge that follows the Menzerath\textendashAltmann’s law of language in full generality and without interference from the details of molecular growth.},

keywords = {Menzerath-Altmann law},

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{JAMES20212796,

title = {Phylogeny and mechanisms of shared hierarchical patterns in birdsong},

author = {Logan S. James and Chihiro Mori and Kazuhiro Wada and Jon T. Sakata},

url = {https://www.sciencedirect.com/science/article/pii/S0960982221005285},

doi = {https://doi.org/10.1016/j.cub.2021.04.015},

issn = {0960-9822},

year  = {2021},

date = {2021-01-01},

journal = {Current Biology},

volume = {31},

number = {13},

pages = {2796-2808.e9},

abstract = {Organizational patterns can be shared across biological systems, and revealing the factors shaping common patterns can provide insight into fundamental biological mechanisms. The behavioral pattern that elements with more constituents tend to consist of shorter constituents (Menzerath’s law [ML]) was described first in speech and language (e.g., words with more syllables consist of shorter syllables) and subsequently in music and animal communication. Menzerath’s law is hypothesized to reflect efficiency in information transfer, but biases and constraints in motor production can also lead to this pattern. We investigated the evolutionary breadth of ML and the contribution of production mechanisms to ML in the songs of 15 songbird species. Negative relationships between the number and duration of constituents (e.g., syllables in phrases) were observed in all 15 species. However, negative relationships were also observed in null models in which constituents were randomly allocated into observed element durations, and the observed negative relationship for numerous species did not differ from the null model; consequently, ML in these species could simply reflect production constraints and not communicative efficiency. By contrast, ML was significantly different from the null model for more than half the cases, suggesting additional organizational rules are imposed onto birdsongs. Production mechanisms are also underscored by the finding that canaries and zebra finches reared without auditory experiences that guide vocal development produced songs with nearly identical ML patterning as typically reared birds. These analyses highlight the breadth with which production mechanisms contribute to this prevalent organizational pattern in behavior.},

keywords = {Menzerath-Altmann law},

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{doi:10.1098/rsbl.2020.0380,

title = {An exploration of Menzerath's law in wild mountain gorilla vocal sequences},

author = {Stuart K. Watson and Raphaela Heesen and Daniela Hedwig and Martha M. Robbins and Simon W. Townsend},

url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsbl.2020.0380},

doi = {10.1098/rsbl.2020.0380},

year  = {2020},

date = {2020-01-01},

journal = {Biology Letters},

volume = {16},

number = {10},

pages = {20200380},

abstract = {Menzerath's law, traditionally framed as a negative relationship between the size of a structure and its constituent parts (e.g. sentences with more clauses have shorter clauses), is widespread across information-coding systems ranging from human language and the vocal and gestural sequences of primates and birds, to the building blocks of DNA, genes and proteins. Here, we analysed an extensive dataset of "close-call" sequences produced by wild mountain gorillas (Gorilla beringei beringei, no. individuals = 10, no. sequences = 2189) to determine whether, in accordance with Menzerath's law, a negative relationship existed between the number of vocal units in a sequence and the duration of its constituent units. We initially found positive evidence for this but, on closer inspection, the negative relationship was driven entirely by the difference between single- and multi-unit (two to six unit) sequences. Once single-unit sequences were excluded from the analysis, we identified a relationship in the opposite direction, with longer sequences generally composed of longer units. The close-call sequences of mountain gorillas therefore represent an intriguing example of a non-human vocal system that only partially conforms to the predictions of Menzerath's law.},

keywords = {Menzerath-Altmann law},

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{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{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{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{10.3389/fmicb.2017.01178,

title = {Phylogenetic Tracings of Proteome Size Support the Gradual Accretion of Protein Structural Domains and the Early Origin of Viruses from Primordial Cells},

author = {Arshan Nasir and Kyung Mo Kim and Gustavo Caetano-Anoll\'{e}s},

url = {https://www.frontiersin.org/article/10.3389/fmicb.2017.01178},

doi = {10.3389/fmicb.2017.01178},

issn = {1664-302X},

year  = {2017},

date = {2017-01-01},

journal = {Frontiers in Microbiology},

volume = {8},

pages = {1178},

abstract = {Untangling the origin and evolution of viruses remains a challenging proposition. We recently studied the global distribution of protein domain structures in thousands of completely sequenced viral and cellular proteomes with comparative genomics, phylogenomics, and multidimensional scaling methods. A tree of life describing the evolution of proteomes revealed viruses emerging from the base of the tree as a fourth supergroup of life. A tree of domains indicated an early origin of modern viral lineages from ancient cells that co-existed with the cellular ancestors. However, it was recently argued that the rooting of our trees and the basal placement of viruses was artifactually induced by small genome (proteome) size. Here we show that these claims arise from misunderstanding and misinterpretations of cladistic methodology. Trees are reconstructed unrooted, and thus, their topologies cannot be distorted a posteriori by the rooting methodology. Tracing proteome size in trees and multidimensional views of evolutionary relationships as well as tests of leaf stability and exclusion/inclusion of taxa demonstrated that the smallest proteomes were neither attracted toward the root nor caused any topological distortions of the trees. Simulations confirmed that taxa clustering patterns were independent of proteome size and were determined by the presence of known evolutionary relatives in data matrices, highlighting the need for broader taxon sampling in phylogeny reconstruction. Instead, phylogenetic tracings of proteome size revealed a slowdown in innovation of the structural domain vocabulary and four regimes of allometric scaling that reflected a Heaps law. These regimes explained increasing economies of scale in the evolutionary growth and accretion of kernel proteome repertoires of viruses and cellular organisms that resemble growth of human languages with limited vocabulary sizes. Results reconcile dynamic and static views of domain frequency distributions that are consistent with the axiom of spatiotemporal continuity that is tenet of evolutionary thinking.},

keywords = {Herdan\'s law},

pubstate = {published},

tppubtype = {article}

}

@article{10.1093/jole/lzx015,

title = {Divergent acoustic properties of gelada and baboon vocalizations and their implications for the evolution of human speech},

author = {Morgan L. Gustison and Thore J. Bergman},

url = {https://doi.org/10.1093/jole/lzx015},

doi = {10.1093/jole/lzx015},

issn = {2058-4571},

year  = {2017},

date = {2017-01-01},

journal = {Journal of Language Evolution},

volume = {2},

number = {1},

pages = {20-36},

abstract = {Human speech has many complex spectral and temporal features traditionally thought to be absent in the vocalizations of other primates. Recent explorations of the vocal capabilities of non-human primates are challenging this view. Here, we continue this trend by exploring the spectro-temporal properties of gelada (Theropithecus gelada) vocalizations. First, we made cross-species comparisons of geladas, chacma baboons, and human vowel space area. We found that adult male and female gelada exhaled grunts\textendasha call type shared with baboons-have formant profiles that overlap more with human vowel space than do baboon grunts. These gelada grunts also contained more modulation of fundamental and formant frequencies than did baboon grunts. Second, we compared formant profiles and modulation of exhaled grunts to the derived call types (those not shared with baboons) produced by gelada males. These derived calls contained divergent formant profiles, and a subset of them, notably wobbles and vocalized yawns, were more modulated than grunts. Third, we investigated the rhythmic patterns of wobbles, a call type shown previously to contain cycles that match the 3\textendash8 Hz tempo of speech. We use a larger dataset to show that the wobble rhythm overlaps more with speech rhythm than previously thought. We also found that variation in cycle duration depends on the production modality; specifically, exhaled wobbles were produced at a slower tempo than inhaled wobbles. Moreover, the variability in cycle duration within wobbles aligns with a linguistic property known as ‘Menzerath’s law’ in that there was a negative association between cycle duration and wobble size (i.e. the number of cycles). Taken together, our results add to growing evidence that non-human primates are anatomically capable of producing modulated sounds. Our results also support and expand on current hypotheses of speech evolution, including the ‘neural hypothesis’ and the ‘bimodal speech rhythm hypothesis’.},

keywords = {Menzerath-Altmann law},

pubstate = {published},

tppubtype = {article}

}

@article{Fedurek2017,

title = {Trade-offs in the production of animal vocal sequences: insights from the structure of wild chimpanzee pant hoots},

author = {Pawel Fedurek and Klaus Zuberb\"{u}hler and Stuart Semple},

url = {https://doi.org/10.1186/s12983-017-0235-8},

doi = {10.1186/s12983-017-0235-8},

issn = {1742-9994},

year  = {2017},

date = {2017-01-01},

journal = {Frontiers in Zoology},

volume = {14},

number = {1},

pages = {50},

abstract = {Vocal sequences - utterances consisting of calls produced in close succession - are common phenomena in animal communication. While many studies have explored the adaptive benefits of producing such sequences, very little is known about how the costs and constraints involved in their production affect their form. Here, we investigated this issue in the chimpanzee (Pan troglodytes schweinfurthii) pant hoot, a long and structurally complex vocal sequence comprising four acoustically distinct phases - introduction, build-up, climax and let-down.},

keywords = {Menzerath-Altmann law},

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1080/09296174.2016.1142323,

title = {The Infochemical Core},

author = {Antoni Hern\'{a}ndez-Fern\'{a}ndez and Ramon Ferrer-i-Cancho},

url = {https://doi.org/10.1080/09296174.2016.1142323},

doi = {10.1080/09296174.2016.1142323},

year  = {2016},

date = {2016-01-01},

journal = {Journal of Quantitative Linguistics},

volume = {23},

number = {2},

pages = {133-153},

publisher = {Routledge},

abstract = {Vocalizations, and less often gestures, have been the object of linguistic research for decades. However, the development of a general theory of communication with human language as a particular case requires a clear understanding of the organization of communication through other means. Infochemicals are chemical compounds that carry information and are employed by small organisms that cannot emit acoustic signals of an optimal frequency to achieve successful communication. Here, we investigate the distribution of infochemicals across species when they are ranked by their degree or the number of species with which they are associated (because they produce them or are sensitive to them). We evaluate the quality of the fit of different functions to the dependency between degree and rank by means of a penalty for the number of parameters of the function. Surprisingly, a double Zipf (a Zipf distribution with two regimes, each with a different exponent) is the model yielding the best fit although it is the function with the largest number of parameters. This suggests that the worldwide repertoire of infochemicals contains a core which is shared by many species and is reminiscent of the core vocabularies found for human language in dictionaries or large corpora.},

keywords = {Polytextuality (polytexty) versus rank},

pubstate = {published},

tppubtype = {article}

}

@article{GustisonE2750,

title = {Gelada vocal sequences follow Menzerath’s linguistic law},

author = {Morgan L. Gustison and Stuart Semple and Ramon Ferrer-i-Cancho and Thore J. Bergman},

url = {https://www.pnas.org/content/113/19/E2750},

doi = {10.1073/pnas.1522072113},

issn = {0027-8424},

year  = {2016},

date = {2016-01-01},

journal = {Proceedings of the National Academy of Sciences},

volume = {113},

number = {19},

pages = {E2750\textendashE2758},

publisher = {National Academy of Sciences},

abstract = {Human language follows a variety of structural principles, known as linguistic laws. One of these, Menzerath’s law, states that, the larger the size of the construct (e.g., the size of a word in terms of syllable number), the smaller the size of the individual constituent parts (e.g., syllables). We show for the first time (to our knowledge) that Menzerath’s law also holds in the vocal communication of a nonhuman species. In the gelada (Theropithecus gelada), a primate living in the highlands of Ethiopia, longer vocal sequences produced by adult males were associated with shorter individual calls. This result suggests that general\textemdashperhaps universal\textemdashprinciples underpin the structure of vocal communication in our own species and others.Identifying universal principles underpinning diverse natural systems is a key goal of the life sciences. A powerful approach in addressing this goal has been to test whether patterns consistent with linguistic laws are found in nonhuman animals. Menzerath’s law is a linguistic law that states that, the larger the construct, the smaller the size of its constituents. Here, to our knowledge, we present the first evidence that Menzerath’s law holds in the vocal communication of a nonhuman species. We show that, in vocal sequences of wild male geladas (Theropithecus gelada), construct size (sequence size in number of calls) is negatively correlated with constituent size (duration of calls). Call duration does not vary significantly with position in the sequence, but call sequence composition does change with sequence size and most call types are abbreviated in larger sequences. We also find that intercall intervals follow the same relationship with sequence size as do calls. Finally, we provide formal mathematical support for the idea that Menzerath’s law reflects compression\textemdashthe principle of minimizing the expected length of a code. Our findings suggest that a common principle underpins human and gelada vocal communication, highlighting the value of exploring the applicability of linguistic laws in vocal systems outside the realm of language.},

keywords = {Menzerath-Altmann law},

pubstate = {published},

tppubtype = {article}

}

@article{Shahzad2015,

title = {The organization of domains in proteins obeys Menzerath-Altmann's law of language},

author = {Khuram Shahzad and Jay E. Mittenthal and Gustavo Caetano-Anoll\'{e}s},

url = {https://doi.org/10.1186/s12918-015-0192-9},

doi = {10.1186/s12918-015-0192-9},

issn = {1752-0509},

year  = {2015},

date = {2015-01-01},

journal = {BMC Systems Biology},

volume = {9},

number = {1},

pages = {44},

abstract = {The combination of domains in multidomain proteins enhances their function and structure but lengthens the molecules and increases their cost at cellular level.},

keywords = {Menzerath-Altmann law},

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1002/cplx.21563,

title = {Self-organization of genic and intergenic sequence lengths in genomes: Statistical properties and linguistic coherence},

author = {Sertac Eroglu},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cplx.21563},

doi = {10.1002/cplx.21563},

year  = {2015},

date = {2015-01-01},

journal = {Complexity},

volume = {21},

number = {1},

pages = {268-282},

abstract = {In a genome, genes (coding constituents) are interrupted by intergenic regions (noncoding constituents). This study provides a general picture of the large-scale self-organization of coding, noncoding, and total constituent lengths in genomes. Ten model genomes were examined and strong correlations between the number of genomic constituents and the constituent lengths were observed. The analysis was carried out by adopting a linguistic distribution model and a structural analogy between linguistic and genomic constructs. The proposed linguistic-based statistical analysis may provide a fundamental basis for both understanding the linear structural formation of genomic constituents and developing insightful strategies to figure out the function of genic and intergenic regions in genomic sequences.},

keywords = {Menzerath-Altmann law},

pubstate = {published},

tppubtype = {article}

}

@article{Hobaiter2014,

title = {The Meanings of Chimpanzee Gestures},

author = {Catherine Hobaiter and Richard W Byrne},

url = {https://doi.org/10.1016/j.cub.2014.05.066},

doi = {10.1016/j.cub.2014.05.066},

issn = {0960-9822},

year  = {2014},

date = {2014-07-21},

journal = {Current Biology},

volume = {24},

number = {14},

pages = {1596-1600},

publisher = {Elsevier},

abstract = {Chimpanzees' use of gesture was described in the first detailed field study [1, 2], and natural use of specific gestures has been analyzed [3-5]. However, it was systematic work with captive groups that revealed compelling evidence that chimpanzees use gestures to communicate in a flexible, goal-oriented, and intentional fashion [6-8], replicated across all great ape species in captivity [9-17] and chimpanzees in the wild [18, 19]. All of these aspects overlap with human language but are apparently missing in most animal communication systems, including great ape vocalization, where extensive study has produced meager evidence for intentional use ([20], but see [21, 22]). Findings about great ape gestures spurred interest in a potential common ancestral origin with components of human language [23-25]. Of particular interest, given the relevance to language origins, is the question of what chimpanzees intend their gestures to mean; surprisingly, the matter of what the intentional signals are used to achieve has been largely neglected. Here we present the first systematic study of meaning in chimpanzee gestural communication. Individual gestures have specific meanings, independently of signaler identity, and we provide a partial 'lexicon'; flexibility is predominantly in the use of multiple gestures for a specific meaning. We distinguish a range of meanings, from simple requests associated with just a few gestures to broader social negotiation associated with a wider range of gesture types. Access to a range of alternatives may increase communicative subtlety during important social negotiations.},

keywords = {Law of meaning distribution, Meaning-frequency law},

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{NIKOLAOU2014134,

title = {Menzerath\textendashAltmann law in mammalian exons reflects the dynamics of gene structure evolution},

author = {Christoforos Nikolaou},

url = {http://www.sciencedirect.com/science/article/pii/S1476927114000978},

doi = {https://doi.org/10.1016/j.compbiolchem.2014.08.018},

issn = {1476-9271},

year  = {2014},

date = {2014-01-01},

journal = {Computational Biology and Chemistry},

volume = {53},

pages = {134 - 143},

abstract = {Genomic sequences exhibit self-organization properties at various hierarchical levels. One such is the gene structure of higher eukaryotes with its complex exon/intron arrangement. Exon sizes and exon numbers in genes have been shown to conform to a law derived from statistical linguistics and formulated by Menzerath and Altmann, according to which the mean size of the constituents of an entity is inversely related to the number of these constituents. We herein perform a detailed analysis of this property in the complete exon set of the mouse genome in correlation to the sequence conservation of each exon and the transcriptional complexity of each gene locus. We show that extensive linear fits, representative of accordance to Menzerath\textendashAltmann law are restricted to a particular subset of genes that are formed by exons under low or intermediate sequence constraints and have a small number of alternative transcripts. Based on this observation we propose a hypothesis for the law of Menzerath\textendashAltmann in mammalian genes being predominantly due to genes that are more versatile in function and thus, more prone to undergo changes in their structure. To this end we demonstrate one test case where gene categories of different functionality also show differences in the extent of conformity to Menzerath\textendashAltmann law.},

note = {Complexity in Genomes},

keywords = {Menzerath-Altmann law},

pubstate = {published},

tppubtype = {article}

}

@article{Ferrer2012h,

title = {When is Menzerath-Altmann law mathematically trivial? A new approach},

author = {R. Ferrer-i-Cancho and A. Hern\'{a}ndez-Fern\'{a}ndez and J. Baixeries and \L. D\k{e}bowski and J. Ma\v{c}utek},

doi = {10.1515/sagmb-2013-0034},

year  = {2014},

date = {2014-01-01},

journal = {Statistical Applications in Genetics and Molecular Biology},

volume = {13},

issue = {6},

pages = {633-644},

abstract = {Menzerath’s law, the tendency of Z (the mean size of the parts) to decrease as X (the number of parts) increases, is found in language, music and genomes. Recently, it has been argued that the presence of the law in genomes is an inevitable consequence of the fact that Z=Y/X, which would imply that Z scales with X as Z∼1/X. That scaling is a very particular case of Menzerath-Altmann law that has been rejected by means of a correlation test between X and Y in genomes, being X the number of chromosomes of a species, Y its genome size in bases and Z the mean chromosome size. Here we review the statistical foundations of that test and consider three non-parametric tests based upon different correlation metrics and one parametric test to evaluate if Z∼1/X in genomes. The most powerful test is a new non-parametric one based upon the correlation ratio, which is able to reject Z∼1/X in nine out of 11 taxonomic groups and detect a borderline group. Rather than a fact, Z∼1/X is a baseline that real genomes do not meet. The view of Menzerath-Altmann law as inevitable is seriously flawed.},

keywords = {Menzerath-Altmann law},

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:10.1002/cplx.21429,

title = {The challenges of statistical patterns of language: The case of Menzerath's law in genomes},

author = {Ramon Ferrer-I-Cancho and N\'{u}ria Forns and Antoni Hern\'{a}ndez-Fern\'{a}ndez and Gemma Bel-enguix and Jaume Baixeries},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cplx.21429},

doi = {10.1002/cplx.21429},

year  = {2013},

date = {2013-01-01},

journal = {Complexity},

volume = {18},

number = {3},

pages = {11-17},

abstract = {Abstract The importance of statistical patterns of language has been debated over decades. Although Zipf's law is perhaps the most popular case, recently, Menzerath's law has begun to be involved. Menzerath's law manifests in language, music and genomes as a tendency of the mean size of the parts to decrease as the number of parts increases in many situations. This statistical regularity emerges also in the context of genomes, for instance, as a tendency of species with more chromosomes to have a smaller mean chromosome size. It has been argued that the instantiation of this law in genomes is not indicative of any parallel between language and genomes because (a) the law is inevitable and (b) noncoding DNA dominates genomes. Here mathematical, statistical, and conceptual challenges of these criticisms are discussed. Two major conclusions are drawn: the law is not inevitable and languages also have a correlate of noncoding DNA. However, the wide range of manifestations of the law in and outside genomes suggests that the striking similarities between noncoding DNA and certain linguistics units could be anecdotal for understanding the recurrence of that statistical law.},

keywords = {Menzerath-Altmann law},

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{FERRERICANCHO2013216,

title = {Erratum to “Random models of Menzerath\textendashAltmann law in genomes” (BioSystems 107(3) (2012) 167\textendash173)},

author = {Ramon Ferrer-i-Cancho and Jaume Baixeries and Antoni Hern\'{a}ndez-Fern\'{a}ndez},

url = {http://www.sciencedirect.com/science/article/pii/S0303264713000191},

doi = {https://doi.org/10.1016/j.biosystems.2013.01.004},

issn = {0303-2647},

year  = {2013},

date = {2013-01-01},

journal = {Biosystems},

volume = {111},

number = {3},

pages = {216 - 217},

abstract = {Here we improve the mathematical arguments of Baixeries et al (BioSystems 107(3) (2012) 167\textendash173). The corrections do not alter the conclusion that the random breakage model yields an insufficient fit to the scaling of mean chromosome length as a function of chromosome number in real genomes.},

keywords = {Menzerath-Altmann law},

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1080/09296174.2013.773141,

title = {The Parameters of the Menzerath-Altmann Law in Genomes},

author = {Jaume Baixeries and Antoni Hern\'{a}ndez-Fern\'{a}ndez and N\'{u}ria Forns and Ramon Ferrer-i-Cancho},

url = {https://doi.org/10.1080/09296174.2013.773141},

doi = {10.1080/09296174.2013.773141},

year  = {2013},

date = {2013-01-01},

journal = {Journal of Quantitative Linguistics},

volume = {20},

number = {2},

pages = {94-104},

publisher = {Routledge},

abstract = {Abstract The relationship between the size of the whole and the size of the parts in language and music is known to follow the Menzerath-Altmann law at many levels of description (morphemes, words, sentences, …). Qualitatively, the law states that the larger the whole, the smaller its parts, e.g. the longer a word (in syllables) the shorter its syllables (in letters or phonemes). This patterning has also been found in genomes: the longer a genome (in chromosomes), the shorter its chromosomes (in base pairs). However, it has been argued recently that mean chromosome length is trivially a pure power function of chromosome number with an exponent of −1. The functional dependency between mean chromosome size and chromosome number in groups of organisms from three different kingdoms is studied. The fit of a pure power function yields exponents between −1.6 and 0.1. It is shown that an exponent of −1 is unlikely for fungi, gymnosperm plants, insects, reptiles, ray-finned fishes and amphibians. Even when the exponent is very close to −1, adding an exponential component is able to yield a better fit with regard to a pure power-law in plants, mammals, ray-finned fishes and amphibians. The parameters of the Menzerath-Altmann law in genomes deviate significantly from a power law with a −1 exponent with the exception of birds and cartilaginous fishes.},

keywords = {Menzerath-Altmann law},

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{doi:10.1002/cplx.20398,

title = {Menzerath's law at the gene-exon level in the human genome},

author = {Wentian Li},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cplx.20398},

doi = {10.1002/cplx.20398},

year  = {2012},

date = {2012-01-01},

journal = {Complexity},

volume = {17},

number = {4},

pages = {49-53},

abstract = {Abstract A previous discussion of a linguistic law called Menzerath's law (the longer a word, the shorter the syllables) in the genomic context was focused on the genome-chromosome-base level (the more number of chromosomes in a genome, the smaller the chromosome size). We apply this linguistic metaphor to more appropriate levels of gene, exon, and base. Using the human gene data, we found that the Menzerath's law at these levels holds true: the more number of exons in a gene, the shorted the averaged exon size. Since this negative correlation can be a trivial consequence of the constant size of the messenger RNA coded by the gene, we also exclude this possibility by showing that messenger RNA size increases with the number of exons. This increase of messenger RNA size is however not fast enough for genes with large number of exons to maintain a constant exon size.},

keywords = {Menzerath-Altmann law},

pubstate = {published},

tppubtype = {article}

}

@article{BAIXERIES2012167,

title = {Random models of Menzerath\textendashAltmann law in genomes},

author = {Jaume Baixeries and Antoni Hern\'{a}ndez-Fern\'{a}ndez and Ramon Ferrer-i-Cancho},

url = {http://www.sciencedirect.com/science/article/pii/S0303264711001924},

doi = {https://doi.org/10.1016/j.biosystems.2011.11.010},

issn = {0303-2647},

year  = {2012},

date = {2012-01-01},

journal = {Biosystems},

volume = {107},

number = {3},

pages = {167 - 173},

abstract = {Recently, a random breakage model has been proposed to explain the negative correlation between mean chromosome length and chromosome number that is found in many groups of species and is consistent with Menzerath\textendashAltmann law, a statistical law that defines the dependency between the mean size of the whole and the number of parts in quantitative linguistics. Here, the central assumption of the model, namely that genome size is independent from chromosome number is reviewed. This assumption is shown to be unrealistic from the perspective of chromosome structure and the statistical analysis of real genomes. A general class of random models, including that random breakage model, is analyzed. For any model within this class, a power law with an exponent of −1 is predicted for the expectation of the mean chromosome size as a function of chromosome length, a functional dependency that is not supported by real genomes. The random breakage and variants keeping genome size and chromosome number independent raise no serious objection to the relevance of correlations consistent with Menzerath\textendashAltmann law across taxonomic groups and the possibility of a connection between human language and genomes through that law.},

keywords = {Menzerath-Altmann law},

pubstate = {published},

tppubtype = {article}

}

@article{e13081465,

title = {Size of the Whole versus Number of Parts in Genomes},

author = {Antoni Hern\'{a}ndez-Fern\'{a}ndez and Jaume Baixeries and N\'{u}ria Forns and Ramon Ferrer-i-Cancho},

url = {https://www.mdpi.com/1099-4300/13/8/1465},

doi = {10.3390/e13081465},

issn = {1099-4300},

year  = {2011},

date = {2011-01-01},

journal = {Entropy},

volume = {13},

number = {8},

pages = {1465\textendash1480},

abstract = {It is known that chromosome number tends to decrease as genome size increases in angiosperm plants. Here the relationship between number of parts (the chromosomes) and size of the whole (the genome) is studied for other groups of organisms from different kingdoms. Two major results are obtained. First, the finding of relationships of the kind “the more parts the smaller the whole” as in angiosperms, but also relationships of the kind “the more parts the larger the whole”. Second, these dependencies are not linear in general. The implications of the dependencies between genome size and chromosome number are two-fold. First, they indicate that arguments against the relevance of the finding of negative correlations consistent with Menzerath-Altmann law (a linguistic law that relates the size of the parts with the size of the whole) in genomes are seriously flawed. Second, they unravel the weakness of a recent model of chromosome lengths based upon random breakage that assumes that chromosome number and genome size are independent.},

keywords = {Menzerath-Altmann law},

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{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}

}