Last update: 16 July, 2022.
Launched: 27 December, 2011.
Note: the largest public bibliography of references on Zipf’s law for word frequencies is available here. Here we only offer a selection of references on Zipf’s law on animal behavior and organic chemistry.
Hint for browsing: Heaps’ law is another name for Herdan’s law.
2022
Ferrer-i-Cancho, R.; Lusseau, D.; McCowan, B.
Parallels of human language in the behavior of bottlenose dolphins Journal Article
In: Linguistic Frontiers, vol. 5, no. 1, pp. 5-11, 2022.
Abstract | Links | BibTeX | Tags: Law of meaning distribution, Meaning-frequency law, Menzerath-Altmann law, theory construction, Zipf's law for word frequencies, Zipf's law of abbreviation
@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}
}
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.
Semple, S.; Ferrer-i-Cancho, R.; Gustison, M.
Linguistic laws in biology Journal Article
In: Trends in Ecology and Evolution, vol. 37, no. 1, pp. 53-66, 2022.
Abstract | Links | BibTeX | Tags: Law of meaning distribution, Meaning-frequency law, Menzerath-Altmann law, Zipf's law for word frequencies, Zipf's law of abbreviation
@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}
}
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.
2021
Valente, Daria; Gregorio, Chiara De; Favaro, Livio; Friard, Olivier; Miaretsoa, Longondraza; Raimondi, Teresa; Ratsimbazafy, Jonah; Torti, Valeria; Zanoli, Anna; Giacoma, Cristina; Gamba, Marco
Linguistic laws of brevity: conformity in Indri indri Journal Article
In: Animal Cognition, 2021, ISSN: 1435-9456.
Abstract | Links | BibTeX | Tags: Menzerath-Altmann law, Zipf's law of abbreviation
@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--Altmann 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--six units). Our results indicate that indris' songs conform to Zipf's and Menzerath--Altmann 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}
}
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--Altmann 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--six units). Our results indicate that indris' songs conform to Zipf's and Menzerath--Altmann 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.
Caetano-Anollés, Gustavo
The compressed vocabulary of microbial life Journal Article
In: Frontiers in Microbiology, vol. 12, pp. 1273, 2021, ISSN: 1664-302X.
Abstract | Links | BibTeX | Tags: Herdan's law, Menzerath-Altmann law, Zipf's law for word frequencies, Zipf's law of abbreviation
@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}
}
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–Altmann’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.
2020
Clink, Abdul Hamid Ahmad Dena J.; Klinck, Holger
Brevity is not a universal in animal communication: evidence for compression depends on the unit of analysis in small ape vocalizations Journal Article
In: Royal Society Open Science, pp. 7200151, 2020.
Abstract | Links | BibTeX | Tags: Menzerath-Altmann law, Zipf's law of abbreviation
@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}
}
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.
Favaro, Livio; Gamba, Marco; Cresta, Eleonora; Fumagalli, Elena; Bandoli, Francesca; Pilenga, Cristina; Isaja, Valentina; Mathevon, Nicolas; Reby, David
Do penguins' vocal sequences conform to linguistic laws? Journal Article
In: Biology Letters, vol. 16, no. 2, pp. 20190589, 2020.
Abstract | Links | BibTeX | Tags: Menzerath-Altmann law, Zipf's law of abbreviation
@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}
}
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–Altmann 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–Altmann Laws in the vocal sequences of a non-primate species, indicating that these laws can coexist with selection pressures specific to the species' ecology.
Huang, Mingpan; Ma, Haigang; Ma, Changyong; Garber, Paul A.; Fan, Pengfei
Male gibbon loud morning calls conform to Zipf's law of brevity and Menzerath's law: insights into the origin of human language Journal Article
In: Animal Behaviour, vol. 160, pp. 145 - 155, 2020, ISSN: 0003-3472.
Abstract | Links | BibTeX | Tags: Menzerath-Altmann law, Zipf's law of abbreviation
@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}
}
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.
2019
Demartsev, Vlad; Gordon, Naomi; Barocas, Adi; Bar-Ziv, Einat; Ilany, Tchia; Goll, Yael; Ilany, Amiyaal; Geffen, Eli
The “Law of Brevity” in animal communication: Sex-specific signaling optimization is determined by call amplitude rather than duration Journal Article
In: Evolution Letters, vol. 3, no. 6, pp. 623-634, 2019.
Abstract | Links | BibTeX | Tags: Menzerath-Altmann law, Zipf's law of abbreviation
@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}
}
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.
Heesen, Raphaela; Hobaiter, Catherine; Ferrer-i-Cancho, Ramon; Semple, Stuart
Linguistic laws in chimpanzee gestural communication Journal Article
In: Proceedings of the Royal Society B: Biological Sciences, vol. 286, no. 1896, pp. 20182900, 2019.
Abstract | Links | BibTeX | Tags: Zipf's law of abbreviation
@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}
}
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.
2013
Ferrer-i-Cancho, Ramon; Hernández-Fernández, Antoni; Lusseau, David; Agoramoorthy, Govindasamy; Hsu, Minna J; Semple, Stuart
Compression as a Universal Principle of Animal Behavior Journal Article
In: Cognitive Science, vol. 37, no. 8, pp. 1565-1578, 2013.
Abstract | Links | BibTeX | Tags: Zipf's law of abbreviation
@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}
}
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.
Ferrer-i-Cancho, R; Hernández-Fernández, A
The failure of the law of brevity in two New World primates. Statistical caveats Journal Article
In: Glottotheory, vol. 4, no. 1, 2013.
Abstract | Links | BibTeX | Tags: Zipf's law of abbreviation
@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}
}
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.
Luo, B.; Jiang, T.; Liu, Y.; Wang, J.; Lin, A.; Wei, X.; Feng, J.
Brevity is prevalent in bat short-range communication Journal Article
In: Journal of Comparative Physiology A, vol. 199, iss. 4, pp. 325-333, 2013.
Abstract | BibTeX | Tags: Zipf's law of abbreviation
@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}
}
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.
Semple, Stuart; Hsu, Minna J.; Agoramoorthy, Govindasamy; Ferrer-i-Cancho, Ramon
The Law of Brevity in Macaque Vocal Communication is not an Artefact of Analysing Mean Call Durations Journal Article
In: Journal of Quantitative Linguistics, vol. 20, no. 3, pp. 209-217, 2013.
Abstract | Links | BibTeX | Tags: Zipf's law of abbreviation
@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}
}
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.
2011
Bezerra, Bruna M; Souto, Antonio S; Radford, Andrew N; Jones, Gareth
Brevity is not always a virtue in primate communication Journal Article
In: Biology Letters, vol. 7, no. 1, pp. 23-25, 2011.
Abstract | Links | BibTeX | Tags: Zipf's law of abbreviation
@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}
}
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.
2010
Semple, Stuart; Hsu, Minna J; Agoramoorthy, Govindasamy
Efficiency of coding in macaque vocal communication Journal Article
In: Biology Letters, vol. 6, no. 4, pp. 469-471, 2010.
Abstract | Links | BibTeX | Tags: Zipf's law of abbreviation
@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}
}
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.
2009
Ferrer-i-Cancho, Ramon; Lusseau, David
Efficient coding in dolphin surface behavioral patterns Journal Article
In: Complexity, vol. 14, no. 5, pp. 23-25, 2009.
Abstract | Links | BibTeX | Tags: Zipf's law of abbreviation
@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}
}
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.
1987
Hailman, J P; Ficken, M S; Ficken, R
Constraints on the structure of combinatorial "chick-a-dee" calls Journal Article
In: Ethology, vol. 75, pp. 62-80, 1987.
Abstract | Links | BibTeX | Tags: Zipf's law of abbreviation
@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}
}
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.
1985
Hailman, J P; Ficken, M S; Ficken, R W
The 'chick-a-dee' calls of em Parus em atricapillus: a recombinant system of animal communication compared with written English Journal Article
In: Semiotica, vol. 56, pp. 121-224, 1985.
Links | BibTeX | Tags: Zipf's law of abbreviation
@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}
}
1978
Ficken, Millicent S; Hailman, Jack P; Ficken, Robert W
A model of repetitive behaviour illustrated by chickadee calling Journal Article
In: Animal Behaviour, vol. 26, pp. 630 - 631, 1978, ISSN: 0003-3472.
Abstract | Links | BibTeX | Tags: Zipf's law of abbreviation
@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}
}
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.