Last update: 14 August, 2025.
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.
2014
Hobaiter, Catherine; Byrne, Richard W
The Meanings of Chimpanzee Gestures Journal Article
In: Current Biology, vol. 24, no. 14, pp. 1596-1600, 2014, ISSN: 0960-9822.
Abstract | Links | BibTeX | Tags: Law of meaning distribution, Meaning-frequency law
@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}
}
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.
2009
Ferrer-i-Cancho, Ramon; McCowan, Brenda
A Law of Word Meaning in Dolphin Whistle Types Journal Article
In: Entropy, vol. 11, no. 4, pp. 688–701, 2009, ISSN: 1099-4300.
Abstract | Links | BibTeX | Tags: Law of meaning distribution, Meaning-frequency law
@article{e11040688,
title = {A Law of Word Meaning in Dolphin Whistle Types},
author = {Ramon Ferrer-i-Cancho and Brenda McCowan},
url = {https://www.mdpi.com/1099-4300/11/4/688},
doi = {10.3390/e11040688},
issn = {1099-4300},
year = {2009},
date = {2009-01-01},
journal = {Entropy},
volume = {11},
number = {4},
pages = {688\textendash701},
abstract = {We show that dolphin whistle types tend to be used in specific behavioral contexts, which is consistent with the hypothesis that dolphin whistle have some sort of . Besides, in some cases, it can be shown that the behavioral context in which a whistle tends to occur or not occur is shared by different individuals, which is consistent with the hypothesis that dolphins are communicating through whistles. Furthermore, we show that the number of behavioral contexts significantly associated with a certain whistle type tends to grow with the frequency of the whistle type, a pattern that is reminiscent of a law of word meanings stating, as a tendency, that the higher the frequency of a word, the higher its number of meanings. Our findings indicate that the presence of Zipf's law in dolphin whistle types cannot be explained with enough detail by a simplistic die rolling experiment.},
keywords = {Law of meaning distribution, Meaning-frequency law},
pubstate = {published},
tppubtype = {article}
}
We show that dolphin whistle types tend to be used in specific behavioral contexts, which is consistent with the hypothesis that dolphin whistle have some sort of . Besides, in some cases, it can be shown that the behavioral context in which a whistle tends to occur or not occur is shared by different individuals, which is consistent with the hypothesis that dolphins are communicating through whistles. Furthermore, we show that the number of behavioral contexts significantly associated with a certain whistle type tends to grow with the frequency of the whistle type, a pattern that is reminiscent of a law of word meanings stating, as a tendency, that the higher the frequency of a word, the higher its number of meanings. Our findings indicate that the presence of Zipf's law in dolphin whistle types cannot be explained with enough detail by a simplistic die rolling experiment.