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@article{Youngblood2026a,

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

author = {Mason Youngblood},

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

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

year  = {2026},

date = {2026-01-01},

journal = {Animal Cognition},

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

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

pubstate = {published},

tppubtype = {article}

}

@article{Liao2026,

title = {Investigating Menzerath’s law in crows and humans during cued vocal ‘counting’},

author = {Diana A. Liao and Akseli Ilmanen and Katharina F. Brecht and Andreas Nieder},

doi = {10.1007/s10071-026-02054-4},

year  = {2026},

date = {2026-01-01},

journal = {Animal Cognition},

abstract = {To uncover universal principles of vocal behavior, studies have examined whether linguistic laws apply across species. Menzerath’s law, for instance, posits that larger constructs have shorter constituent parts, reflecting an efficiency principle that reduces articulatory and energetic demands. Another proposed universal is final lengthening, where end-of-sequence vocalizations are extended to potentially signal sequence boundaries. While studies have examined these temporal patterns in ecological communicative contexts, it remains unclear whether they also emerge in more constrained, externally instructed vocal responses. This study examines temporal patterns in vocal sequences during a numerically cued production task in crows and humans. While both species performed the same task, they differ in their numerical representations: crows rely on an approximate number system, whereas humans possess a symbolic understanding of number. Crows showed a negative correlation between sequence length and vocalization duration\textemdashconsistent with Menzerath’s law\textemdashand a positive correlation between sequence position and duration, consistent with final lengthening. In contrast, humans exhibited the opposite: vocalization duration increased with sequence size and decreased with position. These findings suggest that Menzerath’s law is not a universal principle but shaped by species-specific cognition, motor constraints, and task demands. This highlights the importance of considering context and cognitive capacities when interpreting temporal patterns in vocal behavior across species.},

keywords = {Menzerath-Altmann law},

pubstate = {published},

tppubtype = {article}

}

@article{Deng2026a,

title = {Signal compression associated with Menzerath’s law affects the reproductive success of male frogs},

author = {Ke Deng and Yan-Mei Liu and Tong-Liang Wang and Ji-Chao Wang and Jian-Guo Cui},

doi = {10.1016/j.anbehav.2026.123484},

year  = {2026},

date = {2026-01-01},

journal = {Animal Behaviour},

volume = {233},

pages = {123484},

abstract = {Linguistic laws are widespread in both human language and nonhuman vocal communication systems. Although it has been proposed that signal compression (i.e. shortening the length) associated with linguistic laws promotes coding efficiency and reduces energy expenditure, the ecological consequences of signal compression remain largely unexplored. The advertisement calls of Hainan frilled treefrogs, Kurixalus hainanus, conform to Menzerath’s law, with the durations of both note and internote interval decreasing as call size increases. Moreover, the duration of notes declines with their position within a call. Using binary choice phonotaxis experiments, we examined whether and how signal compression affects mate attraction in K. hainanus. We show that female frogs exhibit a significant preference for advertisement calls with fixed note durations over natural advertisement calls, suggesting that the sexual attractiveness of compressed calls is reduced. In contrast, variation in internote intervals does not affect female choice preference. We provide the first experimental evidence that shortening the length of constituents in a vocal sequence with a specific construct size, while potentially efficient, can reduce sexual attractiveness and thus individual fitness. Our findings reveal a trade-off between signalling efficiency and information transmission effectiveness, highlighting how evolutionary and ecological pressures jointly shape animal communication systems.},

keywords = {Menzerath-Altmann law},

pubstate = {published},

tppubtype = {article}

}

@article{Wascher2025a,

title = {Vocal efficiency in crows},

author = {Claudia A. F. Wascher and Mason Youngblood},

doi = {10.1007/s10071-025-01985-8},

year  = {2025},

date = {2025-01-01},

journal = {Animal Cognition},

volume = {28},

number = {1},

publisher = {Springer Science and Business Media LLC},

abstract = {Many communicative systems have been selected for efficiency, shaped by the trade-off between information transmission and energetic or temporal constraints. Linguistic laws such as Menzerath’s law\textemdashpredicting shorter elements in longer sequences\textemdashhave emerged as widespread principles across vocal communication in many species. While these laws have been predominantly studied at the species level, the influence of individual and social factors remain underexplored. In this study, we investigated adherence to Menzerath’s law in the vocal communication of carrion crows, Corvus corone corone, hooded crows, Corvus corone cornix and hybrids. Our findings show that crow call sequences adhere to Menzerath’s law, with shorter calls occurring in longer sequences, demonstrating structural efficiency in vocal communication. In carrion crows specifically, we analysed call sequences in relation to individual characteristics (sex, age) and social variables (group size, dominance status, strength of affiliative relationships). Interestingly, adherence to Menzerath’s law was stronger in males and younger individuals, while no effects were found for group size, dominance, or affiliative relationships. This study provides the first evidence of Menzerath’s law in corvid vocal communication and suggests that individual-level traits, rather than broader social dynamics, may shape vocal efficiency. These findings broaden our understanding of widespread principles in animal communication and raise new questions about the ontogeny and flexibility of vocal efficiency in complex social species.},

keywords = {Menzerath-Altmann law},

pubstate = {published},

tppubtype = {article}

}

@article{Stepanov2025a,

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

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

doi = {10.3390/a18070392},

year  = {2025},

date = {2025-01-01},

journal = {Algorithms},

volume = {18},

number = {7},

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

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

pubstate = {published},

tppubtype = {article}

}

@article{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{Deng2024a,

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

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

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

year  = {2024},

date = {2024-01-01},

journal = {Animal Behaviour},

volume = {213},

pages = {51-59},

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

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

pubstate = {published},

tppubtype = {article}

}

@article{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{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{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{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{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{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{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{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{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{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{Clink2020b,

title = {Adherence to Menzerath's Law is the exception (not the rule) in three duetting primate species},

author = {Dena J. Clink and Allison R. Lau},

url = {https://doi.org/10.1098/rsos.201557},

doi = {10.1098/rsos.201557},

year  = {2020},

date = {2020-01-01},

journal = {Royal Society Open Science},

volume = {7},

number = {11},

pages = {201557},

abstract = {Across diverse systems including language, music and genomes, there is a tendency for longer sequences to contain shorter constituents; this phenomenon is known as Menzerath's Law. Whether Menzerath's Law is a universal in biological systems, is the result of compression (wherein shortest possible strings represent the maximum amount of information) or emerges from an inevitable relationship between sequence and constituent length remains a topic of debate. In non-human primates, the vocalizations of geladas, male gibbons and chimpanzees exhibit patterns consistent with Menzerath's Law. Here, we use existing datasets of three duetting primate species (tarsiers, titi monkeys and gibbons) to examine the wide-scale applicability of Menzerath's Law. Primate duets provide a useful comparative model to test for the broad-scale applicability of Menzerath's Law, as they evolved independently under presumably similar selection pressures and are emitted under the same context(s) across taxa. Only four out of the eight call types we examined were consistent with Menzerath's Law. Two of these call types exhibited a negative relationship between the position of the note in the call and note duration, indicating that adherence to Menzerath's Law in these call types may be related to breathing constraints. Exceptions to Menzerath's Law occur when notes are relatively homogeneous, or when species-specific call structure leads to a deterministic decrease in note duration. We show that adherence to Menzerath's Law is the exception rather than the rule in duetting primates. It is possible that selection pressures for long-range signals that can travel effectively over large distances was stronger than that of compression in primate duets. Future studies investigating adherence to Menzerath's Law across the vocal repertoires of these species will help us better elucidate the pressures that shape both short- and long-distance acoustic signals.},

keywords = {Menzerath-Altmann law},

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{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{10.1093/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{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{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{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{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{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{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:10.1080/09296174.2013.773141,

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{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{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{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{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:10.1002/cplx.20326,

title = {Genome size, self-organization and DNA's dark matter},

author = {Ricard V. Sol\'{e}},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cplx.20326},

doi = {10.1002/cplx.20326},

year  = {2010},

date = {2010-01-01},

journal = {Complexity},

volume = {16},

number = {1},

pages = {20-23},

abstract = {Abstract Chromosomes exhibit several features indicating that its spatiotemporal dynamics is self-organized. It has been recently suggested that a negative correlation between genome size and mean chromosome number would also be a fingerprint of selforganization, related to how human language is organized at the level of words and syllables. However, the vast dominance of non-coding DNA in eukaryotic genomes should prevent an interpretation of genome/chromosome size based on functional trade-offs related to information storage and transmission. Moreover, the reported negative correlation is shown to be an inevitable consequence of the definitions of chromosome and genome length and it is thus unrelated to any type of special generative process.},

keywords = {Menzerath-Altmann law},

pubstate = {published},

tppubtype = {article}

}

@article{doi:10.1002/cplx.20296,

title = {The self-organization of genomes},

author = {Ramon Ferrer-i-Cancho and N\'{u}ria Forns},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cplx.20296},

doi = {10.1002/cplx.20296},

year  = {2010},

date = {2010-01-01},

journal = {Complexity},

volume = {15},

number = {5},

pages = {34-36},

abstract = {Abstract Menzerath-Altmann law is a general law of human language stating, for instance, that the longer a word, the shorter its syllables. With the metaphor that genomes are words and chromosomes are syllables, we examine if genomes also obey the law. We find that longer genomes tend to be made of smaller chromosomes in organisms from three different kingdoms: fungi, plants, and animals. Our findings suggest that genomes self-organize under principles similar to those of human language},

keywords = {Menzerath-Altmann law},

pubstate = {published},

tppubtype = {article}

}