Bibliography on laws of language outside human language.
Statistical laws of language in the behavior of other species, genomes and beyond.

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Last update: 24 August, 2017.
Launched: 27 December, 2011.


Currently, the bibliography covers the following statistical 'laws' of human language:
Heaps' law
Nasir, A., Kim, K.M. and Caetano-Anollés, G. (2017). Phylogenetic tracings of proteome size support the gradual accretion of protein structural domains and the early origin of viruses from primordial cells. Frontiers in Microbioly 8, 1178.
[ doi: 10.3389/fmicb.2017.01178 ]
Law of abbreviation

Luo, B., Jiang, T., Liu, Y., Wang, J., Lin, A., Wei, X. and Feng, J. (2013). Brevity is prevalent in bat short-range communication. Journal of Comparative Physiology A 199 (4), 325-333.
[ doi: 10.1007/s00359-013-0793-y ]

Semple, S., Hsu, M. J., Agoramoorthy, G., Ferrer-i-Cancho, R. (2013). The law of brevity in macaque vocal communication is not an artifact of analyzing mean call durations. Journal of Quantitative Linguistics 20 (3), 209-217.
[ doi: 10.1080/09296174.2013.799917 ]

Ferrer-i-Cancho, R., Hernández-Fernández, A., Lusseau, D., Agoramoorthy, G., Hsu, M. J. & Semple, S. (2013). Compression as a universal principle of animal behavior. Cognitive Science 37 (8), 1565–1578..
[ doi: 10.1111/cogs.12061, e-print ]

Ferrer-i-Cancho, R. & Hernández-Fernández, A. (2013). The failure of the law of brevity in two New World primates. Statistical caveats. Glottotheory 4 (1), 45-55.
[ doi: 10.524/glot.2013.0004 ]

Bezerra, B. M., Souto, A. S., Radford, A.N. & Jones, G. (2011). Brevity is not always a virtue in primate communication. Biology Letters 7, 23-25.
[ doi: 10.1098/rsbl.2010.0455 ]

Semple, S., Hsu, M.J. & Agoramoorthy, G. (2010). Efficiency of coding in macaque vocal communication. Biology Letters 6, 469-471.
[ doi: 10.1098/rsbl.2009.1062 ]

Ferrer-i-Cancho, R. & Lusseau, D. (2009). Efficient coding in dolphin surface behavioral patterns. Complexity 14 (5), 23-25.
[ doi: 10.1002/cplx.20266 ]

Hailman, J. (1987). Constraints on the structure of combinatorial 'chick-a-dee' calls. Ethology 75, 62-80.

Hailman, J. P., Ficken, M. S. & Ficken, R. W. (1985). The ‘chick-a-dee’ calls of Parus atricapillus: a recombinant system of animal communication compared with written English. Semiotica 56, 191–224.

Ficken, M. S., Hailman, J. P., & Ficken, R. W. (1978). A model of repetitive behaviour illustrated by chickadee calling. Animal Behaviour 26 (2), 630-631.
[ doi: 10.1016/0003-3472(78)90075-1 ]

Menzerath-Altmann law

Gustison, M.L, Semple, S., Ferrer-i-Cancho, R. & Bergman, T. J.  (2016). Gelada vocal sequences follow Menzerath’s linguistic law.  Proceedings of the National Academy of Sciences USA 113 (19), E2750-E2758.
[ doi: 10.1073/pnas.1522072113 ]

Shahzad, K., Caetano-Anolls, G., & Mittenthal, J.E. (2015). The organization of domains in proteins obeys Menzerath-Altmann’s law of language.  BMC Systems Biology 9 (44), 1-13.
[ doi: 10.1186/s12918-015-0192-9 ]

Nikolaou, C. (2014). Menzerath–Altmann law in mammalian exons reflects the dynamics of gene structure evolution. Computational Biology and Chemistry 53, 134-143.
[ doi: 10.1016/j.compbiolchem.2014.08.018 ]

Ferrer-i-Cancho, R., Hernández-Fernández, A., Baixeries, J., Dębowski, Ł. & Macutek, J. (2014). When is Menzerath-Altmann law mathematically trivial? A new approach. Statistical Applications in Genetics and Molecular Biology 13 (6), 633–644.
[ doi: 10.1515/sagmb-2013-0034 ]

Eroglu, S. (2014). Self-organization of genic and intergenic sequence lengths in genomes: Statistical properties and linguistic coherence. Complexity 21 (1), 268–282.
[ doi: 10.1002/cplx.21563 ]

Ferrer-i-Cancho, R., Baixeries, J. & Hernández-Fernández, A. (2013). Erratum to "Random models of Menzerath-Altmann law in genomes" (BioSystems 107 (3), 167–173). BioSystems 111 (3), 216-217.
[ doi: 10.1016/j.biosystems.2013.01.004 ]

Baixeries, J., Hernández-Fernández, A., Forns, N. & Ferrer-i-Cancho, R. (2013). The parameters of Menzerath-Altmann law in genomes. Journal of Quantitive Linguistics 20 (2), 94–104.
[ doi: 10.1080/09296174.2013.773141 ]

Ferrer-i-Cancho, R., Forns, N., Hernández-Fernández, A., Bel-Enguix, G. & Baixeries, J. (2012). The challenges of statistical patterns of language: the case of Menzerath’s law in genomes. Complexity 18 (3), 11–17.
[ doi: 10.1002/cplx.21429 , e-print ]

Li, W. (2012). Menzerath’s law at the gene-exon level in the human genome. Complexity 17 (4), 49–53.
[ doi: 10.1002/cplx.20398 ]

Baixeries, J., Hernández-Fernández, A. & Ferrer-i-Cancho, R. (2012). Random models of Menzerath-Altmann law in genomes. BioSystems 107 (3), 167–173.
[ doi: 10.1016/j.biosystems.2011.11.010 ]

Hernández-Fernández, A., Baixeries, J., Forns, N. & Ferrer-i-Cancho, R. (2011). Size of the whole versus number of parts in genomes. Entropy 13 (8), 1465-1480.
[ doi: 10.3390/e13081465 ]


Solé, R. V.  (2010). Genome size, self-organization and DNA's dark matter.  Complexity 16 (1), 20-23.
[ doi: 10.1002/cplx.20326 ]

Ferrer-i-Cancho, R. & Forns, N. (2009). The self-organization of genomes. Complexity 15 (5), 34-36.
doi: 10.1002/cplx.20296 ]

Wilde, J. & Schwibbe, M. H. (1989). Organizationsformen von Erbinformation Im Hinblick auf die Menzerathsche Regel, G. Altmann, M.H. Schwibbe, Editors, Das Menzerathsche Gesetz in informationsverarbeitenden Systemen, Olms, Hildesheim (1989), pp. 92–107.

Law of meaning distribution / Meaning-frequency law

Hobaiter, C. & Byrne, R. W. (2014). The meanings of chinpanzee gestures. Current Biology 24, 1596-1600.
[ doi: 10.1016/j.cub.2014.05.066 ]
Ferrer-i-Cancho, R. & McCowan, B. (2009). A law of word meaning in dolphin whistle types. Entropy 11 (4), 688-701.
[ doi: 10.3390/e11040688 ]

Polytextuality (polytexty) versus rank

Hernández-Fernández, A. & Ferrer-i-Cancho, R. (2016). The infochemical core. Journal of Quantitative Linguistics 23 (2), 133-153.
[ doi: 10.1080/09296174.2016.1142323 ]

Zipf's law

The largest public bibliography of references on Zipf's law can be found here.
In this section, we plan to offer a selection of references on Zipf's law on animal behavior and organic chemistry.

Cadeddu, A., Wylie, E. K., Jurczak, J., Wampler-Doty, M. & Grzybowski, B.A. (2014). Organic chemistry as a language and the implications of chemical linguistics for structural and retrosynthetic analyses. Angewandte Communications International Edition 53, 8108-8112.
[ doi: 10.1002/anie.201403708 ]

Ferrer-i-Cancho, R. & McCowan, B. (2012). The span of correlations in dolphin whistle sequences. Journal of Statistical Mechanics, P06002.
[ doi: 10.1088/1742-5468/2012/06/P06002 ]

Freeberg, T. M. & Lucas, J. R. (2012). Information theoretical approaches to chick-a-dee calls of Carolina chickadees (Poecile carolinensis). Journal of Comparative Psychology 126 (1), 68-81.
[ doi: 10.1037/a0024906 ]

Doyle, L. R., McCowan, B., Johnston, S. & Hanser, S. F. (2011). Information theory, animal communication, and the search for extraterrestrial intelligence, Acta Astronautica 68 (3-4), 406-417.
[ doi: 10.1016/j.actaastro.2009.11.018 ]

Genty, E. & Byrne (2010). Why do gorillas make sequences of gestures? Animal Cognition 13 (2), 287-301.
[ doi: 10.1007/s10071-009-0266-4 ]

Lucas, J. R. & Freeberg, T. M. (2007). “Information” and the chick-a-dee call: communicating with a complex vocal system. In K. Otter (Ed.), Ecology and Behavior of Chickadees and Titmice: An Integrated Approach, (pp. 199-213). Oxford: Oxford University Press.

McCowan, B., Doyle, L. R., Jenkins, J. & Hanser, S. F. (2005) The appropriate use of Zipf’s law in animal communication studies. Animal Behaviour 69, F1-F7.
[ doi: 10.1016/j.anbehav.2004.09.002 ]

Suzuki, R., Buck, J. R. & Tyack, P.L. (2005). The use of Zipf's law in animal communication. Animal Behaviour 69, F9-F17.
[ doi: 10.1016/j.anbehav.2004.08.004 ]

McCowan, B., Doyle, L. R. & Hanser, S. F. (2002). Using information theory to assess the diversity, complexity and development of communicative repertoires. Journal of Comparative Psychology 116, 166-172.
[ doi: 10.1037/0735-7036.116.2.166 ]

Searls, D. A. (2002). The language of genes. Nature 420, 211-217.
[ doi: 10.1038/nature01255 ]

McCowan, B., Hanser, S. F. & Doyle, L. R. (1999). Quantitative tools for comparing animal communication systems: information theory applied to bottlenose dolphin whistle repertoires. Animal Behaviour 57, 409-419.
[ doi: 10.1006/anbe.1998.1000 ]

Ficken, M. S., Hailman, E. D. & Hailman, J. P. (1994). The chick-adee call system of the Mexican chickadee. Condor 96, 70–82.

Hailman, J. P. (1994). Constrained permutation in ‘chick-a-dee’-like calls of the black-lored tit, Parus xanthogenys. Bioacoustics, 6, 33–50.

Markov, V. I. & Ostrovskaya, V. M. (1990). Organization of communication system in Tursiops truncatus Montagu. In: Sensory abilities of cetaceans, Thomas, J. & Kastelein, R. (eds.). NATO ASI Series. Vol. 196,  New York: Plenum Press. pp. 599-622
[ doi: 10.1007/978-1-4899-0858-2_42 ]

Hailman, J. P., Ficken, M. S. & Ficken, R. W. (1985). The ‘chick-a-dee’ calls of Parus atricapillus: a recombinant system of animal communication compared with written English. Semiotica 56, 191–224.

Related bibliographies

Bibliography on Quantitative Linguistics (BQL)
Zipf's law (by Wentian Li)
Webgraph bibliography (by Dragomir R. Radev)
Linguistic and cognitive networks (by Ramon Ferrer-i-Cancho)
Language evolution and computation


If you have corrections to suggest or find references that could be added to this repository, please send an email to with the details of the publication.


This bibliography has been compiled with the help of Stuart Semple and Antoni Hernández-Fernández.