The challenges of statistical patterns of language: The case of Menzerath's law in genomes

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.2012 Wiley Periodicals, Inc. Complexity 18: [11][12][13][14][15][16][17] 2013 Key Words: statistical laws; language; genomes; music; non-coding DNA; Menzerath's law INTRODUCTIONA ttempts to demonstrate that statistical patterns of language have a trivial explanation have a long history that goes back at least to the research by G. A. Miller and collaborators questioning the relevance of Zipf's law for word frequencies around 1960 [1-3]. Zipf's law states that the curve that relates the frequency of a word f and its rank r (the most frequent word having rank 1, the second most frequent word having rank 2, and so on) should follow f $ r 2a [4]. Miller argued that if monkeys were chained ''to typewriters until they had produced some very long and random sequence of characters'' one would find ''exactly the same 'Zipf curves' for the monkeys as for the human authors '' [3]. Under his view, Zipf's law would be an inevitable consequence of the fact that words are made of units, e.g., letters or phonemes. The typewriter argument has been revived many times since then [5][6][7][8]. However, rigorous analyses indicate that the curves do not really look the same and the parameters of this random typing model giving a good fit to real word frequencies are not forthcoming [9,10] claim that the finding of another statistical pattern of language, Menzerath's law, is also inevitable [11]. P. Menzerath hypothesized that ''the greater the whole, the smaller its constituents'' (''Je größer das Ganze, desto kleiner die Teile'') in the context of language [12] (pp. 101). Converging research in music and genomes [13][14][15][16] suggests that Menzerath's law is a general law of natural and humanmade systems. In this article, we leave the term Menzerath-Altmann law for referring to the exact mathematical dependency that has been proposed by the quantitative linguistics traditi...

Gelada vocal sequences follow Menzerath’s linguistic law

“…The full power of linguistic laws may, however, extend far beyond the field in which they were developed (4, 5). Testing for conformity to linguistic laws in other biological systems facilitates a move from exploration of universal properties of language (62) to the development and testing of hypotheses about the fundamental principles that may explain the repeated occurrence of these statistical patterns across diverse biological contexts (4,5). Our demonstration of a pattern consistent with Menzerath's law in gelada vocal communication further highlights the value of exploring the full scope of linguistic laws outside the realm of language.…”

“…Finally, our demonstration of how a generalized principle of compression produces Menzerath's law, in conjunction with our previous work indicating that Zipf's law of abbreviation also reflects this principle (5), suggests that compression may underpin biological information systems in a broad sense. Compression exists not only at different levels of the chemistry of life-codons (63), proteins (23), genes (22), and entire genomes (18)-but also in multiple forms of animal behavior, from elementary patterns of behavior (7) to vocal communication in nonhumans (8,10) and human language (4,6,25).…”

“…There is currently great controversy about why diverse biological systems exhibit Menzerath's law and related laws (4,5,8,18,20,35), and indeed about whether such laws hold at all (9, 36). Our findings make a significant contribution to this ongoing debate, providing (to our knowledge) the first evidence for Menzerath's law in nonhuman animal vocal systems, and complementing a growing body of comparable evidence from a range of mammalian species (7,8,10) that behavior can be described by another, related linguistic law-Zipf's law of abbreviation (6).…”

“…The existence of such principles, revealed by the occurrence of common statistical patterns, can shed light on the basic processes shaping biological systems (3). In recent years, exploration of the universality of the statistical laws of human language has proved a fruitful starting point for identification and investigation of these fundamental principles (4,5). The power of such an approach is illustrated by recent studies of the generality of Zipf's law of abbreviation (6).…”

“…15). Although Menzerath's law was originally induced as a linguistic law, it has since been applied to a wide range of systems beyond human language: a negative correlation between construct and constituent size has been found in domains such as music (16) and at the molecular level, with species that have a larger number of chromosomes tending to have a smaller mean chromosome size (4,(17)(18)(19)(20), genes that have a higher number of exons having shorter exons on average (21,22), and proteins with a higher number of domains having on average shorter domains (23). This broad adherence to Menzerath's law can be interpreted as a manifestation of self-organization (24) and compression of information (14,25), and suggests that these processes may be widespread in shaping multilevel systems as diverse as macromolecules, language, and music.…”