Linguistic laws in biology.

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 organisation underpinning natural systems, unifying linguistic laws and core theory in biology.

Variable expression of linguistic laws in ape gesture: a case study from chimpanzee sexual solicitation.

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.

Optimality of syntactic dependency distances.

It is often stated that human languages, as other biological systems, are shaped by cost-cutting pressures but, to what extent? Attempts to quantify the degree of optimality of languages by means of an optimality score have been scarce and focused mostly on English. Here we recast the problem of the optimality of the word order of a sentence as an optimization problem on a spatial network where the vertices are words, arcs indicate syntactic dependencies, and the space is defined by the linear order of the words in the sentence. We introduce a score to quantify the cognitive pressure to reduce the distance between linked words in a sentence. The analysis of sentences from 93 languages representing 19 linguistic families reveals that half of languages are optimized to a 70% or more. The score indicates that distances are not significantly reduced in a few languages and confirms two theoretical predictions: that longer sentences are more optimized and that distances are more likely to be longer than expected by chance in short sentences. We present a hierarchical ranking of languages by their degree of optimization. The score has implications for various fields of language research (dependency linguistics, typology, historical linguistics, clinical linguistics, and cognitive science). Finally, the principles behind the design of the score have implications for network science.

Linguistic laws in biology.

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 organisation underpinning natural systems, unifying linguistic laws and core theory in biology.

Zipf's laws of meaning in Catalan.

In his pioneering research, G. K. Zipf formulated a couple of statistical laws on the relationship between the frequency of a word with its number of meanings: the law of meaning distribution, relating the frequency of a word and its frequency rank, and the meaning-frequency law, relating the frequency of a word with its number of meanings. Although these laws were formulated more than half a century ago, they have been only investigated in a few languages. Here we present the first study of these laws in Catalan. We verify these laws in Catalan via the relationship among their exponents and that of the rank-frequency law. We present a new protocol for the analysis of these Zipfian laws that can be extended to other languages. We report the first evidence of two marked regimes for these laws in written language and speech, paralleling the two regimes in Zipf's rank-frequency law in large multi-author corpora discovered in early 2000s. Finally, the implications of these two regimes will be discussed.

Paradigmatic De Novo GRIN1 Variants Recapitulate Pathophysiological Mechanisms Underlying GRIN1-Related Disorder Clinical Spectrum.

BACKGROUND: GRIN-related disorders (GRD), the so-called grinpathies, is a group of rare encephalopathies caused by mutations affecting GRIN genes (mostly GRIN1, GRIN2A and GRIN2B genes), which encode for the GluN subunit of the N-methyl D-aspartate (NMDA) type ionotropic glutamate receptors. A growing number of functional studies indicate that GRIN-encoded GluN1 subunit disturbances can be dichotomically classified into gain- and loss-of-function, although intermediate complex scenarios are often present. METHODS: In this study, we aimed to delineate the structural and functional alterations of GRIN1 disease-associated variants, and their correlations with clinical symptoms in a Spanish cohort of 15 paediatric encephalopathy patients harbouring these variants. RESULTS: Patients harbouring GRIN1 disease-associated variants have been clinically deeply-phenotyped. Further, using computational and in vitro approaches, we identified different critical checkpoints affecting GluN1 biogenesis (protein stability, subunit assembly and surface trafficking) and/or NMDAR biophysical properties, and their association with GRD clinical symptoms. CONCLUSIONS: Our findings show a strong correlation between GRIN1 variants-associated structural and functional outcomes. This structural-functional stratification provides relevant insights of genotype-phenotype association, contributing to future precision medicine of GRIN1-related encephalopathies.

Distinct flavors of Zipf's law and its maximum likelihood fitting: Rank-size and size-distribution representations.

In recent years, researchers have realized the difficulties of fitting power-law distributions properly. These difficulties are higher in Zipfian systems, due to the discreteness of the variables and to the existence of two representations for these systems, i.e., two versions depending on the random variable to fit: rank or size. The discreteness implies that a power law in one of the representations is not a power law in the other, and vice versa. We generate synthetic power laws in both representations and apply a state-of-the-art fitting method to each of the two random variables. The method (based on maximum likelihood plus a goodness-of-fit test) does not fit the whole distribution but the tail, understood as the part of a distribution above a cutoff that separates non-power-law behavior from power-law behavior. We find that, no matter which random variable is power-law distributed, using the rank as the random variable is problematic for fitting, in general (although it may work in some limit cases). One of the difficulties comes from recovering the "hidden" true ranks from the empirical ranks. On the contrary, the representation in terms of the distribution of sizes allows one to recover the true exponent (with some small bias when the underlying size distribution is a power law only asymptotically).

Linguistic laws in chimpanzee gestural communication.

Studies testing linguistic laws outside language have provided important insights into the organization of biological systems. For example, patterns consistent with Zipf's law of abbreviation (which predicts a negative relationship between word length and frequency of use) have been found in the vocal and non-vocal behaviour of a range of animals, and patterns consistent with Menzerath's law (according to which longer sequences are made up of shorter constituents) have been found in primate vocal sequences, and in genes, proteins and genomes. Both laws have been linked to compression-the information theoretic principle of minimizing code length. Here, we present the first test of these laws in animal gestural communication. We initially did not find the negative relationship between gesture duration and frequency of use predicted by Zipf's law of abbreviation, but this relationship was seen in specific subsets of the repertoire. Furthermore, a pattern opposite to that predicted was seen in one subset of gestures-whole body signals. We found a negative correlation between number and mean duration of gestures in sequences, in line with Menzerath's law. These results provide the first evidence that compression underpins animal gestural communication, and highlight an important commonality between primate gesturing and language.

Scarcity of crossing dependencies: A direct outcome of a specific constraint?

The structure of a sentence can be represented as a network where vertices are words and edges indicate syntactic dependencies. Interestingly, crossing syntactic dependencies have been observed to be infrequent in human languages. This leads to the question of whether the scarcity of crossings in languages arises from an independent and specific constraint on crossings. We provide statistical evidence suggesting that this is not the case, as the proportion of dependency crossings of sentences from a wide range of languages can be accurately estimated by a simple predictor based on a null hypothesis on the local probability that two dependencies cross given their lengths. The relative error of this predictor never exceeds 5% on average, whereas the error of a baseline predictor assuming a random ordering of the words of a sentence is at least six times greater. Our results suggest that the low frequency of crossings in natural languages is neither originated by hidden knowledge of language nor by the undesirability of crossings per se, but as a mere side effect of the principle of dependency length minimization.

Gelada vocal sequences follow Menzerath's linguistic law.

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-the 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.

Acoustic sequences in non-human animals: a tutorial review and prospectus.

Animal acoustic communication often takes the form of complex sequences, made up of multiple distinct acoustic units. Apart from the well-known example of birdsong, other animals such as insects, amphibians, and mammals (including bats, rodents, primates, and cetaceans) also generate complex acoustic sequences. Occasionally, such as with birdsong, the adaptive role of these sequences seems clear (e.g. mate attraction and territorial defence). More often however, researchers have only begun to characterise - let alone understand - the significance and meaning of acoustic sequences. Hypotheses abound, but there is little agreement as to how sequences should be defined and analysed. Our review aims to outline suitable methods for testing these hypotheses, and to describe the major limitations to our current and near-future knowledge on questions of acoustic sequences. This review and prospectus is the result of a collaborative effort between 43 scientists from the fields of animal behaviour, ecology and evolution, signal processing, machine learning, quantitative linguistics, and information theory, who gathered for a 2013 workshop entitled, 'Analysing vocal sequences in animals'. Our goal is to present not just a review of the state of the art, but to propose a methodological framework that summarises what we suggest are the best practices for research in this field, across taxa and across disciplines. We also provide a tutorial-style introduction to some of the most promising algorithmic approaches for analysing sequences. We divide our review into three sections: identifying the distinct units of an acoustic sequence, describing the different ways that information can be contained within a sequence, and analysing the structure of that sequence. Each of these sections is further subdivided to address the key questions and approaches in that area. We propose a uniform, systematic, and comprehensive approach to studying sequences, with the goal of clarifying research terms used in different fields, and facilitating collaboration and comparative studies. Allowing greater interdisciplinary collaboration will facilitate the investigation of many important questions in the evolution of communication and sociality.

Zipf's Law for Word Frequencies: Word Forms versus Lemmas in Long Texts.

Zipf's law is a fundamental paradigm in the statistics of written and spoken natural language as well as in other communication systems. We raise the question of the elementary units for which Zipf's law should hold in the most natural way, studying its validity for plain word forms and for the corresponding lemma forms. We analyze several long literary texts comprising four languages, with different levels of morphological complexity. In all cases Zipf's law is fulfilled, in the sense that a power-law distribution of word or lemma frequencies is valid for several orders of magnitude. We investigate the extent to which the word-lemma transformation preserves two parameters of Zipf's law: the exponent and the low-frequency cut-off. We are not able to demonstrate a strict invariance of the tail, as for a few texts both exponents deviate significantly, but we conclude that the exponents are very similar, despite the remarkable transformation that going from words to lemmas represents, considerably affecting all ranges of frequencies. In contrast, the low-frequency cut-offs are less stable, tending to increase substantially after the transformation.

When is Menzerath-Altmann law mathematically trivial? A new approach.

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.

Compression as a universal principle of animal behavior.

A key aim in biology and psychology is to identify fundamental principles underpinning the behavior of animals, including humans. Analyses of human language and the behavior of a range of non-human animal species have provided evidence for a common pattern underlying diverse behavioral phenomena: Words follow Zipf's law of brevity (the tendency of more frequently used words to be shorter), and conformity to this general pattern has been seen in the behavior of a number of other animals. It has been argued that the presence of this law is a sign of efficient coding in the information theoretic sense. However, no strong direct connection has been demonstrated between the law and compression, the information theoretic principle of minimizing the expected length of a code. Here, we show that minimizing the expected code length implies that the length of a word cannot increase as its frequency increases. Furthermore, we show that the mean code length or duration is significantly small in human language, and also in the behavior of other species in all cases where agreement with the law of brevity has been found. We argue that compression is a general principle of animal behavior that reflects selection for efficiency of coding.

Networks in cognitive science.

Networks of interconnected nodes have long played a key role in Cognitive Science, from artificial neural networks to spreading activation models of semantic memory. Recently, however, a new Network Science has been developed, providing insights into the emergence of global, system-scale properties in contexts as diverse as the Internet, metabolic reactions, and collaborations among scientists. Today, the inclusion of network theory into Cognitive Sciences, and the expansion of complex-systems science, promises to significantly change the way in which the organization and dynamics of cognitive and behavioral processes are understood. In this paper, we review recent contributions of network theory at different levels and domains within the Cognitive Sciences.

The evolution of the exponent of Zipf's law in language ontogeny.

It is well-known that word frequencies arrange themselves according to Zipf's law. However, little is known about the dependency of the parameters of the law and the complexity of a communication system. Many models of the evolution of language assume that the exponent of the law remains constant as the complexity of a communication systems increases. Using longitudinal studies of child language, we analysed the word rank distribution for the speech of children and adults participating in conversations. The adults typically included family members (e.g., parents) or the investigators conducting the research. Our analysis of the evolution of Zipf's law yields two main unexpected results. First, in children the exponent of the law tends to decrease over time while this tendency is weaker in adults, thus suggesting this is not a mere mirror effect of adult speech. Second, although the exponent of the law is more stable in adults, their exponents fall below 1 which is the typical value of the exponent assumed in both children and adults. Our analysis also shows a tendency of the mean length of utterances (MLU), a simple estimate of syntactic complexity, to increase as the exponent decreases. The parallel evolution of the exponent and a simple indicator of syntactic complexity (MLU) supports the hypothesis that the exponent of Zipf's law and linguistic complexity are inter-related. The assumption that Zipf's law for word ranks is a power-law with a constant exponent of one in both adults and children needs to be revised.

Random models of Menzerath-Altmann law in genomes.

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-Altmann 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-Altmann law across taxonomic groups and the possibility of a connection between human language and genomes through that law.

Scaling laws in cognitive sciences.

Scaling laws are ubiquitous in nature, and they pervade neural, behavioral and linguistic activities. A scaling law suggests the existence of processes or patterns that are repeated across scales of analysis. Although the variables that express a scaling law can vary from one type of activity to the next, the recurrence of scaling laws across so many different systems has prompted a search for unifying principles. In biological systems, scaling laws can reflect adaptive processes of various types and are often linked to complex systems poised near critical points. The same is true for perception, memory, language and other cognitive phenomena. Findings of scaling laws in cognitive science are indicative of scaling invariance in cognitive mechanisms and multiplicative interactions among interdependent components of cognition.

Random texts do not exhibit the real Zipf's law-like rank distribution.

BACKGROUND: Zipf's law states that the relationship between the frequency of a word in a text and its rank (the most frequent word has rank , the 2nd most frequent word has rank ,...) is approximately linear when plotted on a double logarithmic scale. It has been argued that the law is not a relevant or useful property of language because simple random texts - constructed by concatenating random characters including blanks behaving as word delimiters - exhibit a Zipf's law-like word rank distribution. METHODOLOGY/PRINCIPAL FINDINGS: In this article, we examine the flaws of such putative good fits of random texts. We demonstrate - by means of three different statistical tests - that ranks derived from random texts and ranks derived from real texts are statistically inconsistent with the parameters employed to argue for such a good fit, even when the parameters are inferred from the target real text. Our findings are valid for both the simplest random texts composed of equally likely characters as well as more elaborate and realistic versions where character probabilities are borrowed from a real text. CONCLUSIONS/SIGNIFICANCE: The good fit of random texts to real Zipf's law-like rank distributions has not yet been established. Therefore, we suggest that Zipf's law might in fact be a fundamental law in natural languages.