Can Menzerath's law be a criterion of complexity in communication?

Language-like efficiency and structure in house finch song

Communication needs to be complex enough to be functional while minimizing learning and production costs. Recent work suggests that the vocalizations and gestures of some songbirds, cetaceans and great apes may conform to linguistic laws that reflect this trade-off between efficiency and complexity. In studies of non-human communication, though, clustering signals into types cannot be done a priori, and decisions about the appropriate grain of analysis may affect statistical signals in the data. The aim of this study was to assess the evidence for language-like efficiency and structure in house finch (Haemorhous mexicanus) song across three levels of granularity in syllable clustering. The results show strong evidence for Zipf's rank-frequency law, Zipf's law of abbreviation and Menzerath's law. Additional analyses show that house finch songs have small-world structure, thought to reflect systematic structure in syntax, and the mutual information decay of sequences is consistent with a combination of Markovian and hierarchical processes. These statistical patterns are robust across three levels of granularity in syllable clustering, pointing to a limited form of scale invariance. In sum, it appears that house finch song has been shaped by pressure for efficiency, possibly to offset the costs of female preferences for complexity.

Scale in Language

A central concern of the cognitive science of language since its origins has been the concept of the linguistic system. Recent approaches to the system concept in language point to the exceedingly complex relations that hold between many kinds of interdependent systems, but it can be difficult to know how to proceed when "everything is connected." This paper offers a framework for tackling that challenge by identifying *scale* as a conceptual mooring for the interdisciplinary study of language systems. The paper begins by defining the scale concept-simply, the possibility for a measure to be larger or smaller in different instances of a system, such as a phonemic inventory, a word's frequency value in a corpus, or a speaker population. We review sites of scale difference in and across linguistic subsystems, drawing on findings from linguistic typology, grammatical description, morphosyntactic theory, psycholinguistics, computational corpus work, and social network demography. We consider possible explanations for scaling differences and constraints in language. We then turn to the question of *dependencies between* sites of scale difference in language, reviewing four sample domains of scale dependency: in phonological systems, across levels of grammatical structure (Menzerath's Law), in corpora (Zipf's Law and related issues), and in speaker population size. Finally, we consider the implications of the review, including the utility of a scale framework for generating new questions and inspiring methodological innovations and interdisciplinary collaborations in cognitive-scientific research on language.

Secondary Structures of Proteins Follow Menzerath–Altmann Law

This article examines the presence of the empirical tendency known as the Menzerath–Altmann Law (MAL) on protein secondary structures. MAL is related to optimization principles observed in natural languages and in genetic information on chromosomes or protein domains. The presence of MAL is examined on a non-redundant dataset of 4728 proteins by verifying significant, negative correlations and testing classical and newly proposed formulas by fitting the observed trend. We conclude that the lengths of secondary structures are specifically dependent on their number inside the protein sequence, while possibly reflecting the formula proposed in this paper. This behavior is observed on average but is individually avoidable and possibly driven by a latent cost function. The data suggest that MAL could provide a useful guiding principle in protein design.

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.