We demonstrate that the frequency distribution of phonemes across languages can be explained at both macroscopic and microscopic levels. Macroscopically, phoneme rank-frequency distributions closely follow the order statistics of a symmetric Dirichlet distribution whose single concentration parameter scales systematically with phonemic inventory size, revealing a robust compensation effect whereby larger inventories exhibit lower relative entropy. Microscopically, a Maximum Entropy model incorporating constraints from articulatory, phonotactic, and lexical structure accurately predicts language-specific phoneme probabilities. Together, these findings provide a unified information-theoretic account of phoneme frequency structure.
Figures & tables
Figure 1: Rank-frequency plots for the five phoneme frequency distributions discussed in Sigurd (1968) , compared with the word frequency distribution in the Brown corpus. Note the logarithmic scales.
Figure 2: Geographic and genetic diversity of the languages included in the UDHR dataset.
Figure 3: (a) Rank-frequency plot for the American English phoneme frequency distribution (red dots and lines) discussed in Sigurd (1968) , overlaid with the predicted rank-frequency distribution for symmetric Dirichlet distributions with estimated concentration parameters α^ . The green lines are the predicted mean order statistics, the darker green shading denotes their standard deviations, and the lighter green shading denotes their 95% C.I. (b) Relationship between the size of the phonemic inventory (horizontal axis; note the logarithmic scale) with the estimated value of the concentration parameter α^ (vertical axis) across the three datasets. Each point denotes the phonemic inventory for a language variety. The black line plots a doubly logarithmic linear regression (whose parameters are given in Equation 1 ) and the shaded area is its 95% C.I. (c) Rank-frequency plot for the American English phoneme frequency distribution (red dots and lines) discussed in Sigurd (1968) , overlaid with its rank-frequency distribution reconstructed from its inventory size using Equation 1 . The green lines are the predicted mean order statistics, the darker green shading denotes their standard deviations, and the lighter green shading denotes their 95% C.I.
Figure 4: (a) Distributions (kernel density estimates) of the estimated values of the maximum entropy Lagrange multipliers across the UDHR datasets. (b) Comparison between the observed (red) and maximum entropy guessed (green) probabilities of the phonemes in the Abkhaz UDHR dataset (the horizontal axis plots the ranks of the observed data). (c) Comparison between the maximum entropy guessed (horizontal axis) and observed (vertical axis) probabilities of the phonemes across all UDHR datasets. The solid line plots a non-linear regression (lowess) and the dashed line plots the identity (note logarithmic scales). (d) Comparison between the maximum entropy guessed (horizontal axis) and observed (vertical axis) relative entropies of the phoneme distributions across all UDHR datasets. The solid line plots a linear regression (the shading denotes its 95% C.I.) and the dashed line plots the identity.
Phoneme frequency distributions exhibit robust statistical regularities across languages, including exponential-tailed rank-frequency patterns and a negative relationship between phonemic inventory size and the relative entropy of the distribution. The origin of these patterns remains largely unexplained. In this paper, we investigate whether they can arise as consequences of the historical processes that shape phonological systems. We introduce a stochastic model of phonological change and simulate the diachronic evolution of phoneme inventories. A naïve version of the model reproduces the general shape of phoneme rank-frequency distributions but fails to capture other empirical properties. Extending the model with two additional assumptions -- an effect related to functional load and a stabilising tendency toward a preferred inventory size -- yields simulations that match both the observed distributions and the negative relationship between inventory size and relative entropy. These results suggest that some statistical regularities of phonological systems may arise as natural consequences of diachronic sound change rather than from explicit optimisation or compensatory mechanisms.
Fermín Moscoso del Prado Martín, Suchir Salhan
Department of Computer Science and Technology, University of Cambridge, UK
We show that short-range phoneme dependencies encode large-scale patterns of linguistic relatedness, with direct implications for quantitative typology and evolutionary linguistics. Specifically, using an information-theoretic framework, we argue that phoneme sequences modeled as second-order Markov chains essentially capture the statistical correlations of a phonological system. This finding enables us to quantify distances among 67 modern languages from a multilingual parallel corpus employing a distance metric that incorporates articulatory features of phonemes. The resulting phonological distance matrix recovers major language families and reveals signatures of contact-induced convergence. Remarkably, we obtain a clear correlation with geographic distance, allowing us to constrain a plausible homeland region for the Indo-European family, consistent with the Steppe hypothesis.
Marius Mavridis, Juan De Gregorio, Raul Toral +1
Institute for Cross-Disciplinary Physics and Complex Systems IFISC (UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain · Universit´e Paris-Saclay, ENS Paris-Saclay, DER de Physique, 91190, Gif-sur-Yvette, France
The iterated learning model was introduced to investigate language evolution: the way in which the characteristic properties of human languages have been shaped, at least partly, by repeated transmission from one language user to another. The key finding is that language compositionality can arise spontaneously as a consequence of language being passed repeatedly through a language learning bottleneck. Here we explore how changing the frequency of different meanings, so that some meanings occur much more frequently than others, affects the character of its compositionality. We find that, as observed in natural languages, high-frequency meanings can escape the pressure to conform to the grammar that characterizes lower-frequency meanings. However, when the frequency structure is instead imposed on parts rather than on whole meaning vectors, the language fails to transmit across generations. This occurs despite the fact that the most frequent elements are reliably learned. These results suggest that frequency can shape emergent linguistic structure only when the frequency distribution is defined over form-meaning units that learners can acquire holistically. When frequency is instead distributed over smaller units, it fails to support the relational structure required for compositional generalisation, thereby preventing stable language transmission.
Fabio De Ponte, Eloise Gaines-White, Conor Houghton +1
Université de Namur and Vrije Universiteit Brussel, Belgium · University of Bristol, UK