Modelling the Diachronic Emergence of Phoneme Frequency Distributions

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.

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.

Why is the past of English "go" the apparently unrelated "went"? Such alternations are frequent in languages. They neither aid communication nor learnability, yet they can be persistent, surviving over centuries or millennia. We present a multi-agent simulation of the emergence of morphological stem and inflection alternations. Alternate forms arise by phonological changes or, as with "go/went", from lexical alternatives associated with a subset of the population. When an agent 'hears' another agent use a novel form for a slot in the paradigm of a word (say, the past tense of go), they will with some probability adopt that form, possibly spreading its use to other slots in the paradigm that shared the same original form. Thus alternative forms can spread through the population and become entrenched as stem or inflectional marker alternants. Unlike many previous computational studies, our system allows for naturalistic lexical forms, realistic phonological rules, lexicons with hundreds or thousands of entries, and agent populations in the tens or hundreds. It supports several network topologies, diffusion patterns and agent adoption policies. One issue with such simulations is evaluation: how realistic is the resulting morphology compared to those of real languages? We introduce the AI Historical Linguist, a novel Large Language Model-driven system that models a debate between two historical linguists. We use this to compare a set of real language morphologies, disguised morphologies, and experimentally evolved morphologies. The results suggest that among the factors that favor more plausible morphologies are scale-free social networks and random Bernoulli adoption of forms. We also present three case studies modeling attested historical changes, allowing us to test what might have happened if history had been different. All code and data are released.