Modelling the Diachronic Emergence of Phoneme Frequency Distributions

TL;DR

This paper presents a stochastic model of phonological change that explains the statistical regularities in phoneme frequency distributions across languages as natural outcomes of diachronic sound change processes.

Contribution

It introduces a novel diachronic model incorporating functional load and stabilizing tendencies, successfully reproducing empirical phoneme distribution patterns.

Findings

Model reproduces rank-frequency distributions

Model explains negative relationship between inventory size and entropy

Regularities may arise from sound change processes

Abstract

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 na\"ive 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.