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.

翻译：音位频率分布在不同语言中展现出稳健的统计规律性，包括指数型尾部的秩频分布模式，以及音位库大小与分布相对熵之间的负相关关系。这些模式的起源在很大程度上仍未得到解释。本文探究这些模式是否可能作为塑造语音系统的历史过程的结果而自然涌现。我们提出了一种语音变化的随机模型，并模拟了音位库的历时演化过程。该模型的朴素版本能够复现音位秩频分布的一般形态，但未能捕捉其他实证特性。通过引入两个附加假设——与功能负荷相关的效应以及朝向偏好音位库规模的稳定化趋势——扩展后的模型所生成的模拟结果，既能匹配观测到的分布特征，也能重现音位库规模与相对熵之间的负相关关系。这些结果表明，语音系统的部分统计规律性可能源于历时音变的自然结果，而非来自显式的优化机制或补偿性机制。