Utterance Selection Model of Language Change

TL;DR

This paper develops a mathematical, evolutionary model of language change using a Fokker-Planck equation, revealing complex dynamics in multi-speaker communication and extinction phenomena.

Contribution

It introduces a novel population genetics-inspired mathematical framework for language evolution, including analytical solutions and insights into extinction and relaxation processes.

Findings

Single speaker case is exactly solvable.

Multi-speaker system shows two-stage relaxation.

Presence of many speakers affects extinction dynamics.

Abstract

We present a mathematical formulation of a theory of language change. The theory is evolutionary in nature and has close analogies with theories of population genetics. The mathematical structure we construct similarly has correspondences with the Fisher-Wright model of population genetics, but there are significant differences. The continuous time formulation of the model is expressed in terms of a Fokker-Planck equation. This equation is exactly soluble in the case of a single speaker and can be investigated analytically in the case of multiple speakers who communicate equally with all other speakers and give their utterances equal weight. Whilst the stationary properties of this system have much in common with the single-speaker case, time-dependent properties are richer. In the particular case where linguistic forms can become extinct, we find that the presence of many speakers causes a two-stage relaxation, the first being a common marginal distribution that persists for a long time as a consequence of ultimate extinction being due to rare fluctuations.