Demographic growth and the distribution of language sizes

TL;DR

This paper presents a stochastic model explaining the log-normal distribution of language sizes through demographic growth dynamics over ten centuries, aligning well with empirical data.

Contribution

It introduces a two-parameter multiplicative process model for language population dynamics that accounts for size distribution without considering language birth or death.

Findings

Model accurately predicts empirical language size distribution.

Numerical simulations support the model's assumptions.

Distribution within language families matches predictions.

Abstract

It is argued that the present log-normal distribution of language sizes is, to a large extent, a consequence of demographic dynamics within the population of speakers of each language. A two-parameter stochastic multiplicative process is proposed as a model for the population dynamics of individual languages, and applied over a period spanning the last ten centuries. The model disregards language birth and death. A straightforward fitting of the two parameters, which statistically characterize the population growth rate, predicts a distribution of language sizes in excellent agreement with empirical data. Numerical simulations, and the study of the size distribution within language families, validate the assumptions at the basis of the model.