Monte Carlo simulation of the rise and the fall of languages

TL;DR

This paper models language evolution using a bit-string representation, revealing a phase transition from dominance by a single language to a diverse language landscape depending on mutation rates, with implications for understanding language dynamics.

Contribution

It introduces a novel Monte Carlo simulation framework for language evolution based on biological evolution principles, highlighting a phase transition phenomenon.

Findings

At low mutation rates, one language dominates.

High mutation rates lead to a diverse, log-normal distribution of languages.

A scaling law describes the transition between dominance and diversity.

Abstract

Similar to biological evolution and speciation we define a language through a string of 8 or 16 bits. The parent gives its language to its children, apart from a random mutation from zero to one or from one to zero; initially all bits are zero. The Verhulst deaths are taken as proportional to the total number of people, while in addition languages spoken by many people are preferred over small languages. For a fixed population size, a sharp phase transition is observed: For low mutation rates, one language contains nearly all people; for high mutation rates, no language dominates and the size distribution of languages is roughly log-normal as for present human languages. A simple scaling law is valid.