Competition and fragmentation: a simple model generating lognormal-like distributions

TL;DR

This paper introduces a simple Monte Carlo model based on competition and fragmentation processes that effectively reproduces the lognormal-like distribution of language sizes, including the power law tail observed in real data.

Contribution

The paper presents a new, minimalistic model that captures the distribution of language sizes and explains the emergence of power law tails through competition and fragmentation.

Findings

The model reproduces the power law tail of language size distribution.

Double-Pareto lognormal distribution fits real data better than simple lognormal.

Poorly connected interaction topologies improve model accuracy.

Abstract

The current distribution of language size in terms of speaker population is generally described using a lognormal distribution. Analyzing the original real data we show how the double-Pareto lognormal distribution can give an alternative fit that indicates the existence of a power law tail. A simple Monte Carlo model is constructed based on the processes of competition and fragmentation. The results reproduce the power law tails of the real distribution well and give better results for a poorly connected topology of interactions.