Random copying in space

TL;DR

This paper explores how spatial structure influences diversity dynamics in random copying models, revealing that local diversity can differ significantly from predictions of unstructured models, especially on small-world networks.

Contribution

It demonstrates the impact of spatial structure on diversity in random copying processes and highlights the importance of considering spatial effects in empirical models.

Findings

Spatial structure affects local diversity levels.

Small-world networks alter expected diversity dynamics.

Unstructured models may overlook local diversity variations.

Abstract

Random copying is a simple model for population dynamics in the absence of selection, and has been applied to both biological and cultural evolution. In this work, we investigate the effect that spatial structure has on the dynamics. We focus in particular on how a measure of the diversity in the population changes over time. We show that even when the vast majority of a population's history may be well-described by a spatially-unstructured model, spatial structure may nevertheless affect the expected level of diversity seen at a local scale. We demonstrate this phenomenon explicitly by examining the random copying process on small-world networks, and use our results to comment on the use of simple random-copying models in an empirical context.