Effects of mobility on ordering dynamics

TL;DR

This paper investigates how individual mobility influences the speed and mechanisms of reaching consensus in models of ordering dynamics, revealing that diffusion significantly alters the time to homogenization regardless of network structure.

Contribution

It introduces a generalized metapopulation framework for Voter and Moran processes incorporating mobility, highlighting its impact on ordering times and mechanisms.

Findings

Diffusion significantly affects the time to reach consensus.

Mobility alters the local and global mechanisms of ordering.

The effects are consistent across different network topologies.

Abstract

Models of ordering dynamics allow to understand natural systems in which an initially disordered population homogenizes some traits via local interactions. The simplest of these models, with wide applications ranging from evolutionary to social dynamics, are the Voter and Moran processes, usually defined in terms of static or randomly mixed individuals that interact with a neighbor to copy or modify a discrete trait. Here we study the effects of diffusion in Voter/Moran processes by proposing a generalization of ordering dynamics in a metapopulation framework, in which individuals are endowed with mobility and diffuse through a spatial structure represented as a graph of patches upon which interactions take place. We show that diffusion dramatically affects the time to reach the homogeneous state, independently of the underlying network's topology, while the final consensus emerges through different local/global mechanisms, depending on the mobility strength. Our results highlight the crucial role played by mobility in ordering processes and set up a general framework that allows to study its effect on a large class of models, with implications in the understanding of evolutionary and social phenomena.