Macroscopic Dominance from Microscopic Extremes: Symmetry Breaking in Spatial Competition

TL;DR

This paper presents a stochastic model of spatial competition showing how initial microscopic advantages, governed by extreme value statistics, influence macroscopic dominance, but require non-reciprocal interactions to stabilize long-term advantage.

Contribution

It introduces a novel stochastic model that decouples discovery and monopolization phases, highlighting the role of extreme value statistics and non-reciprocal interactions in spatial competition.

Findings

Initial advantage depends exponentially on population size

Transient superiority alone cannot ensure dominance

Non-reciprocal interactions are essential for stable dominance

Abstract

How do competing populations convert a spatial advantage into macroscopic dominance? We introduce a stochastic model for resource competition that decouples the transient discovery phase from monopolization. Initial symmetry breaking is governed by extreme value statistics of first-passage times: a linear spatial disadvantage requires an exponentially larger population to overcome. However, transient superiority cannot stabilize dominance. A non-reciprocal interaction bias is strictly necessary to arrest local fluctuations and drive the system into a robust absorbing state.