A note on the replicator equation with explicit space and global regulation

TL;DR

This paper introduces a spatially explicit replicator equation with global regulation, extending classical evolutionary game concepts to spatially distributed populations and providing conditions for stability.

Contribution

It develops a novel spatial replicator model with global regulation and defines spatial Nash equilibrium and evolutionary stability concepts.

Findings

Provides a sufficient condition for spatially distributed evolutionary stability.

Illustrates the concepts with concrete examples.

Extends classical evolutionary game theory to include spatial effects.

Abstract

A replicator equation with explicit space and global regulation is considered. This model provides a natural framework to follow frequencies of species that are distributed in the space. For this model, analogues to classical notions of the Nash equilibrium and evolutionary stable strategy are provided. A sufficient condition for a uniform stationary state to be a spatially distributed evolutionary stable state is presented and illustrated with examples.