How to explore replicator equations?

TL;DR

This paper introduces a method to reduce complex replicator equations to simpler escort systems of ODEs, facilitating analytical exploration in evolutionary dynamics.

Contribution

The paper presents a novel reduction technique for a broad class of replicator equations, enabling easier analysis and potential applications.

Findings

Reduction of replicator equations to escort systems of ODEs

Analytical exploration of reduced systems demonstrated

Potential applications in evolutionary dynamics

Abstract

Replicator equations (RE) are among the basic tools in mathematical theory of selection and evolution. We develop a method for reducing a wide class of the RE, which in general are systems of differential equations in Banach space to escort systems of ODEs that in many cases can be explored analytically. The method has potential for different applications; some examples are given.