Coevolutionary Dynamics: From Finite to Infinite Populations

TL;DR

This paper explores the relationship between deterministic and stochastic models of evolutionary dynamics, revealing how microscopic processes influence macroscopic behavior in finite populations and can even reverse evolutionary trends.

Contribution

It explicitly connects stochastic processes with replicator dynamics in large populations, clarifying how individual-level differences affect overall evolutionary outcomes.

Findings

Different stochastic processes lead to standard or adjusted replicator dynamics.

Individual-level differences can invert the direction of evolution.

Population size influences the qualitative behavior of evolutionary dynamics.

Abstract

Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics in finite populations. However, the relationship between deterministic and stochastic approaches remained unclear. Here we solve this problem by explicitly considering large populations. In particular, we identify different microscopic stochastic processes that lead to the standard or the adjusted replicator dynamics. Moreover, differences on the individual level can lead to qualitatively different dynamics in asymmetric conflicts and, depending on the population size, can even invert the direction of the evolutionary process.