Mean extinction times in cyclic coevolutionary rock-paper-scissors dynamics

TL;DR

This paper investigates the stability of biodiversity in cyclic rock-paper-scissors dynamics by analyzing mean extinction times through simulations and analytical methods, highlighting the impact of population size and stochastic fluctuations.

Contribution

It introduces two analytical approaches to derive mean extinction times in cyclic RPS dynamics and compares them with extensive simulation results for various population sizes.

Findings

Mean extinction time scales with population size N

Analytical approaches closely match simulation results

Stochastic fluctuations lead to strategy extinction in finite populations

Abstract

Dynamical mechanisms that can stabilize the coexistence or diversity in biology are generally of fundamental interest. In contrast to many two-strategy evolutionary games, games with three strategies and cyclic dominance like the rock-paper-scissors game (RPS) stabilize coexistence and thus preserve biodiversity in this system. In the limit of infinite populations, resembling the traditional picture of evolutionary game theory, replicator equations predict the existence of a fixed point in the interior of the phase space. But in finite populations, strategy frequencies will run out of the fixed point because of stochastic fluctuations, and strategies can even go extinct. For three different processes and for zero-sum and non-zero-sum RPS as well, we present results of extensive simulations for the mean extinction time (MET), depending on the number of agents N, and we introduce two analytical approaches for the derivation of the MET.