Rock-paper-scissors games in expanding populations: the effects of cyclic dominance and domain growth on diversity

Abstract

Discovering mechanisms for the maintenance of species diversity is central in ecology. Conditions of cyclic dominance arise frequently in nature and are thought to be a major promoter of diversity. Rock-paper-scissors (RPS) games can be used to characterize conditions of cyclic dominance involving three competing strategies: rock crushes scissors, scissors cuts paper, and paper wraps rock. The role of RPS in maintaining diversity among competing strategies has been detailed in spatially explicit models of fixed-size microbial populations. However, we find that RPS does not necessarily contribute to diversity in growing populations. To explore the effects of population growth, we use agent-based modeling (ABM). We consider two regimes: surface-only growth and bulk growth. In the case of surface-only growth, RPS increases the rate of interface diffusion, thereby accelerating the formation of sectors at the expanding front and decreasing diversity. In the case of bulk growth, we observe both regions characterized by RPS attacks that keep domain sizes in check and regions dominated by domain growth. When domains of sufficient size become established early on and attack rates are sufficiently low, growth in the bulk of these domains outweighs attacks at the interface; coexistence of these established domains can result. Therefore, while RPS games can promote diversity in expanding populations, the growth of domains can lead to an entirely different mechanism for the maintenance of diversity. We conclude that diversity in growing microbial populations can stem not only from the dynamics associated with RPS games but also from the formation of domains that become too big to fail.