Metapopulation model of rock-scissors-paper game with subpopulation-specific victory rates stabilized by heterogeneity.

Highlights • We presented a metapopulation model with different victory rates in the rock-scissors-paper game. • We numerically obtained the solutions of reaction-diffusion equations on the graphs with two and three nodes. • We also analytically derived the approximate solutions of the equations. • When victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. • The heterogeneity of victory rates promoted the coexistence of species. Abstract Recently, metapopulation models for rock-paper-scissors games have been presented. Each subpopulation is represented by a node on a graph. An individual is either rock (R), scissors (S) or paper (P); it randomly migrates among subpopulations. In the present paper, we assume victory rates differ in different subpopulations. To investigate the dynamic state of each subpopulation (node), we numerically obtain the solutions of reaction-diffusion equations on the graphs with two and three nodes. In the case of homogeneous victory rates, we find each subpopulation has a periodic solution with neutral stability. However, when victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. The heterogeneity of victory rates promotes the coexistence of species. [ABSTRACT FROM AUTHOR]