1. Metapopulation model of rock-scissors-paper game with subpopulation-specific victory rates stabilized by heterogeneity
- Author
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Genki Ichinose, Takashi Nagatani, and Kei-ichi Tainaka
- Subjects
0301 basic medicine ,Statistics and Probability ,General Immunology and Microbiology ,Applied Mathematics ,Victory ,Metapopulation ,General Medicine ,Models, Theoretical ,Random walk ,01 natural sciences ,General Biochemistry, Genetics and Molecular Biology ,Graph ,Combinatorics ,03 medical and health sciences ,030104 developmental biology ,Game Theory ,Homogeneous ,Modeling and Simulation ,0103 physical sciences ,Neutral stability ,Computer Simulation ,010306 general physics ,General Agricultural and Biological Sciences ,Mathematics - 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.
- Published
- 2018
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