Abstract
Understanding mechanisms of biodiversity has been a central question in ecology. The coexistence of three species in rock-paper-scissors (RPS) systems are discussed by many authors; however, the relation between coexistence and network structure is rarely discussed. Here we present a metapopulation model for RPS game. The total population is assumed to consist of three subpopulations (nodes). Each individual migrates by random walk; the destination of migration is randomly determined. From reaction-migration equations, we obtain the population dynamics. It is found that the dynamic highly depends on network structures. When a network is homogeneous, the dynamics are neutrally stable: each node has a periodic solution, and the oscillations synchronize in all nodes. However, when a network is heterogeneous, the dynamics approach stable focus and all nodes reach equilibriums with different densities. Hence, the heterogeneity of the network promotes biodiversity.
Highlights
Understanding mechanisms of biodiversity has been a central question in ecology
By solving the reaction-migration equations analytically or numerically, we show that the RPS dynamics between homogeneous and heterogeneous graphs are significantly different
We have developed the metapopulation model for RPS games with three subpopulations
Summary
Understanding mechanisms of biodiversity has been a central question in ecology. The coexistence of three species in rock-paper-scissors (RPS) systems are discussed by many authors; the relation between coexistence and network structure is rarely discussed. He mathematically proved that the population dynamics are represented by classical Lotka-Volterra equation: the densities of three species (R, S, P) oscillate periodically (“neutrally stable”). By solving the reaction-migration equations analytically or numerically, we show that the RPS dynamics between homogeneous and heterogeneous graphs are significantly different.
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