title: Mesoscopic interactions and species coexistence in evolutionary game dynamics of cyclic competitions.
abstract: Evolutionary dynamical models for cyclic competitions of three species (e.g., rock, paper, and scissors, or RPS) provide a paradigm, at the microscopic level of individual interactions, to address many issues in coexistence and biodiversity. Real ecosystems often involve competitions among more than three species. By extending the RPS game model to five (rock-paper-scissors-lizard-Spock, or RPSLS) mobile species, we uncover a fundamental type of mesoscopic interactions among subgroups of species. In particular, competitions at the microscopic level lead to the emergence of various local groups in different regions of the space, each involving three species. It is the interactions among the groups that fundamentally determine how many species can coexist. In fact, as the mobility is increased from zero, two transitions can occur: one from a five- to a three-species coexistence state and another from the latter to a uniform, single-species state. We develop a mean-field theory to show that, in order to understand the first transition, group interactions at the mesoscopic scale must be taken into account. Our findings suggest, more broadly, the importance of mesoscopic interactions in coexistence of great many species.
authors.affiliation: 1] School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China [2] School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA.
authors.forename: Hongyan
authors.initials: H
authors.lastname: Cheng
authors.affiliation: 1] School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA [2] Department of Physics, Beijing Normal University, Beijing 100875, China.
authors.forename: Nan
authors.initials: N
authors.lastname: Yao
authors.affiliation: 1] School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA [2] School of Physical Science and Technology, Lanzhou University, and Institute of Modern Physics, CAS, Lanzhou 730000, China.
authors.forename: Zi-Gang
authors.initials: ZG
authors.lastname: Huang
authors.affiliation: Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea.
authors.forename: Junpyo
authors.initials: J
authors.lastname: Park
authors.affiliation: Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea.
authors.forename: Younghae
authors.initials: Y
authors.lastname: Do
authors.affiliation: 1] School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA [2] Department of Physics, Arizona State University, Tempe, Arizona 85287, USA.
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai
mesh_terms: D044822:Biodiversity; D005075:Biological Evolution; D003163:Competitive Behavior; D003198:Computer Simulation; D003299:Cooperative Behavior; D017753:Ecosystem; D005716:Game Theory; D008962:Models, Theoretical; D011157:Population Dynamics; D062211:Spatio-Temporal Analysis