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Mesoscopic interactions and species coexistence in evolutionary game dynamics of cyclic competitions.

Cheng H, Yao N, Huang ZG, Park J, Do Y, Lai YC - Sci Rep (2014)

Bottom Line: 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.

View Article: PubMed Central - PubMed

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.

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.

Show MeSH
Spiral interaction graph (SIG).The SIG lists the interaction rules among the five different kinds of spirals (or groups). The nearest neighbor interaction (blue thick arrows) specifies “incursion” from one to another, and the next-nearest neighbor interaction (gray dashed lines) corresponds to reaction that generates two new spirals. Each spiral is composed of three species as distinguished by colors and numbers.
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f3: Spiral interaction graph (SIG).The SIG lists the interaction rules among the five different kinds of spirals (or groups). The nearest neighbor interaction (blue thick arrows) specifies “incursion” from one to another, and the next-nearest neighbor interaction (gray dashed lines) corresponds to reaction that generates two new spirals. Each spiral is composed of three species as distinguished by colors and numbers.

Mentions: A remarkable phenomenon is that coexistence of the five species in the low mobility regime is supported by the competition among the diversified three-species spirals. In particular, from the first snapshot in Fig. 2(a), we see that several different kinds of three-species spirals (e.g., those consisting of species 2, 3, and 4, or species 4, 5, and 1, etc.) coexist and are located in different spatial regions. Extinction from the five species coexistence state corresponds to the disappearance of certain spirals. This phenomenon thus points to the importance of spiral interactions, i.e., group interactions at the mesoscopic scale, in species coexistence. As shown in Fig. 3, there are in total five different kinds of three-species spirals or groups, each containing three cyclically competitive species. Transition from five- to three-species coexistence state at Mc5 can be understood through the interactions among the five groups.


Mesoscopic interactions and species coexistence in evolutionary game dynamics of cyclic competitions.

Cheng H, Yao N, Huang ZG, Park J, Do Y, Lai YC - Sci Rep (2014)

Spiral interaction graph (SIG).The SIG lists the interaction rules among the five different kinds of spirals (or groups). The nearest neighbor interaction (blue thick arrows) specifies “incursion” from one to another, and the next-nearest neighbor interaction (gray dashed lines) corresponds to reaction that generates two new spirals. Each spiral is composed of three species as distinguished by colors and numbers.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4265771&req=5

f3: Spiral interaction graph (SIG).The SIG lists the interaction rules among the five different kinds of spirals (or groups). The nearest neighbor interaction (blue thick arrows) specifies “incursion” from one to another, and the next-nearest neighbor interaction (gray dashed lines) corresponds to reaction that generates two new spirals. Each spiral is composed of three species as distinguished by colors and numbers.
Mentions: A remarkable phenomenon is that coexistence of the five species in the low mobility regime is supported by the competition among the diversified three-species spirals. In particular, from the first snapshot in Fig. 2(a), we see that several different kinds of three-species spirals (e.g., those consisting of species 2, 3, and 4, or species 4, 5, and 1, etc.) coexist and are located in different spatial regions. Extinction from the five species coexistence state corresponds to the disappearance of certain spirals. This phenomenon thus points to the importance of spiral interactions, i.e., group interactions at the mesoscopic scale, in species coexistence. As shown in Fig. 3, there are in total five different kinds of three-species spirals or groups, each containing three cyclically competitive species. Transition from five- to three-species coexistence state at Mc5 can be understood through the interactions among the five groups.

Bottom Line: 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.

View Article: PubMed Central - PubMed

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.

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.

Show MeSH