Rock is wrapped by paper, paper is cut by scissors and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart of predator–prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms and competition in microbial populations. Cyclical interactions also emerge spontaneously in evolutionary games entailing volunteering, reward, punishment, and in fact are common when the competing strategies are three or more, regardless of the particularities of the game. Here, we review recent advances on the rock–paper–scissors (RPS) and related evolutionary games, focusing, in particular, on pattern formation, the impact of mobility and the spontaneous emergence of cyclic dominance. We also review mean-field and zero-dimensional RPS models and the application of the complex Ginzburg–Landau equation, and we highlight the importance and usefulness of statistical physics for the successful study of large-scale ecological systems. Directions for future research, related, for example, to dynamical effects of coevolutionary rules and invasion reversals owing to multi-point interactions, are also outlined.

/pdf/cyclic-dominance-in-evolutionary-games-a-review-34pqhh53un.pdf

Cyclic dominance in evolutionary games: A review

https://cyberleninka.org/article/n/890491.pdf

Nanofluids for Solar Collector Applications: A Review

Rock is wrapped by paper, paper is cut by scissors, and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart of predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms, and the competition in microbial populations. Cyclical interactions also emerge spontaneously in evolutionary games entailing volunteering, reward, punishment, and in fact are common when the competing strategies are three or more regardless of the particularities of the game. Here we review recent advances on the rock-paper-scissors and related evolutionary games, focusing in particular on pattern formation, the impact of mobility, and the spontaneous emergence of cyclic dominance. We also review mean-field and zero-dimensional rock-paper-scissors models and the application of the complex Ginzburg-Landau equation, and we highlight the importance and usefulness of statistical physics for the successful study of large-scale ecological systems. Directions for future research, related for example to dynamical effects of coevolutionary rules and invasion reversals due to multi-point interactions, are outlined as well.

Global, population-wide oscillations in models of cyclic dominance may result in the collapse of biodiversity due to the accidental extinction of one species in the loop. Previous research has shown that such oscillations can emerge if the interaction network has small-world properties, and more generally, because of long-range interactions among individuals or because of mobility. But although these features are all common in nature, global oscillations are rarely observed in actual biological systems. This begets the question what is the missing ingredient that would prevent local oscillations to synchronize across the population to form global oscillations. Here we show that, although heterogeneous species-specific invasion rates fail to have a noticeable impact on species coexistence, randomness in site-specific invasion rates successfully hinders the emergence of global oscillations and thus preserves biodiversity. Our model takes into account that the environment is often not uniform but rather spatially heterogeneous, which may influence the success of microscopic dynamics locally. This prevents the synchronization of locally emerging oscillations, and ultimately results in a phenomenon where one type of randomness is used to mitigate the adverse effects of other types of randomness in the system.

/pdf/biodiversity-in-models-of-cyclic-dominance-is-preserved-by-1quq24fm65.pdf

Biodiversity in models of cyclic dominance is preserved by heterogeneity in site-specific invasion rates.

Cooperation in the snowdrift game on directed small-world networks under self-questioning and noisy conditions

We study a spatial rock−scissors−paper model in a square lattice and a quenched small-world network. The system exhibits a global oscillation in the quenched small-world network, but the oscillation disappears in the square lattice. We find that there is a local oscillation in the square lattice the same as in the quenched small-world network. We define (where di is the density of a kind of species and di is the average value) as the variance of the oscillation amplitude in a certain local patch. It is found that s decays in a power law with an increase of the local patch size R in the square lattice σ ∝ R−δ, but it remains constant with an increase of the patch size in the quenched small-world network. We can speculate that in the square lattice, superposition between the local oscillations in different patches leads to global stabilization, while in the quenched small-world network, long-range interactions can synchronize the local oscillations, and their coherence results in the global oscillation.

http://iopscience.iop.org/article/10.1088/0256-307X/26/8/086403/pdf

Sun Rong-Sheng

Papers

Synchronization of Local Oscillations in a Spatial Rock?Scissors?Paper Game Model

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