Basins of attraction for species extinction and coexistence in spatial rock-paper-scissors games

Shi, Hongjing; Wang, Wen Xu; Yang, Rui; Lai, Ying–Cheng

doi:10.1103/physreve.81.030901

Cited by 70 publications

(49 citation statements)

References 28 publications

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“…Another interesting phenomenon to consider that is directly related to mobility is epidemic spreading. The effects of epidemic spreading on species coexistence in a spatial RPS game have been studied in [51,54,141]. It has been shown that in the absence of epidemic spreading, there exist extinction basins that are spirally entangled for m > m c , while basins of coexistence emerge for m < m c .…”

Section: B Mobilitymentioning

confidence: 99%

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Cyclic dominance in evolutionary games: a review

Szolnoki

Mobilia

Jiang

et al. 2014

J. R. Soc. Interface.

449

338

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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 rockpaper-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.

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Section: B Mobilitymentioning

confidence: 99%

“…It has been shown that in the absence of epidemic spreading, there exist extinction basins that are spirally entangled for m > m c , while basins of coexistence emerge for m < m c . Moreover, it has been discovered that intra-species infection promotes coexistence, while inter-species spreading fails to evoke the same effect [51,54,141].…”

Section: B Mobilitymentioning

confidence: 99%

Cyclic dominance in evolutionary games: a review

Szolnoki

Mobilia

Jiang

et al. 2014

J. R. Soc. Interface.

449

338

View full text Add to dashboard Cite

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“…Phase transitions and selection have also been studied in the predator-prey models allowing some motion throughout inhabitable vacant sites [13,14]. Recent theoretical studies focused on biodiversity and the emergence of self-organizing patterns by competing associations with homogeneous and heterogeneous invasion rates [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], elevating models of cyclical interactions to an enthusiastically approached field of research.…”

Section: Introductionmentioning

confidence: 99%

Effects of competition on pattern formation in the rock-paper-scissors game

et al. 2011

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We investigate the impact of cyclic competition on pattern formation in the rock-paper-scissors game. By separately considering random and prepared initial conditions, we observe a critical influence of the competition rate p on the stability of spiral waves and on the emergence of biodiversity. In particular, while increasing values of p promote biodiversity, they may act detrimentally on spatial pattern formation. For random initial conditions, we observe a phase transition from biodiversity to an absorbing phase, whereby the critical value of mobility grows linearly with increasing values of p on a log-log scale but then saturates as p becomes large. For prepared initial conditions, we observe the formation of single-armed spirals, but only for values of p that are below a critical value. Once above that value, the spirals break up and form disordered spatial structures, mainly because of the percolation of vacant sites. Thus there exists a critical value of the competition rates p(c) for stable single-armed spirals in finite populations. Importantly though, p(c) increases with increasing system size because noise reinforces the disintegration of ordered patterns. In addition, we also find that p(c) increases with the mobility. These phenomena are reproduced by a deterministic model that is based on nonlinear partial differential equations. Our findings indicate that competition is vital for the sustenance of biodiversity and the emergence of pattern formation in ecosystems governed by cyclical interactions.

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“…Rock-paperscissors (RPS)-type models incorporate some of the crucial ingredients associated with the dynamics of a network of competing species; they have been used as powerful tools in the study of complex biological systems. In its simplest form, the RPS game describes the evolution of three species that cyclically dominate each other [1][2][3] (see also Refs. [4,5] for the pioneer work by Lotka and Volterra).…”

mentioning

confidence: 99%

von Neummann's and related scaling laws in rock-paper-scissors-type games

et al. 2012

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We introduce a family of rock-paper-scissors-type models with Z(N) symmetry (N is the number of species), and we show that it has a very rich structure with many completely different phases. We study realizations that lead to the formation of domains, where individuals of one or more species coexist, separated by interfaces whose (average) dynamics is curvature driven. This type of behavior, which might be relevant for the development of biological complexity, leads to an interface network evolution and pattern formation similar to the ones of several other nonlinear systems in condensed matter and cosmology.

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Basins of attraction for species extinction and coexistence in spatial rock-paper-scissors games

Cited by 70 publications

References 28 publications

Cyclic dominance in evolutionary games: a review

Cyclic dominance in evolutionary games: a review

Effects of competition on pattern formation in the rock-paper-scissors game

von Neummann's and related scaling laws in rock-paper-scissors-type games

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