Oscillations and patterns in interacting populations of two species

Peltomäki, Matti; Rost, Martin; Alava, Mikko J.

doi:10.1103/physreve.78.050903

Cited by 49 publications

(113 citation statements)

References 33 publications

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“…This is the reason why the corresponding games exhibit similar behaviors resembling those observed for the rockpaper-scissors games on square lattice at different evolutionary rules. Due to the "cyclic" symmetries for all the three basis games the four strategies are present with the same frequency [35][36][37][38][39]. The strategy frequencies can be tuned by varying the strength of these components [40][41][42].…”

Section: Cyclic Gamesmentioning

confidence: 99%

Four classes of interactions for evolutionary games

et al. 2015

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The symmetric four-strategy games are decomposed into a linear combination of 16 basis games represented by orthogonal matrices. Among these basis games four classes can be distinguished as it is already found for the three-strategy games. The games with self-dependent (cross-dependent) payoffs are characterized by matrices consisting of uniform rows (columns). Six of 16 basis games describe coordination-type interactions among the strategy pairs and three basis games span the parameter space of the cyclic components that are analogous to the rock-paper-scissors games. In the absence of cyclic components the game is a potential game and the potential matrix is evaluated. The main features of the four classes of games are discussed separately and we illustrate some characteristic strategy distributions on a square lattice in the low noise limit if logit rule controls the strategy evolution. Analysis of the general properties indicates similar types of interactions at larger number of strategies for the symmetric matrix games.

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Section: Cyclic Gamesmentioning

confidence: 99%

Four classes of interactions for evolutionary games

et al. 2015

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“…In recent years, many models for the RPS cyclic competition have been considered. In particular, various two-dimensional versions of the model introduced by May and Leonard [22] have been studied [15,[17][18][19]21,23]. In spatial variants of the May-Leonard model, it was found that mobility implemented by pair-exchange among neighbors can significantly influence species diversity: Below a certain mobility threshold species coexist over long periods of time and selforganize by forming fascinating spiraling patterns, whereas biodiversity is lost when that threshold is exceeded [15].…”

Section: Introductionmentioning

confidence: 99%

“…[15][16][17][18][19][20][21]. In recent years, many models for the RPS cyclic competition have been considered.…”

Section: Introductionmentioning

confidence: 99%

Characterization of spiraling patterns in spatial rock-paper-scissors games

2014

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The spatiotemporal arrangement of interacting populations often influences the maintenance of species diversity and is a subject of intense research. Here, we study the spatiotemporal patterns arising from the cyclic competition between three species in two dimensions. Inspired by recent experiments, we consider a generic metapopulation model comprising "rock-paper-scissors" interactions via dominance removal and replacement, reproduction, mutations, pair exchange, and hopping of individuals. By combining analytical and numerical methods, we obtain the model's phase diagram near its Hopf bifurcation and quantitatively characterize the properties of the spiraling patterns arising in each phase. The phases characterizing the cyclic competition away from the Hopf bifurcation (at low mutation rate) are also investigated. Our analytical approach relies on the careful analysis of the properties of the complex Ginzburg-Landau equation derived through a controlled (perturbative) multiscale expansion around the model's Hopf bifurcation. Our results allow us to clarify when spatial "rock-paper-scissors" competition leads to stable spiral waves and under which circumstances they are influenced by nonlinear mobility.

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“…In experiments with Escherichia coli, for example, it has been shown that arranging the bacteria on a Petri dish is crucial for keeping all three competing strains alive [8,36]. Accordingly, simulations of spatial rock-paper-scissors and related games of cyclic dominance have a long and fruitful history [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56], which is firmly rooted in methods of statistical physics. In general, if the mobility in the population is sufficiently small [7], the spatial rock-paper-scissors game leads to the stable coexistence of all three competing strategies, whereby the coexistence is maintained by the spontaneous formation of complex spatial patterns.…”

Section: Introductionmentioning

confidence: 99%

From pairwise to group interactions in games of cyclic dominance

2014

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We study the rock-paper-scissors game in structured populations, where the invasion rates determine individual payoffs that govern the process of strategy change. The traditional version of the game is recovered if the payoffs for each potential invasion stem from a single pairwise interaction. However, the transformation of invasion rates to payoffs also allows the usage of larger interaction ranges. In addition to the traditional pairwise interaction, we therefore consider simultaneous interactions with all nearest neighbors, as well as with all nearest and next-nearest neighbors, thus effectively going from single pair to group interactions in games of cyclic dominance. We show that differences in the interaction range affect not only the stationary fractions of strategies but also their relations of dominance. The transition from pairwise to group interactions can thus decelerate and even revert the direction of the invasion between the competing strategies. Like in evolutionary social dilemmas, in games of cyclic dominance, too, the indirect multipoint interactions that are due to group interactions hence play a pivotal role. Our results indicate that, in addition to the invasion rates, the interaction range is at least as important for the maintenance of biodiversity among cyclically competing strategies.

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Oscillations and patterns in interacting populations of two species

Cited by 49 publications

References 33 publications

Four classes of interactions for evolutionary games

Four classes of interactions for evolutionary games

Characterization of spiraling patterns in spatial rock-paper-scissors games

From pairwise to group interactions in games of cyclic dominance

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