Intransitivity and coexistence in four species cyclic games

Lütz, Alessandra F.; Risau-Gusmán, Sebastián; Arenzon, Jeferson J.

doi:10.1016/j.jtbi.2012.10.024

Cited by 53 publications

(64 citation statements)

References 71 publications

(90 reference statements)

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“…Although many these models lead to more complex network patterns with Y-type and higher order junctions [19,20], the dynamics of the structures at the interfaces is essentially analogous to that studied in the present paper in the context of simpler models. The generalisation of the analysis to models whose food webs are more complex and involve less mutually neutral pairs as in [18][19][20][23][24][25][26] shall be left for future work.…”

Section: Ending Commentsmentioning

confidence: 99%

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Interfaces with internal structures in generalized rock-paper-scissors models

et al. 2014

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In this work we investigate the development of stable dynamical structures along interfaces separating domains belonging to enemy partnerships, in the context of cyclic predator-prey models with an even number of species N ≥ 8. We use both stochastic and field theory simulations in one and two spatial dimensions, as well as analytical arguments, to describe the association at the interfaces of mutually neutral individuals belonging to enemy partnerships and to probe their role in the development of the dynamical structures at the interfaces. We identify an interesting behaviour associated to the symmetric or asymmetric evolution of the interface profiles depending on whether N/2 is odd or even, respectively. We also show that the macroscopic evolution of the interface network is not very sensitive internal structure of the interfaces. Although this work focus on cyclic predator prey-models with an even number of species, we argue that the results are expected to be quite generic in the context of spatial stochastic May-Leonard models.

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Section: Ending Commentsmentioning

confidence: 99%

“…See also Refs. [10][11][12][13][13][14][15][16][17][18][19][20][21][22][23][24][25] for other investigations of direct interest to the current work.…”

Section: Introductionmentioning

confidence: 99%

Interfaces with internal structures in generalized rock-paper-scissors models

et al. 2014

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“…6b is closely related to the one in Ref. [40]. The invasion is either direct as in the first four columns (or, equivalently, along the perimeter of the interaction graph) or, as seen in the last two columns, involves the creation of an intermediate domain.…”

Section: Cc-by-nc-nd 40 International License Not Peer-reviewed) Is mentioning

confidence: 69%

“…Differently from the model in Ref. [40], here the crossed interactions are not direct, as discussed above. Thus, even if 01 has two predators and a single prey (00), this prey also helps by eliminating 11, that also happens to prey on 01.…”

Section: Cc-by-nc-nd 40 International License Not Peer-reviewed) Is mentioning

confidence: 97%

Spatial organization, grouping strategies and cyclic dominance in asymmetric predator-prey games

Cazaubiel

Arenzon

2016

Preprint

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Predators may attack isolated or grouped preys in a cooperative, collective way. Whether a gregarious behavior is advantageous to each species depends on several conditions and game theory is a useful tool to deal with such a problem. We here extend the Lett-Auger-Gaillard model [Theor. Pop. Biol. 65, 263 (2004)] to spatially distributed groups and compare the resulting behavior with their mean field predictions for the coevolving densities of predator and prey strategies. We show that the coexistence phase in which both strategies for each group are present is stable because of an effective, cyclic dominance behavior similar to a well studied generalizations of the RockPaper-Scissors game with four species (without neutral pairs), a further example of how ubiquitous this mechanism is. In addition, inside the coexistence phase (but interestingly, only for finite size systems) there is a realization of the survival of the weakest effect that is triggered by a percolation crossover.

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“…The simplest models usually consider three species and allow for three basic actions (motion, reproduction and predation) but several generalizations incorporating other interactions and further species have also been proposed in the literature [6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

String networks in ZN Lotka–Volterra competition models

Avelino¹,

Bazeia²,

Menezes³

et al. 2014

Physics Letters A

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In this letter we give specific examples of Z N Lotka-Volterra competition models leading to the formation of string networks. We show that, in order to promote coexistence, the species may arrange themselves around regions with a high number density of empty sites generated by predator-prey interactions between competing species. These configurations extend into the third dimension giving rise to string networks. We investigate the corresponding dynamics using both stochastic and mean field theory simulations, showing that the coarsening of these string networks follows a scaling law which is analogous to that found in other physical systems in condensed matter and cosmology.

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Intransitivity and coexistence in four species cyclic games

Cited by 53 publications

References 71 publications

Interfaces with internal structures in generalized rock-paper-scissors models

Interfaces with internal structures in generalized rock-paper-scissors models

Spatial organization, grouping strategies and cyclic dominance in asymmetric predator-prey games

String networks in ZN Lotka–Volterra competition models

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