Self-organizing patterns maintained by competing associations in a six-species predator-prey model

Szabó, György; Szolnoki, Attila; Borsos, István

doi:10.1103/physreve.77.041919

Cited by 66 publications

(53 citation statements)

References 24 publications

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“…In particular, S = 4 is the simplest case in which neutral pairs may form noninteracting, passive alliances that prevent or delay invasions [16][17][18][19][20][21][22][23][24][25][26]. On the other hand, active defensive alliances [27] may appear among non-mutually-neutral species (cyclic alliances) when the interaction graph has more than a single loop [22,[28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. This is obtained for S = 4 by introducing crossed interactions with rate χ (see Fig.…”

Section: Introductionmentioning

confidence: 99%

Globally synchronized oscillations in complex cyclic games

Rulquin

Arenzon

2014

Phys. Rev. E

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The rock-paper-scissors game and its generalizations with S > 3 species are well-studied models for cyclically interacting populations. Four is, however, the minimum number of species that, by allowing other interactions beyond the single, cyclic loop, breaks both the full intransitivity of the food graph and the one-predator, one-prey symmetry. Lütz et al. [J. Theor. Biol. 317, 286 (2013)] have shown the existence, on a square lattice, of two distinct phases, with either four or three coexisting species. In both phases, each agent is eventually replaced by one of its predators, but these strategy oscillations remain localized as long as the interactions are short ranged. Distant regions may be either out of phase or cycling through different food-web subloops (if any). Here we show that upon replacing a minimum fraction Q of the short-range interactions by long-range ones, there is a Hopf bifurcation, and global oscillations become stable. Surprisingly, to build such long-distance, global synchronization, the four-species coexistence phase requires fewer long-range interactions than the three-species phase, while one would naively expect the opposite to be true. Moreover, deviations from highly homogeneous conditions (χ = 0 or 1) increase Q c , and the more heterogeneous is the food web, the harder the synchronization is. By further increasing Q, while the three-species phase remains stable, the four-species one has a transition to an absorbing, single-species state. The existence of a phase with global oscillations for S > 3, when the interaction graph has multiple subloops and several possible local cycles, leads to the conjecture that global oscillations are a general characteristic, even for large, realistic food webs.

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Section: Introductionmentioning

confidence: 99%

Globally synchronized oscillations in complex cyclic games

Rulquin

Arenzon

2014

Phys. Rev. E

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“…Similar studies of more complicated systems composed of multiple species interacting in less trivial ways have been scarce until recently [61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77].…”

Section: Introductionmentioning

confidence: 99%

Spirals and coarsening patterns in the competition of many species: a complex Ginzburg–Landau approach

Mowlaei¹,

Roman²,

Pleimling³

2014

J. Phys. A: Math. Theor.

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Abstract. In order to model real ecological systems one has to consider many species that interact in complex ways. However, most of the recent theoretical studies have been restricted to few species systems with rather trivial interactions. The few studies dealing with larger number of species and/or more complex interaction schemes are mostly restricted to numerical explorations. In this paper we determine, starting from the deterministic meanfield rate equations, for large classes of systems the space of coexistence fixed points at which biodiversity is maximal. For systems with a single coexistence fixed point we derive complex Ginzburg-Landau equations that allow to describe space-time pattern realized in two space dimensions. For selected cases we compare the theoretical predictions with the pattern observed in numerical simulations.

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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%

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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Self-organizing patterns maintained by competing associations in a six-species predator-prey model

Cited by 66 publications

References 24 publications

Globally synchronized oscillations in complex cyclic games

Globally synchronized oscillations in complex cyclic games

Spirals and coarsening patterns in the competition of many species: a complex Ginzburg–Landau approach

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

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