Coexistence and Survival in Conservative Lotka-Volterra Networks

Knebel, Johannes; Krüger, Torben; Weber, Markus; Frey, Erwin

doi:10.1103/physrevlett.110.168106

Cited by 85 publications

(101 citation statements)

References 54 publications

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“…Indeed, several recent works (e.g., Refs. [23,42,43,48]) have shown that the structure of the interaction graph alone is not enough to predict the asymptotic temporal evolution of the system, stressing the importance of the invasion rates.…”

Section: Model Dynamics and Network Topologymentioning

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: Model Dynamics and Network Topologymentioning

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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“…Much work has been devoted to cyclic cases as for example the three-species cyclic game [21] or the corresponding game with four species where each species is preying on one other species while being at the same time the prey of another species [22][23][24][25][26][27][28][29]. Whereas some earlier papers have considered spatial and stochastic effects in systems with a larger number of species [30][31][32][33][34][35][36][37][38][39][40][41], it is only in the last few years that systematic theoretical studies of more complicated food networks with five or more species 2 have become available [19,[42][43][44][45][46][47][48][49][50][51][52][53][54]. One of the intriguing results of these studies has been the discovery of a rich variety of space-time patterns, including spirals where each wavefront is formed by a single species, fuzzy spirals due to the mixing of different species inside the waves, coarsening domains where every domain is formed by an alliance of mutually neutral species as well as coarsening processes where inside every domain spirals are formed, thus yielding non-trivial dynamics inside the coarsening domains [19,48,51,55].…”

Section: Introductionmentioning

confidence: 99%

Coarsening with nontrivial in-domain dynamics: Correlations and interface fluctuations

Brown

Pleimling

2017

Phys. Rev. E

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Using numerical simulations we investigate the space-time properties of a system in which spirals emerge within coarsening domains, thus giving rise to non-trivial internal dynamics. Initially proposed in the context of population dynamics, the studied six-species model exhibits growing domains composed of three species in a rock-paper-scissors relationship. Through the investigation of different quantities, such as space-time correlations and the derived characteristic length, autocorrelation, density of empty sites, and interface width, we demonstrate that the non-trivial dynamics inside the domains affects the coarsening process as well as the properties of the interfaces separating different domains. Domain growth, aging, and interface fluctuations are shown to be governed by exponents whose values differ from those expected in systems with curvature driven coarsening.

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Coexistence and Survival in Conservative Lotka-Volterra Networks

Cited by 85 publications

References 54 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

Coarsening with nontrivial in-domain dynamics: Correlations and interface fluctuations

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