Mobility and asymmetry effects in one-dimensional rock-paper-scissors games

Venkat, Siddharth; Pleimling, Michel

doi:10.1103/physreve.81.021917

Cited by 50 publications

(39 citation statements)

References 30 publications

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“…As a result increasing the swapping rate in that case does not yield an acceleration of the coarsening, and the domain growth exponent remains unchanged. It is only for very large swapping rates that a notable change sets in, yielding a non-equilibrium steady state with constant average domain size, as the system is then well mixed [21]. We expect the scenario observed in the present paper for the four species case to be very generic for systems with cyclic dominance composed of multiple species, as long as different species can form neutral alliances to fight off their predators.…”

Section: Coarsening In One Dimensionmentioning

confidence: 54%

“…Recent years saw a flurry of studies of systems composed of multiple species that interact in a cyclic way. Most of these studies focused on the case of three species [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39], a special situation where every species interact with every other species. Only rather few papers, however, dealt with more realistic cases where a given species interacts with only a subgroup of all species living in the same ecological environment [6,8,9,29,40,41,42,43,44,45,46,47,48,50,51,…”

Section: Introductionmentioning

confidence: 99%

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Cyclic competition of four species: domains and interfaces

Roman¹,

Konrad²,

Pleimling³

2012

J. Stat. Mech.

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Abstract. We study numerically domain growth and interface fluctuations in oneand two-dimensional lattice systems composed of four species that interact in a cyclic way. Particle mobility is implemented through exchanges of particles located on neighboring lattice sites. For the chain we find that the details of the domain growth strongly depend on the mobility, with a higher mobility yielding a larger effective domain growth exponent. In two space dimensions, when also exchanges between mutually neutral particles are possible, both domain growth and interface fluctuations display universal regimes that are independent of the predation and exchange rates.

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Section: Coarsening In One Dimensionmentioning

confidence: 54%

Section: Introductionmentioning

confidence: 99%

Cyclic competition of four species: domains and interfaces

Roman¹,

Konrad²,

Pleimling³

2012

J. Stat. Mech.

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“…In this sense, it is of current interest to investigate the importance of mobility for the preservation of diversity, and how this can be related with the Hamming distance. The issue here is similar to the case developed in [10], but one notes that it has been studied more recently in several works, in particular in [19][20][21][22][23] with distinct motivation. The purpose of this section is then to study the extinction of diversity with focus similar to the cases presented before in [10,20,22].…”

mentioning

confidence: 86%

Hamming distance and mobility behavior in generalized rock-paper-scissors models

Bazeia¹,

Menezes²,

Oliveira³

et al. 2017

EPL

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-This work reports on two related investigations of stochastic simulations which are widely used to study biodiversity and other related issues. We first deal with the behavior of the Hamming distance under the increase of the number of species and the size of the lattice, and then investigate how the mobility of the species contributes to jeopardize biodiversity. The investigations are based on the standard rules of reproduction, mobility and predation or competition, which are described by specific rules, guided by generalization of the rock-paper-scissors game, valid in the case of three species. The results on the Hamming distance indicate that it engenders universal behavior, independently of the number of species and the size of the square lattice. The results on the mobility confirm the prediction that it may destroy diversity, if it is increased to higher and higher values.Introduction. -Despite the many ways to study complex systems, stochastic simulations represent an important tool that has been largely used to investigate collective behavior in nature. The procedure is based on a set of simple rules that are assessed randomly and, in particular, has been employed to model and understand biodiversity in nature; see, e.g., Refs. [1-11] and references therein.In this work we deal with generalized rock-paper-scissors models to describe stochastic network simulations of the May and Leonard type [3,6]. We consider a square lattice of size N × N and follow three recent investigations, the first [8] describing how local dispersal may promote biodiversity in a real-life game, in which the predictions based on the rock-paper-scissors rules are empirically tested using a non-transitive model community containing three populations of Escherichia coli, the second [10] suggesting that population mobility may be central feature to describe real ecosystems, and the third [12] that shows how to use the Hamming distance [13] to unveil the presence

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“…The crossing conditions can be determined using (27) and (28). A new fixation scenario emerges when the switching rate varies across ν * : φ i+1 > φ i when ν > ν * , while φ i+1 ≤ φ i when ν ≤ ν * .…”

Section: Stagementioning

confidence: 99%

Fixation properties of rock-paper-scissors games in fluctuating populations

West

Mobilia

2020

Journal of Theoretical Biology

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Rock-paper-scissors games metaphorically model cyclic dominance in ecology and microbiology. In a static environment, these models are characterized by fixation probabilities obeying two different "laws" in large and small well-mixed populations. Here, we investigate the evolution of these three-species models subject to a randomly switching carrying capacity modeling the endless change between states of resources scarcity and abundance. Focusing mainly on the zero-sum rock-paper-scissors game, equivalent to the cyclic Lotka-Volterra model, we study how the coupling of demographic and environmental noise influences the fixation properties. More specifically, we investigate which species is the most likely to prevail in a population of fluctuating size and how the outcome depends on the environmental variability. We show that demographic noise coupled with environmental randomness "levels the field" of cyclic competition by balancing the effect of selection. In particular, we show that fast switching effectively reduces the selection intensity proportionally to the variance of the carrying capacity. We determine the conditions under which new fixation scenarios arise, where the most likely species to prevail changes with the rate of switching and the variance of the carrying capacity. Random switching has a limited effect on the mean fixation time that scales linearly with the average population size. Hence, environmental randomness makes the cyclic competition more egalitarian, but does not prolong the species coexistence. We also show how the fixation probabilities of close-to-zero-sum rock-paper-scissors games can be obtained from those of the zero-sum model by rescaling the selection intensity.

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Mobility and asymmetry effects in one-dimensional rock-paper-scissors games

Cited by 50 publications

References 30 publications

Cyclic competition of four species: domains and interfaces

Cyclic competition of four species: domains and interfaces

Hamming distance and mobility behavior in generalized rock-paper-scissors models

Fixation properties of rock-paper-scissors games in fluctuating populations

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