# Invasion-controlled pattern formation in a generalized multispecies predator-prey system.

@article{Bazeia2019InvasioncontrolledPF, title={Invasion-controlled pattern formation in a generalized multispecies predator-prey system.}, author={Dionisio Bazeia and B. F. de Oliveira and Attila Szolnoki}, journal={Physical review. E}, year={2019}, volume={99 5-1}, pages={ 052408 } }

Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of competitors we may face a novel situation because beside the mentioned unidirectional predator-prey-like dominance a balanced or peer relation can emerge between some competitors. By utilizing this possibility in the present work we generalize a four-state predator…

## 7 Citations

Breaking unidirectional invasions jeopardizes biodiversity in spatial May-Leonard systems

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Mortality makes coexistence vulnerable in evolutionary game of rock-paper-scissors.

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This work performs a Monte Carlo simulation followed by a stability analysis of different fixed points of defined rate equations and observes that the natural death rate is surprisingly one of the most significant factors in deciding whether an ecosystem would come up with a coexistence or a single-species survival.

Coevolutionary dynamics of a variant of the cyclic Lotka–Volterra model with three-agent interactions

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The magnitude of the stochastic noise at the bifurcation point is estimated and the effects of mobility in a lattice metapopulation model with patches hosting several agents are investigated, finding that strategies propagate along the arms of rotating spirals, as they usually do in models of cyclic dominance.

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- MathematicsPhysical review. E
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It is found that the relatively large oscillations at the initial stages of simulations with random initial conditions may result in a significant dependence of the probability of species survival on the lattice size.

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- PhysicsProceedings of the Royal Society A
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This work investigates the application of the line-graph operator to one-dimensional spin models with periodic boundary conditions and proposes a model of information growth and evolution based on this operator, which can generate frustrations in newly formed spin chains.

Performance of weak species in the simplest generalization of the rock-paper-scissors model to four species.

- Environmental SciencePhysical review. E
- 2020

It is shown, using lattice based spatial stochastic simulations with random initial conditions, that if only one of the four species has its probability reduced, then the most abundant species is the prey of the "weakest" (assuming that the simulations are large enough for coexistence to prevail).

## References

SHOWING 1-10 OF 111 REFERENCES

Phase transitions in dependence of apex predator decaying ratio in a cyclic dominant system

- Environmental ScienceEPL (Europhysics Letters)
- 2018

The results highlight that cyclic dominant competition can offer a stable way to survive even in a predator-prey-like system that can be maintained for large interval of critical parameter values.

Competing associations in six-species predator–prey models

- Environmental Science
- 2005

Under some conditions the survival of all the species can be maintained by the cyclic dominance occurring between these associations, and under some conditions larger and larger invasion processes precede the prevalence of one of the stable associations.

Diverging fluctuations in a spatial five-species cyclic dominance game.

- Environmental SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

A five-species predator-prey model is studied on a square lattice where each species has two prey and two predators on the analogy to the rock-paper-scissors-lizard-Spock game, revealing diverging fluctuations at a specific invasion rate which can be related to the vanishing dominance between all pairs of species associations.

Phase transition and selection in a four-species cyclic predator-prey model.

- Environmental SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

According to the Monte Carlo simulations, the observed phase transition seems to be equivalent to those found in spreading models with two equivalent absorbing states although the present model has continuous sets of absorbing states with different portions of the two neutral species.

Cyclical interactions with alliance-specific heterogeneous invasion rates.

- Environmental SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

A six-species Lotka-Volterra-type system when each species has two superior and two inferior partners is studied, revealing an unexpected nonmonotonous dependence of alliance survival on the difference of alliance-specific invasion rates.

Collective strategies and cyclic dominance in asymmetric predator-prey spatial games.

- Environmental ScienceJournal of theoretical biology
- 2017

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

- Environmental SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

Within an intermediate range of X all the five associations coexist due to the fact that cyclic invasions between the two- Species associations reduce their resistance temporarily against the invasion of three-species associations.

Pattern formation, synchronization, and outbreak of biodiversity in cyclically competing games.

- Environmental SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

This work incorporates both intra- and inter-patch migrations in stochastic games of cyclic competitions and finds that the interplay between the migrations at the local and global scales can lead to robust species coexistence characterized dynamically by the occurrence of remarkable target-wave patterns in the absence of any external control.

Intransitivity and coexistence in four species cyclic games.

- MathematicsJournal of theoretical biology
- 2013

Local dispersal promotes biodiversity in a real-life game of rock–paper–scissors

- Environmental ScienceNature
- 2002

It is found that diversity is rapidly lost in the experimental community when dispersal and interaction occur over relatively large spatial scales, whereas all populations coexist when ecological processes are localized.