Global attractors and extinction dynamics of cyclically competing species.

@article{Rulands2013GlobalAA,
  title={Global attractors and extinction dynamics of cyclically competing species.},
  author={Steffen Rulands and Alejandro Zielinski and Erwin Frey},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2013},
  volume={87 5},
  pages={
          052710
        }
}
Transitions to absorbing states are of fundamental importance in nonequilibrium physics as well as ecology. In ecology, absorbing states correspond to the extinction of species. We here study the spatial population dynamics of three cyclically interacting species. The interaction scheme comprises both direct competition between species as in the cyclic Lotka-Volterra model, and separated selection and reproduction processes as in the May-Leonard model. We show that the dynamic processes leading… 

The effect of habitats and fitness on species coexistence in systems with cyclic dominance.

Rare extinction events in cyclic predator–prey games

TLDR
The mean time to extinction (MTE) of the May–Leonard model of three cyclically competing species, in which all three species go extinct due to strong but rare fluctuations, is determined by using a WKB-ansatz in the master equation that represents the stochastic description of this model.

Asymmetric interplay leads to robust coexistence by means of a global attractor in the spatial dynamics of cyclic competition.

TLDR
It is found that mobility can facilitate coexistence in the limited cases of asymmetric competition and can be well predicted by the basin structure of the deterministic system and that the co existence in the spatial dynamics ultimately becomes a global attractor.

Coevolutionary dynamics in structured populations ofthree species

TLDR
The research presented in this thesis unifies and generalises these models by combining the birth, selection-removal, Selection-replacement and mutation processes as well as two forms of mobility into a generic metapopulation model and the emergence of spiral waves facilitating the long term biodiversity is confirmed in the computer simulations.

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

TLDR
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.

Coevolution of nodes and links: Diversity-driven coexistence in cyclic competition of three species.

TLDR
It is shown that if the competing individuals also have a "social temperament" to be either introverted or extroverted, leading them to cut or add links, respectively, then long-living states in which all species coexist can occur.

Stochastic population dynamics in spatially extended predator–prey systems

TLDR
Stochastic spatial variants of cyclic competition with rock-paper-scissors interactions illustrate connections between population dynamics and evolutionary game theory, and demonstrate how space can help maintain diversity.

Characterization of spiraling patterns in spatial rock-paper-scissors games.

TLDR
A generic metapopulation model comprising "rock-paper-scissors" interactions via dominance removal and replacement, reproduction, mutations, pair exchange, and hopping of individuals is considered, and the properties of the spiraling patterns arising in each phase are characterized.

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

TLDR
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.

Extinction in four species cyclic competition

TLDR
This paper study through numerical simulations the extinction processes that can take place in this system both in the well mixed case as well as on different types of lattices.

References

SHOWING 1-10 OF 139 REFERENCES

Coexistence in the two-dimensional May-Leonard model with random rates

TLDR
It is demonstrated that quenched disorder in either the reaction or in the mobility rates hardly impacts the dynamical evolution, the emergence and structure of spiral patterns, or the mean extinction time in this system.

Supplementary material: When does cyclic dominance lead to stable spiral waves?

TLDR
A two-dimensional three-species population model is considered and it is shown that spiral waves are stable in only one of the four phases, and a phase where nonlinearity leads to the annihilation of spirals and to the spatially uniform dominance of each species in turn is characterised.

Mobility promotes and jeopardizes biodiversity in rock–paper–scissors games

TLDR
It is established that this phenomenon is robust; it does not depend on the details of cyclic competition or spatial environment, and are relevant for the formation and propagation of patterns in microbial populations or excitable media.

On the relationship between cyclic and hierarchical three-species predator-prey systems and the two-species Lotka-Volterra model

TLDR
It is demonstrated that the evolutionary properties of both minority species in the (quasi-)steady state of this stochastic spatial three-species “corner” RPS model are well approximated by the two-species LV system, with its emerging characteristic features of localized population clustering, persistent oscillatory dynamics, correlated spatio-temporal patterns, and fitness enhancement through quenched spatial disorder in the predation rates.

Competing associations in bacterial warfare with two toxins.

Population oscillations in spatial stochastic Lotka–Volterra models: a field-theoretic perturbational analysis

Field theory tools are applied to analytically study fluctuation and correlation effects in spatially extended stochastic predator–prey systems. In the mean-field rate equation approximation, the

The edge of neutral evolution in social dilemmas

TLDR
The studies demonstrate that fluctuations can provide a surprisingly simple way to partly resolve social dilemmas and identify and quantify an emerging ‘edge of neutral evolution’ that delineates regimes of neutral and Darwinian evolution.
...