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- Tobias Reichenbach, Mauro Mobilia, Erwin Frey
- Nature
- 2007

Biodiversity is essential to the viability of ecological systems. Species diversity in ecosystems is promoted by cyclic, non-hierarchical interactions among competing populations. Central features of such non-transitive relations are represented by the 'rock-paper-scissors' game, in which rock crushes scissors, scissors cut paper, and paper wraps rock. In… (More)

We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka–Volterra type interactions defined on a d-dimensional lattice. Introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidates the classical, deterministic mean-field picture. Already within… (More)

- Tobias Reichenbach, Mauro Mobilia, Erwin Frey
- Physical review letters
- 2007

Noise and spatial degrees of freedom characterize most ecosystems. Some aspects of their influence on the coevolution of populations with cyclic interspecies competition have been demonstrated in recent experiments [e.g., B. Kerr, Nature (London) 418, 171 (2002)10.1038/nature00823]. To reach a better theoretical understanding of these phenomena, we consider… (More)

- Mauro Mobilia
- Physical review. E, Statistical, nonlinear, and…
- 2012

In the framework of the paradigmatic prisoner's dilemma game, we investigate the evolutionary dynamics of social dilemmas in the presence of "cooperation facilitators." In our model, cooperators and defectors interact as in the classical prisoner's dilemma, where selection favors defection. However, here the presence of a small number of cooperation… (More)

– Species diversity in ecosystems is often accompanied by the self-organisation of the population into fascinating spatio-temporal patterns. Here, we consider a two-dimensional three-species population model and study the spiralling patterns arising from the combined effects of generic cyclic dominance, mutation, pair-exchange and hopping of the… (More)

A class of two-species (three-states) bimolecular diffusion-limited models of classical particles with hard-core reacting and diffusing in a hypercubic lattice of arbitrary dimension is investigated. The manifolds on which the equations of motion of the correlation functions close, are determined explicitly. This property allows to solve for the density and… (More)

- Tobias Reichenbach, Mauro Mobilia, Erwin Frey
- Physical review. E, Statistical, nonlinear, and…
- 2006

Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see, e.g., B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature 418, 171 (2002)] and B. Kirkup and M. A. Riley [Nature 428, 412 (2004)]. Through analytical methods supported by numerical simulations, we address this issue by studying the… (More)

- Mauro Mobilia
- Physical review letters
- 2003

A method for studying the exact properties of a class of inhomogeneous stochastic many-body systems is developed and presented in the framework of a voter model perturbed by the presence of a "zealot," an individual allowed to favor an "opinion." We compute exactly the magnetization of this model and find that in one (1D) and two dimensions (2D) it evolves,… (More)

- M Mobilia, A Petersen, S Redner
- 2007

We study the voter model with a finite density of zealots—voters that never change opinion. For equal numbers of zealots of each species, the distribution of magnetization (opinions) is Gaussian in the mean-field limit, as well as in one and two dimensions, with a width that is proportional to 1/ √ Z, where Z is the number of zealots, independent of the… (More)

- Tobias Reichenbach, Mauro Mobilia, Erwin Frey
- Journal of theoretical biology
- 2008

The formation of out-of-equilibrium patterns is a characteristic feature of spatially extended, biodiverse, ecological systems. Intriguing examples are provided by cyclic competition of species, as metaphorically described by the 'rock-paper-scissors' game. Both experimentally and theoretically, such non-transitive interactions have been found to induce… (More)