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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)

Mauro Mobilia, 2, ∗ Ivan T. Georgiev, 2, † and Uwe C. Täuber ‡ Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, D-80333 Munich, Germany Department of Physics and Center for Stochastic Processes in Science and Engineering, Virginia Polytechnic Institute and State… (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
- 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)

- Bartosz Szczesny, Mauro Mobilia, Alastair M Rucklidge
- Physical review. E, Statistical, nonlinear, and…
- 2014

The spatiotemporal arrangement of interacting populations often influences the maintenance of species diversity and is a subject of intense research. Here, we study the spatiotemporal patterns arising from the cyclic competition between three species in two dimensions. Inspired by recent experiments, we consider a generic metapopulation model comprising… (More)

Abstract. We study large fluctuations in evolutionary games belonging to the coordination and anti-coordination classes. The dynamics of these games, modeling cooperation dilemmas, is characterized by a coexistence fixed point separating two absorbing states. We are particularly interested in the problem of fixation that refers to the possibility that a few… (More)

One of the most striking effect of fluctuations in evolutionary game theory is the possibility for mutants to fixate (take over) an entire population. Here, we generalize a recent WKB-based theory to study fixation in evolutionary games under non-vanishing selection, and investigate the relation between selection intensity w and demographic (random)… (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)

- Mauro Mobilia
- Journal of theoretical biology
- 2010

We study the oscillatory dynamics in the generic three-species rock-paper-scissors games with mutations. In the mean-field limit, different behaviors are found: (a) for high mutation rate, there is a stable interior fixed point with coexistence of all species; (b) for low mutation rates, there is a region of the parameter space characterized by a limit… (More)