Phase Transitions and Spatio-Temporal Fluctuations in Stochastic Lattice Lotka–Volterra Models

By Mauro Mobilia, I. Georgiev, Uwe Claus Täuber. 2005

127 citations recorded by the source corpus.

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 mean-field theory, however, spatial constraints, modeling locally limited resources, lead to the emergence of a continuous active-to-absorbing state phase transition. Field-theoretic arguments, supported by Monte Carlo simulation results, indicate that this transition, which represents an extinction threshold for the predator population, is governed by the directed percolation universality class. In the active state, where predators and prey coexist, the classical center singularities with associated population cycles are replaced by either nodes or foci. In the vicinity of the stable nodes, the system is characterized by essentially stationary localized clusters of predators in a sea of prey. Near the stable foci, however, the stochastic lattice Lotka–Volterra system displays complex, correlated spatio-temporal patterns of competing activity fronts. Correspondingly, the population densities in our numerical simulations turn out to oscillate irregularly in time, with amplitudes that tend to zero in the thermodynamic limit. Yet in finite systems these oscillatory fluctuations are quite persistent, and their features are determined by the intrinsic interaction rates rather than the initial conditions. We emphasize the robustness of this scenario with respect to various model perturbations.

Subfields: Condensed Matter Physics, Mathematical Physics, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/d5bf0bdbf1afc12954400f055c85b061008d566d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

In Mathematical Physics

In Sociology and Political Science

Citations in the corpus

Evolutionary games on graphs (2006, background): “For instance, cyclic dominance for four strategies was discussed by Nowak and Sigmund (2004). They considered a game where unconditional defectors (AllD) get replaced by the more successful Tit-for-Tat players, who are transformed into Generous Tit-for-Tat strategists due to environmental noise. The”
Evolutionary game theory: Theoretical concepts and applications to microbial communities (2010, methodology): “In this situation, the quantitative analysis of the spatiotemporal properties of interacting particle systems requires the development of other analytical methods, e.g. relying on eld theoretic techniques [ 108 ].”
On competitive Lotka-Volterra model in random environments (2009, background): “One possible way to incorporate this spatial structure is to consider interacting particles and stochastic partial differential equations, see, for example, [33,36,38] among many others.”
Stochastic population dynamics in spatially extended predator–prey systems (2017, methodology): “The Monte Carlo simulation data are of course amenable to a quantitative analysis of the emerging spatial and temporal correlations in stochastic lattice LV systems [50, 65].”