2017/08/31 by Ulrich Dobramysl, Mauro Mobilia, Michel Pleimling +2 · 133 citations
Biochemistry, Genetics and Molecular Biology · Medicine · Physics and Astronomy · Social Sciences · #Competition (biology) #Directed percolation #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Evolutionary dynamics #Extinction (optical mineralogy) #Mathematical and Theoretical Epidemiology and Ecology Models #Percolation (cognitive psychology) #Population #Stochastic dynamics #Stochastic modelling #Stochastic process #cond-mat.stat-mech #nlin.PS #q-bio.PE
paper · pdf · doi:10.1088/1751-8121/aa95c7
published in Journal of Physics A Mathematical and Theoretical 51(6), 063001 (Institute of Physics) · Topical review, to appear in: J. Phys. A: Math. Theor.; 53+ pages, 16 figures
openalex created_date 2017/08/31 · openalex publication_date 2017/10/25 · arxiv created 2017/12/26 · arxiv updated 2018/01/09 · openalex updated_date 2026/08/06
Abstract Spatially extended population dynamics models that incorporate demographic noise serve as case studies for the crucial role of fluctuations and correlations in biological systems. Numerical and analytic tools from non-equilibrium statistical physics capture the stochastic kinetics of these complex interacting many-particle systems beyond rate equation approximations. Including spatial structure and stochastic noise in models for predator–prey competition invalidates the neutral Lotka–Volterra population cycles. Stochastic models yield long-lived erratic oscillations stemming from a resonant amplification mechanism. Spatially extended predator–prey systems display noise-stabilized activity fronts that generate persistent correlations. Fluctuation-induced renormalizations of the oscillation parameters can be analyzed perturbatively via a Doi–Peliti field theory mapping of the master equation; related tools allow detailed characterization of extinction pathways. The critical steady-state and non-equilibrium relaxation dynamics at the predator extinction threshold are governed by the directed percolation universality class. Spatial predation rate variability results in more localized clusters, enhancing both competing species’ population densities. Affixing variable interaction rates to individual particles and allowing for trait inheritance subject to mutations induces fast evolutionary dynamics for the rate distributions. Stochastic spatial variants of three-species competition with ‘rock-paper-scissors’ interactions metaphorically describe cyclic dominance. These models illustrate intimate connections between population dynamics and evolutionary game theory, underscore the role of fluctuations to drive populations toward extinction, and demonstrate how space can support species diversity. Two-dimensional cyclic three-species May–Leonard models are characterized by the emergence of spiraling patterns whose properties are elucidated by a mapping onto a complex Ginzburg–Landau equation. Multiple-species extensions to general ‘food networks’ can be classified on the mean-field level, providing both fundamental understanding of ensuing cooperativity and profound insight into the rich spatio-temporal features and coarsening kinetics in the corresponding spatially extended systems. Novel space-time patterns emerge as a result of the formation of competing alliances; e.g. coarsening domains that each incorporate rock-paper-scissors competition games.