Stochastic population dynamics in spatially extended predator-prey systems

Abstract

Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey competition invalidates the deterministic Lotka-Volterra picture of neutral population cycles. Stochastic models yield long-lived erratic population oscillations stemming from a resonant amplification mechanism. In spatially extended predator-prey systems, one observes noise-stabilized activity and persistent correlations. Fluctuation-induced renormalizations of the oscillation parameters can be analyzed perturbatively. The critical dynamics and the non-equilibrium relaxation kinetics at the predator extinction threshold are characterized by the directed percolation universality class. Spatial or environmental variability results in more localized patches which enhances both species densities. Affixing variable rates to individual particles and allowing for trait inheritance subject to mutations induces fast evolutionary dynamics for the rate distributions. 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. In two dimensions, three-species cyclic competition models of the May-Leonard type are characterized by the emergence of spiral patterns whose properties are elucidated by a mapping onto a complex Ginzburg-Landau equation. Extensions to general food networks can be classified on the mean-field level, which provides both a fundamental understanding of ensuing cooperativity and emergence of alliances. Novel space-time patterns emerge as a result of the formation of competing alliances, such as coarsening domains that each incorporate rock-paper-scissors competition games.

Topical review, to appear in: J. Phys. A: Math. Theor.; 53+ pages, 16 figures

References in corpus (91)

• Evolutionary games on graphs
• Coevolutionary games - a mini review
• The World of the Complex Ginzburg-Landau Equation
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
• Cyclic dominance in evolutionary games: A review
• Predator-prey cycles from resonant amplification of demographic stochasticity
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model
• Self-Organization of Mobile Populations in Cyclic Competition
• Noise and Correlations in a Spatial Population Model with Cyclic Competition
• Rock-scissors-paper game on regular small-world networks
• The Field Theory Approach to Percolation Processes
• WKB theory of large deviations in stochastic populations
• Stochastic Lattice Gas Model for a Predator-Prey System
• Oscillatory Dynamics in Rock-Paper-Scissors Games with Mutations
• Robust ecological pattern formation induced by demographic noise
• Phase Transitions and Spatio-Temporal Fluctuations in Stochastic Lattice Lotka-Volterra Models
• Cyclic dominance and biodiversity in well-mixed populations
• Spatial organization in cyclic Lotka-Volterra systems
• Fluctuation-driven Turing patterns
• Cyclical interactions with alliance-specific heterogeneous invasion rates
• Zero-one survival behavior of cyclically competing species
• Quasi-cycles in a spatial predator-prey model
• Instability of spatial patterns and its ambiguous impact on species diversity
• Spatial Rock-Paper-Scissors Models with Inhomogeneous Reaction Rates
• Junctions and spiral patterns in Rock-Paper-Scissors type models
• Ecological collapse and the emergence of traveling waves at the onset of shear turbulence
• Chemical warfare and survival strategies in bacterial range expansions
• Extinction in neutrally stable stochastic Lotka-Volterra models
• Coexistence and Survival in Conservative Lotka-Volterra Networks
• Phase transition and selection in a four-species cyclic Lotka-Volterra model
• Fluctuations and Correlations in Lattice Models for Predator-Prey Interaction
• Nonlinear Dynamics of the Rock-Paper-Scissors Game with Mutations
• Diverging fluctuations in a spatial five-species cyclic dominance game
• Phase transition in a spatial Lotka-Volterra model
• Effects of competition on pattern formation in the rock-paper-scissors game
• Phase Transitions and Oscillations in a Lattice Prey-Predator Model
• Extinction in Lotka-Volterra model
• Defensive alliances in spatial models of cyclical population interactions
• Characterization of spiraling patterns in spatial rock-paper-scissors games
• Von-Neumann's and related scaling laws in Rock-Paper-Scissors type models
• Entropy production of cyclic population dynamics
• Self-organizing patterns maintained by competing associations in a six-species predator-prey model
• Oscillatory behaviour in a lattice prey-predator system
• Evolutionary games of condensates in coupled birth-death processes
• A three-state cyclic voter model extended with Potts energy
• Competing associations in six-species predator-prey models
• Cyclic competition of four species: domains and interfaces
• Segregation process and phase transition in cyclic predator-prey models with even number of species
• When does cyclic dominance lead to stable spiral waves?
• Population oscillations in spatial stochastic Lotka-Volterra models: A field-theoretic perturbational analysis
• Mobility and asymmetry effects in one-dimensional rock-paper-scissors games
• Intransitivity and coexistence in four species cyclic games
• Phase transitions induced by variation of invasion rates in spatial cyclic predator-prey models with four or six species
• Co-existence in the two-dimensional May-Leonard model with random rates
• Interplay between partnership formation and competition in generalized May-Leonard games
• Interfaces with internal structures in generalized rock-paper-scissors models
• Environmental vs. demographic variability in two-species predator-prey models
• Influence of local carrying capacity restrictions on stochastic predator-prey models
• String networks in Z_N Lotka-Volterra competition models
• Spatial variability enhances species fitness in stochastic predator-prey interactions
• Global attractors and extinction dynamics of cyclically competing species
• Cyclic competition of four species: mean field theory and stochastic evolution
• Non-equilibrium relaxation in a stochastic lattice Lotka-Volterra model
• Mean Field Approximation to a Spatial Host-Pathogen Model
• Saddles, Arrows, and Spirals: Deterministic Trajectories in Cyclic Competition of Four Species
• A theoretical approach to understand spatial organization in complex ecologies
• Globally synchronized oscillations in complex cyclic games
• Spirals and heteroclinic cycles in a spatially extended Rock-Paper-Scissors model of cyclic dominance
• The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games
• Oscillations and dynamics in a two-dimensional prey-predator system
• Labyrinthine clustering in a spatial rock-paper-scissors ecosystem
• On the relationship between cyclic and hierarchical three-species predator-prey systems and the two-species Lotka-Volterra model
• Stochastic evolution of four species in cyclic competition
• Coarsening with non-trivial in-domain dynamics: correlations and interface fluctuations
• Mobility-Dependent Selection of Competing Strategy Associations
• Spirals and coarsening patterns in the competition of many species: A complex Ginzburg-Landau approach
• Survival and Extinction in Cyclic and Neutral Three--Species Systems
• Coexistence in a One-Dimensional Cyclic Dominance Process
• String networks with junctions in competition models
• Three-fold way to extinction in populations of cyclically competing species
• Synchronization and extinction in cyclic games with mixed strategies
• Boundary Effects on Population Dynamics in Stochastic Lattice Lotka-Volterra Models
• A stochastic analysis of the spatially extended May-Leonard model
• Rock-paper-scissors played within competing domains in predator-prey games
• Environmental vs demographic variability in stochastic predator-prey models
• Three is much more than two in coarsening dynamics of cyclic competitions
• Stochastic effects on biodiversity in cyclic coevolutionary dynamics
• Disturbance accelerates the transition from low- to high- diversity state in a model ecosystem

Cited by in corpus (62)

• Pattern formations driven by cyclic interactions: a brief review of recent developments
• Imitate or innovate: competition of strategy updating attitudes in spatial social dilemma games
• Cooperator driven oscillation in a time-delayed feedback-evolving game
• Population Dynamics in a Changing Environment: Random versus Periodic Switching
• Uneven rock-paper-scissors models: patterns and coexistence
• Cooperation and competition between pair and multi-player social games in spatial populations
• Evolutionary dynamics and competition stabilize three-species predator-prey communities
• The effect of habitats and fitness on species coexistence in systems with cyclic dominance
• Expanding spatial domains and transient scaling regimes in populations with local cyclic competition
• Non-Hermitian topology in rock-paper-scissors games
• Perturbing cyclic predator-prey systems: how a six-species coarsening system with non-trivial in-domain dynamics responds to sudden changes
• Dynamically generated hierarchies in games of competition
• Competition of alliances in a cyclically dominant eight-species population
• Entropy evaluation sheds light on ecosystem complexity
• Invasion controlled pattern formation in a generalized multi-species predator-prey system
• Interactions and migration rescuing ecological diversity
• Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series
• Survival behavior in the cyclic Lotka-Volterra model with a randomly switching reaction rate
• Dynamical mean-field theory: from ecosystems to reaction networks
• Influence of the neighborhood on cyclic models of biodiversity
• Genome heterogeneity drives the evolution of species
• Evolutionary Dynamics in a Varying Environment: Continuous versus Discrete Noise
• Phase transitions in dependence of apex predator decaying ratio in a cyclic dominant system
• Dynamical universality of the contact process
• Breaking unidirectional invasions jeopardizes biodiversity in spatial May-Leonard systems
• Environment driven oscillation in an off-lattice May--Leonard model
• Demographic noise can promote abrupt transitions in ecological systems
• Coexistence of Competing Microbial Strains under Twofold Environmental Variability and Demographic Fluctuations
• Lotka-Volterra predator-prey model with periodically varying carrying capacity
• Delays in fitness adjustment can lead to coexistence of hierarchically interacting species
• Equal partners do better in defensive alliances
• Effects of a pestilent species on the stability of cyclically dominant species
• When faster rotation is harmful: the competition of alliances with inner blocking mechanism
• Eco-evolutionary dynamics of cooperative antimicrobial resistance in a population of fluctuating volume and size
• Stochastic control of spiking activity bump expansion: monotonic and resonant phenomena
• Stabilizing spiral structures in the asymmetric May-Leonard model
• Oppressed species can form a winning pair in a multi-species ecosystem
• Multiplexing-based control of wavefront propagation: the interplay of inter-layer coupling, asymmetry and noise
• Rock-paper-scissors models with a preferred mobility direction
• Macroscopic behaviour in a two-species exclusion process via the method of matched asymptotics
• Deterministic and stochastic coarsening control in optically-addressed spatial light modulators subject to optical feedback
• Death by starvation in May-Leonard models
• Spatiotemporal Patterns in Active Four-State Potts Models
• A probabilistic cellular automata model for the dynamics of a population driven by logistic growth and weak Allee effect
• Reaction Diffusion Systems and Extensions of Quantum Stochastic Processes
• Perturbative Field-Theoretical Analysis of Three-Species Cyclic Predator-Prey Models
• Emergence of first-order and second-order phase transitions in a cyclic ecosystem exposed to environmental impact
• Mesoscopic Description of the Equal Load Sharing Fiber Bundle Model
• Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations
• Fixation and extinction in time-fluctuating spatially structured metapopulations
• Travelling waves and heteroclinic networks in models of spatially-extended cyclic competition
• Time Series Path Integral Expansions for Stochastic Processes
• An Insight of Heart-Like Systems with Percolation
• Effective one-dimension reduction of multi-compartment complex systems dynamics
• Non-Markovian Rock-Paper-Scissors games
• Agent-based Monte Carlo simulations for reaction-diffusion models, population dynamics, and epidemic spreading
• Dynamics of a linearly-perturbed May-Leonard competition model
• Parametric resonance, chaos and spatial structure in the Lotka-Volterra model
• Dynamic modes of active Potts models with factorizable numbers of states
• Renormalization of stochastic differential equations with multiplicative noise using effective potential methods
• Snowdrift game induces pattern formation in systems of self-propelled particles
• Logistic dynamics of small populations with demographic stochasticity