Fixation of strategies for an evolutionary game in finite populations

Abstract

A stochastic evolutionary dynamics of two strategies given by 2 x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire population. The process is discussed in the framework of a random walk with arbitrary hopping rates. The time of fixation is found to be identical for both strategies in any particular game. The asymptotic behavior of the fixation time and fixation probabilities in the large population size limit is also discussed. We show that fixation is fast when there is at least one pure evolutionary stable strategy (ESS) in the infinite population size limit, while fixation is slow when the ESS is the coexistence of the two strategies.

22 pages, 2 eps figures

References in corpus (1)

• Nongaussian fluctuations arising from finite populations: Exact results for the evolutionary Moran process

Cited by in corpus (48)

• Evolutionary games on graphs
• Universality of weak selection
• Mutation-selection equilibrium in games with multiple strategies
• Fixation times in evolutionary games under weak selection
• Instability of spatial patterns and its ambiguous impact on species diversity
• Strategy abundance in 2x2 games for arbitrary mutation rates
• Fixation in finite populations evolving in fluctuating environments
• Coexistence and Survival in Conservative Lotka-Volterra Networks
• Evolutionary Multiplayer Games
• Evolution of a Fluctuating Population in a Randomly Switching Environment
• The pace of evolution across fitness valleys
• Population Dynamics in a Changing Environment: Random versus Periodic Switching
• Intransitivity and coexistence in four species cyclic games
• Evolution Equation of Phenotype Distribution: General Formulation and Application to Error Catastrophe
• The edge of neutral evolution in social dilemmas
• Stochastic dynamics of the prisoner's dilemma with cooperation facilitators
• Stochastic slowdown in evolutionary processes
• Globally synchronized oscillations in complex cyclic games
• The effect of habitats and fitness on species coexistence in systems with cyclic dominance
• Critical mass effect in evolutionary games triggered by zealots
• Commitment versus persuasion in the three-party constrained voter model
• Stochastic tunneling and metastable states during the somatic evolution of cancer
• The Emergence of Cooperation from a Single Mutant during Microbial Life-Cycles
• Evaluating the structure-coefficient theorem of evolutionary game theory
• Anomalous finite-size effects in the Battle of the Sexes
• Replicator equations induced by microscopic processes in nonoverlapping population playing bimatrix games
• Frequency-dependent fitness induces multistability in coevolutionary dynamics
• Coupled environmental and demographic fluctuations shape the evolution of cooperative antimicrobial resistance
• Synchronization and extinction in cyclic games with mixed strategies
• Evolutionary Dynamics in a Varying Environment: Continuous versus Discrete Noise
• The prisoners dilemma on a stochastic non-growth network evolution model
• How Social Rewiring Preferences Bridge Polarized Communities
• Flocking in One Dimension: Asters and Reversals
• Effects of population growth on the success of invading mutants
• Coexistence of Competing Microbial Strains under Twofold Environmental Variability and Demographic Fluctuations
• Eco-evolutionary dynamics of cooperative antimicrobial resistance in a population of fluctuating volume and size
• Evolutionary Games on Networks: Phase Transition, Quasi-equilibrium, and Mathematical Principles
• Deterministic and stochastic cooperation transitions in evolutionary games on networks
• Spatial effect on stochastic dynamics of bistable evolutionary games
• Effect of the degree of an initial mutant in Moran processes in structured populations
• More can be better: An analysis of single-mutant fixation probability functions under $2\times 2$ games
• Stochastic foundations in nonlinear density-regulation growth
• Fixation and extinction in time-fluctuating spatially structured metapopulations
• Fixation and Fluctuations in Two-Species Cooperation
• First-passage on disordered intervals
• When Less is More: Evolutionary Dynamics of Deception in a Sender-Receiver Game
• Non-equilibrium time-dependent solution to discrete choice with social interactions
• Finite Population Dynamics Resolve the Central Paradox of the Inspection Game