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

Abstract

The appropriate description of fluctuations within the framework of evolutionary game theory is a fundamental unsolved problem in the case of finite populations. The Moran process recently introduced into this context [Nowak et al., Nature (London) 428, 646 (2004)] defines a promising standard model of evolutionary game theory in finite populations for which analytical results are accessible. In this paper, we derive the stationary distribution of the Moran process population dynamics for arbitrary $2\times 2$ games for the finite size case. We show that a nonvanishing background fitness can be transformed to the vanishing case by rescaling the payoff matrix. In contrast to the common approach to mimic finite-size fluctuations by Gaussian distributed noise, the finite size fluctuations can deviate significantly from a Gaussian distribution.

4 pages (2 figs). Published in Physical Review E (Rapid Communications)

References in corpus (6)

• Novel type of phase transition in a system of self-driven particles
• Coevolutionary Dynamics: From Finite to Infinite Populations
• Similarity based cooperation and spatial segregation
• Stochastic gain in population dynamics
• Molecular Discreteness in Reaction-Diffusion Systems Yields Steady States Not Seen in the Continuum Limit
• Cooperation driven by mutations in multi-person Prisoner's Dilemma

Cited by in corpus (12)

• Coevolutionary Dynamics: From Finite to Infinite Populations
• Fixation of strategies for an evolutionary game in finite populations
• Time Scales in Evolutionary Dynamics
• Coevolutionary dynamics in large, but finite populations
• Stochasticity and evolutionary stability
• Fixation times in evolutionary games under weak selection
• Phase diagrams for three-strategy evolutionary prisoner's dilemma games on regular graphs
• Strategy abundance in 2x2 games for arbitrary mutation rates
• Anomalous finite-size effects in the Battle of the Sexes
• Frequency-dependent fitness induces multistability in coevolutionary dynamics
• Replicator equations induced by microscopic processes in nonoverlapping population playing bimatrix games
• Evolutionary dynamics of imatinib-treated leukemic cells by stochastic approach