Evolutionary dynamics, intrinsic noise and cycles of co-operation

Abstract

We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of amplification of demographic noise can give rise to coherent oscillations in parameter regimes where deterministic descriptions converge to fixed points with complex eigenvalues. These quasi-cycles between co-operation and defection have previously been observed in computer simulations; here we provide a systematic and comprehensive analytical characterization of their properties. We are able to predict their power spectra as a function of the mutation rate and other model parameters, and to compare the relative magnitude of the cycles induced by different types of underlying microscopic dynamics. We also extend our analysis to the iterated prisoner's dilemma game with a win-stay lose-shift strategy, appropriate in situations where players are subject to errors of the trembling-hand type.

14 pages, 12 figures, accepted for publication by Phys. Rev. E

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• Consensus and diversity in multi-state noisy voter models
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• Cycles of cooperation and defection in imperfect learning
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• Noise-driven oscillations in microbial population dynamics
• Frequency-dependent fitness induces multistability in coevolutionary dynamics
• Limit Cycles Sparked by Mutation in the Repeated Prisoner's Dilemma
• Replicator dynamics with diffusion on multiplex networks
• Effects of population growth on the success of invading mutants
• Analysis of a spatial Lotka-Volterra model with a finite range predator-prey interaction
• Learning to play public good games
• Chaos and unpredictability in evolution of cooperation in continuous time
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• Fixation and escape times in stochastic game learning
• Nash equilibrium mapping vs Hamiltonian dynamics vs Darwinian evolution for some social dilemma games in the thermodynamic limit
• Landscape and flux for quantifying global stability and dynamics of game theory
• Demographic noise in complex ecological communities
• Stochastic evolution in populations of ideas
• Effects of noise on convergent game learning dynamics
• The effects of heterogeneity on stochastic cycles in epidemics
• Coordination problems on networks revisited: statics and dynamics
• q-deformed evolutionary dynamics in simple matrix games
• Periodic vs. intermittent adaptive cycles in quasispecies co-evolution
• Vaccination Dilemma in the thermodynamic limit
• Fluctuations in meta-population exclusion processes
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