Evolutionary Dynamics in Finite Populations: Oscillations, Diffusion, and Drift Reversal
published: Nov. 28, 2007, recorded: October 2007, views: 4124
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Coevolutionary dynamics arises in a wide range from biological to social dynamical systems. For infinite populations, a standard approach to analyze the dynamics are deterministic replicator equations, however lacking a systematic derivation. In finite populations modelling finite-size stochasticity by Gaussian noise is not in general warranted . We show that for the evolutionary Moran process and a Local update process, the explicit limit of infinite populations leads to the adjusted or the standard replicator dynamics, respectively . In addition, the first-order corrections in the population size are given by the finite-size update stochasticity and can be derived as a generalized diffusion term of a Fokker-Planck equation . This framework can be readily transferred to other microscopic processes, as the local Fermi process  or the inclusion of mutations in the process . We explicitely discuss the differences for the Prisoner's Dilemma, and Dawkin's Battle of the Sexes, where we show that the stochastic update fluctuations in the Moran process lead to a finite-size dependent drift reversal .  J.C. Claussen and A. Traulsen, Phys. Rev. E 71, 025101(R) (2005);  A. Traulsen, J.C. Claussen, C. Hauert, Phys. Rev. Lett, 95, 238701;  A.Traulsen, M.A.Nowak, J.M.Pacheco, Phys. Rev. E 74, 011909 (2006);  A. Traulsen, J.C. Claussen, C. Hauert, Phys. Rev. E 74, 011901 (2006).
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