Evolutionary Dynamics in Finite Populations: Oscillations, Diffusion, and Drift Reversal

author: Jens Christian Claussen, Institute of Theoretical Physics and Astrophysics, University of Kiel
published: Nov. 28, 2007,   recorded: October 2007,   views: 487
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Description

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 [1]. 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 [2]. 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 [2]. This framework can be readily transferred to other microscopic processes, as the local Fermi process [3] or the inclusion of mutations in the process [4]. 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 [2]. [1] J.C. Claussen and A. Traulsen, Phys. Rev. E 71, 025101(R) (2005); [2] A. Traulsen, J.C. Claussen, C. Hauert, Phys. Rev. Lett, 95, 238701; [3] A.Traulsen, M.A.Nowak, J.M.Pacheco, Phys. Rev. E 74, 011909 (2006); [4] A. Traulsen, J.C. Claussen, C. Hauert, Phys. Rev. E 74, 011901 (2006).

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Reviews and comments:

Comment1 ok, December 13, 2009 at 3:47 a.m.:

SO see he makes sense, moreover, he tires to make sense, to make sense of what of a field descending into -- or OK i cannot tell, never having ascending out of -- well you know ..


Comment2 ok, December 13, 2009 at 3:49 a.m.:

SO see he makes sense, moreover, he tires to make sense, to make sense of a field descending into -- or OK i cannot tell, a field never having ascending out of -- well you know ..

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