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DY: Fachverband Dynamik und Statistische Physik
DY 9: Statistical physics in biological systems
DY 9.2: Talk
Monday, March 26, 2007, 16:45–17:00, H3
Meanfield dynamics of evolutionary and coevolutionary processes in infinite populations and finite-size corrections in finite populations — Arne Traulsen1, •Jens Christian Claussen2, and Christoph Hauert1 — 1Center for Evolutionary Dynamics, Harvard — 2Institut f. Theoret. Physik & Astrophys., Univ. Kiel, Germany
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]. 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 exhibit a finite-size dependent drift reversal [2]. This framework can be readily transferred to other microscopic processes, as the local Fermi process [3] or the inclusion of mutations [4].
[1] J.C.Claussen & 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)