Dresden 2006 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 46: Poster
DY 46.11: Poster
Donnerstag, 30. März 2006, 16:00–18:00, P1
Relation between microscopic coevolutionary processes and macroscopic replicator equations: Meanfield dynamics in infinite populations and first-order corrections in finite populations — •Jens Christian Claussen1, Arne Traulsen2, and Christoph Hauert2 — 1Institut für Theoretische Physik und Astrophysik, Universität Kiel, Germany — 2Center for Evolutionary Dynamics, Harvard
Evolutionary game theory since Maynard Smith has served a powerful approach in biological systems as well as in agent-based models of social and economic systems. For infinite populations, a standard approach to analyze the dynamics are deterministic replicator equations, however lacking a systematic derivation. Additionally, 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. 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] thus giving a convenient framework of description. We explicitely discuss the differences for the Prisoner’s Dilemma, where Moran evolution fixates faster [2], 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].
[1] J.C. Claussen & A. Traulsen, Phys. Rev. E 71, 025101(R)
[2] A. Traulsen, J.C. Claussen, C. Hauert, Phys. Rev. Lett, 2005, in print