Berlin 2012 – wissenschaftliches Programm

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 3: Economic Models and Evolutionary Game Theory I

SOE 3.2: Vortrag

Montag, 26. März 2012, 11:15–11:30, H 0110

Multidimensional multiplicative noise arising in evolutionary dynamics — Arne Traulsen¹, •Jens Christian Claussen², and Christoph Hauert³ — ¹Evolutionary Theory Group, Max-Planck-Institute for Evolutionary Biology, Plön — ²Institut für Neuro- und Bioinformatik, Univ. Lübeck — ³Dept. of Mathematics, Univ. of British Columbia, Vancouver

We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations. For large, but finite populations this allows to include demographic noise without requiring explicit simulations. Instead, the population size only rescales the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types, provided that mutation rates, µ, are not too small compared to the population size N, i.e., limitations occur for µ N ≪ 1. We illustrate our approach by a Rock-Scissors-Paper game with mutations, where we demonstrate excellent agreement with simulation based results for sufficiently large populations. In the absence of mutations the excellent agreement extends to small population sizes.