Coevolutionary Dynamics: From Finite to Infinite Populations

Arne Traulsen, Jens Christian Claussen, and Christoph Hauert
Phys. Rev. Lett. 95, 238701 – Published 2 December 2005

Abstract

Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics in finite populations. However, the relationship between deterministic and stochastic approaches remained unclear. Here we solve this problem by explicitly considering large populations. In particular, we identify different microscopic stochastic processes that lead to the standard or the adjusted replicator dynamics. Moreover, differences on the individual level can lead to qualitatively different dynamics in asymmetric conflicts and, depending on the population size, can even invert the direction of the evolutionary process.

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  • Received 14 July 2005

DOI:https://doi.org/10.1103/PhysRevLett.95.238701

©2005 American Physical Society

Authors & Affiliations

Arne Traulsen1,2,*, Jens Christian Claussen1, and Christoph Hauert2

  • 1Institut für Theoretische Physik und Astrophysik, Christian-Albrechts Universität, Olshausenstraße 40, 24098 Kiel, Germany
  • 2Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA

  • *Electronic address: traulsen@fas.harvard.edu

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Vol. 95, Iss. 23 — 2 December 2005

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