Dresden 2006 – wissenschaftliches Programm
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AKB: Biologische Physik
AKB 17: Population Dynamics
AKB 17.2: Vortrag
Mittwoch, 29. März 2006, 14:45–15:00, ZEU 260
Coevolutionary dynamics: From finite to infinite populations — •Jens Christian Claussen1, Arne Traulsen2, and Christoph Hauert2 — 1Institut für Theoretische Physik und Astrophysik, Universität Kiel, Germany — 2Center for Evolutionary Dynamics, Harvard
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently, stochastic processes have 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 explicitely considering the limit of infinite 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.
[1] J.C. Claussen & A. Traulsen, Phys. Rev. E 71, 025101(R)
[2] Arne Traulsen, Jens Christian Claussen, Christoph Hauert, Phys. Rev. Lett (2005, in print; arXiv.org e-print cond-mat/0409655)