Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-09-24
Physical Review Letters 95, 238701 (2005)
Physics
Condensed Matter
Statistical Mechanics
4 pages (2 figs included). Published in Phys. Rev. Lett., December 2005
Scientific paper
10.1103/PhysRevLett.95.238701
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.
Claussen Jens Christian
Hauert Christoph
Traulsen Arne
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