Coevolutionary dynamics: from finite to infinite populations.
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.
Traulsen
Arne
A
Institut für Theoretische Physik und Astrophysik, Christian-Albrechts Universität, Olshausenstrasse 40, 24098 Kiel, Germany. traulsen@fas.harvard.edu
Claussen
Jens Christian
JC
Hauert
Christoph
C
D000818:Animals; D005075:Biological Evolution; D003198:Computer Simulation; D005716:Game Theory; D005828:Genetics, Population; D006801:Humans; D008957:Models, Genetic; D015233:Models, Statistical; D011157:Population Dynamics; D012641:Selection, Genetic; D013269:Stochastic Processes