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.
In previous work, we have noted that even simple coevolutionary dynamics
of 2x2 games in finite populations can lead to unexpected stationary
distributions of strategies significantly deviating from the Gaussian [1].
However, the relationship between deterministic and stochastic approaches
remained unclear. In [2], we address 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] Jens Christian Claussen and Arne Traulsen, Nongaussian fluctuations
arising from finite populations: Exact results for the evolutionary Moran
process, Physical Review E 71, 025101(R) (2005) (cond-mat/0409656).

[2] Arne Traulsen, Jens Christian Claussen and Christoph Hauert,
Coevolutionary dynamics: From finite to infinite populations, Physical
Review Letters 95, 238701 (2006) (cond-mat/0409655).