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Finite-size fluctuations in coevolutionary dynamics arise in models ofbiological as well as of social and economic systems. This brief tutorialreview surveys a systematic approach starting from a stochastic processdiscrete both in time and state. The limit $N\to \infty$ of an infinitepopulation can be considered explicitly, generally leading to a replicator-typeequation in zero order, and to a Fokker-Planck-type equation in first order in$1/\sqrt{N}$. Consequences and relations to some previous approaches areoutlined.

Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations