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This paper is concerned with exploring the microscopic basis for the discreteversions of the standard replicator equation and the adjusted replicatorequation. To this end, we introduce frequency-dependent selection -- as aresult of competition fashioned by game-theoretic consideration -- into theWright--Fisher process, a stochastic birth-death process. The process isfurther considered to be active in a generation-wise nonoverlapping finitepopulation where individuals play a two-strategy bimatrix population game.Subsequently, connections among the corresponding master equation, theFokker--Planck equation, and the Langevin equation are exploited to arrive atthe deterministic discrete replicator maps in the limit of infinite populationsize.

Replicator equations induced by microscopic processes in nonoverlapping population playing bimatrix games