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The modelling of evolutionary game dynamics in finite populations requiresmicroscopic processes that determine how strategies spread. The exact detailsof these processes are often chosen without much further consideration.Different types of microscopic models, including in particular fitness-basedselection rules and imitation-based dynamics, are often used as if they wereinterchangeable. We challenge this view and investigate how robust thesechoices on the micro-level really are. Focusing on a key macroscopicobservable, the probability for a single mutant to take over a population ofwild-type individuals, we show that there is a unique pair of a fitness-basedprocess and an imitation process leading to identical outcomes for arbitrarygames and for all intensities of selection. This highlights the perils ofmaking arbitrary choices at the micro-level without regard of the consequencesat the macro-level.

When do microscopic assumptions determine the outcome in evolutionary game dynamics?