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