Different evolutionary models are known to make disparate predictions for the success of an invading mutant in some situations. For example, some evolutionary mechanics lead to amplification of selection in structured populations, while others suppress it. Here, we use computer simulations to study evolutionary populations moved by flows, and show how the speed of this motion impacts the fixation probability of an invading mutant. Flows of different speeds interpolate between evolutionary dynamics on fixed heterogeneous graphs and in well-stirred populations. We find that the motion has an active role in amplifying or suppressing selection, accomplished by fragmenting and reconnecting the interaction graph. While increasing flow speeds suppress selection for most evolutionary models, we identify characteristic responses to flow for the different update rules we test. We suggest these responses as a potential aid for choosing the most suitable update rule for a given biological system.