Predicting range expansion dynamics is challenging for fundamental and applied research, especially if ecological and evolutionary processes occur over similar time scales. We assessed the predictability of evolutionary outcomes in laboratory range expansions of the ciliate Paramecium caudatum. Experimental range core and front treatments were recreated in a predictive mathematical model, parametrized with dispersal and growth data of the 20 founder strains. Short-term evolution from standing genetic variation was driven by selection for dispersal at the front and general selection for growth rate in all treatments. The quantitative match between predicted and observed trait changes was mirrored by genetic divergence between treatments, with the repeated fixation of strains identified as most likely winners in our model. Long-term evolution in range front lines produced a dispersal syndrome (competition - colonisation trade-off). Our work suggests that short-term evolution at range fronts can follow predictable trajectories, based on few key parameters.