All species are restricted in their distribution. Currently, ecological models can only explain such limits if patches vary in quality, leading to asymmetrical dispersal, or if genetic variation is too low at the margins for adaptation. However, population genetic models suggest that the increase in genetic variance resulting from dispersal should allow adaptation to almost any ecological gradient. Clearly therefore, these models miss something that prevents evolution in natural populations. We developed an individual-based simulation to explore stochastic effects in these models. At high carrying capacities, our simulations largely agree with deterministic predictions. However, when carrying capacity is low, the population fails to establish for a wide range of parameter values where adaptation was expected from previous models. Stochastic or transient effects appear critical around the boundaries in parameter space between simulation behaviours. Dispersal, gradient steepness, and population density emerge as key factors determining adaptation on an ecological gradient.