Studies of trait-mapping and local adaptation often identify signatures of genetically parallel evolution, where different species evolve similar phenotypes using the same genes. Such patterns appear incongruent with current estimations of quantitative trait architecture. With hundreds or thousands or genes contributing to a trait, why would selection make repeated use of the same genes? Here, we use individual-based simulations to explore a two-patch model with quantitative, pleiotropic traits to understand the parameters which may lead to repeated use of a particular locus during independent bouts of adaptation. We find that repeatability can be driven by increased phenotypic effect size, a reduction in trait dimensionality and a reduction in mutational correlations at a particular locus relative to other loci in the genome, and that these patterns are magnified by increased migration between demes. These results suggest that evolutionary convergence can arise from multiple characteristics of a locus, and provide a framework for the interpretation of quantitative signatures of convergence in empirical studies.