Climate change is expected to favor shifts in plant distributions; some such shifts are already being observed along elevation gradients. However, the rate of such shifts may be limited by their ability to reach newly suitable areas and by competition from resident species. The degree of local adaptation and genetic variation may also play a role in the interaction between migrants and residents by affecting relative fitness. We used a simulation model to explore the interacting effects of dispersal, fecundity, disturbance, and genetic variation on range-edge dynamics between a pair of demographically similar tree species. Ideal climate for an individual is determined by genotype. The simulated landscape undergoes an 80-year period of climate change in which climate bands shift upslope; subsequently, climate is held constant for 300 years. The presence of a high-elevation competitor caused a significant lag in the range shift of the low-elevation species relative to competition-free scenarios. Increases in fecundity and dispersal distance both helped to speed up the replacement of the high-elevation species by the low-elevation species at their range boundary. While some disturbance scenarios facilitated this transition, frequent canopy disturbance inhibited colonization by removing reproductive adults and led to range contractions in both species. Differences between dispersal scenarios were more pronounced when disturbance was frequent (15 vs. 25 year return interval) and dispersal was limited. When the high-elevation species lacked genetic variation, its range was more-easily invaded by the low-elevation species, while a similar lack of variation in the low-elevation species inhibited colonization-but only when this lack of variation decreased the fitness of the affected species near the range boundary. Our model results support the importance of measuring and including dispersal/fecundity, disturbance type and frequency, and genetic variation when assessing the potential for range shifts and species vulnerability to climate change.