Changes in the seasonal timing of life history events are documented effects of climate change. We used a general model to study how dispersal and competitive interactions affect eco-evolutionary responses to changes in the temporal distribution of resources over the season. Specifically, we modeled adaptation of the timing of reproduction and population dynamic responses in two competing populations that disperse between two habitats characterized by an early and late resource peak. We investigated three scenarios of environmental change: (1) food peaks advance in both habitats, (2) in the late habitat only and (3) in the early habitat only. At low dispersal rates the evolutionarily stable timing of reproduction closely matched the local resource peak and the environmental change typically caused population decline. Larger dispersal rates rendered less intuitive eco-evolutionary population responses. First, dispersal caused mismatch between evolutionarily stable timing of reproduction and local resource peaks and as a result, reproductive output for subpopulations could increase as well as decrease when resource availability underwent temporal shifts. Second, population responses were contingent on competition between populations. This could accelerate population declines and cause extinctions or even reverse population trends from negative to positive compared to the low dispersal case. When dispersal rate was large and the early resource peak was advanced available niche space was reduced. Hence, even when a population survived the environmental change and obtained positive equilibrium population density, subsequent adaptation of competing populations could drive it to extinction due to convergent evolution and competitive exclusion. These results shed new light on the role of competition and dispersal for the evolution of timing of life history events and provide guidelines for understanding short and long-term population response to climate change.