We consider the evolution of ecological specialization in a landscape with two discrete habitat types connected by migration, for example, a plant-insect system with two plant hosts. Using a quantitative genetic approach. we study the joint evolution of a quantitative character determining performance in each habitat together with the changes in the population density. We find that specialization on a single habitat evolves with intermediate migration rates, whereas a generalist species evolves with both very low and very large rates of movement between habitats. There is a threshold at which a small increase in the connectivity of the two habitats will result in dramatic decrease in the total population size and the nearly complete loss of use of one of the two habitats through a process of "migrational meltdown." In some situations, equilibria corresponding to a specialist and a generalist species are simultaneously stable. Analysis of our model also shows cases of hysteresis in which small transient changes in the landscape structure or accidental demographic disturbances have irreversible effects on the evolution of specialization.