We consider the evolution of ecological specialization in alandscape with two discrete habitat types connected by migration,for example, a plant-insect system with two plant hosts. Using aquantitative genetic approach, we study the joint evolution of aquantitative character determining performance in each habitattogether with the changes in the population density. We find thatspecialization on a single habitat evolves with intermediatemigration rates, whereas a generalist species evolves with bothvery low and very large rates of movement between habitats. Thereis a threshold at which a small increase in the connectivity ofthe two habitats will result in dramatic decrease in the totalpopulation size and the nearly complete loss of use of one of thetwo habitats through a process of "migrational meltdown." In somesituations, equilibria corresponding to a specialist and ageneralist species are simultaneously stable. Analysis of ourmodel also shows cases of hysteresis in which small transientchanges in the landscape structure or accidental demographicdisturbances have irreversible effects on the evolution ofspecialization.