In this paper we reexamine how heterogeneous heterogeneous environments can enable protected polymorphisms. Building on the classical models by Levene and Dempster of dispersal and selection in two habitats, we systematically investigate how the maintenance of polymorphisms is affected by (i) local versus global density regulation and (ii) constant versus variable output from habitats to the next generation. We show that, for populations capable of habitat choice, a third independent and fundamental class of models needs to be considered. It is characterized by local density regulation (like Levene's model) and variable habitat output (like Dempster's model). Our results indicate that the conditions determining whether a system allows for protected polymorphisms qualitatively differ in the presence and absence of matching habitat choice (which occurs when individuals prefer the habitat to which they are best adapted). Without such habitat choice, the salient distinction is not between local or global density regulation but rather between constant or variable habitat output. With matching habitat choice this situation is reversed. Analysis of the third class of models introduced here suggests that the joint evolution of matching habitat choice and local- adaptation polymorphism is easier than was previously understood
