Previous analyses of polymorphism in a subdivided population (Levene 1953; Deakin 1966) have made assumptions about the mode of migration from one niche to another. These are generally of a highly artificial character . We here adopt a more plausible approach based on the use of stochastic matrices. This yields not only a sufficient condition for genetic polymorphism [in the sense defined by the author (Deakin 1966)], but also a necessary one.