SELECTION-MIGRATION REGIMES CHARACTERIZED BY A GLOBALLY STABLE EQUILIBRIUM

The principle that a subdivided population subject to overdominance viability selection in each habitat will manifest a unique, globally attractng polymorphic equilibrium is posited. This follows as a corollary to the stronger principle that, if haploid selection or submultiplicative diploid selection (definition: the geometric mean of the homozygote viabilities is less than or equal to the heterozygote viability) is operating in each habitat,there is a unique, globally attracting stable equilibrium that may be monomorphic or polymorphic. These principles are proven for a broad spectrum of migration patterns. In all such migration selection systems, multiple fixation states cannot be simultaneously stable under submultiplicative viability regimes. Contrasting examples where sub-multiplicative viabilities are not in force are given.