Uniqueness and multiplicity of clines in an environmental pocket

The number of clines (i.e., polymorphic equilibria) maintained by a step-environment in a unidimensional pocket at a single diallelic locus is investigated. The monoecious population is locally panmictic; its density is uniform. Migration and viability selection are both weak; the former is homogeneous and symmetric; the latter is directional and usually specified by a unimodal function f(p) of the gene frequency p. If the ratio of the selection intensity to the migration rate exceeds a critical value, at least one cline exists. The general theorems on equilibrium structure determine it in detail for many classes of f(p), including the cubic for frequency-independent selection. Numerical examples demonstrate that for suitable f(p), many equilibria can occur simultaneously.