Evolutionary branching of a magic trait.

We study the adaptive dynamics of a so-called magic trait, which is under natural selection and which also serves as a cue for assortative mating. We derive general results on the monomorphic evolutionary singularities. Next, we study the long-term evolution of single-locus genetic polymorphisms under various strengths of assortativity in a version of Levene's soft-selection model, where natural selection favours different values of a continuous trait within two habitats. If adaptive dynamics leads to a polymorphism with sufficiently different alleles, then the corresponding homozygotes cease to interbreed so that sympatric speciation occurs.