Quantitative models of hybrid dysgenesis: rapid evolution under transposition, extrachromosomal inheritance, and fertility selection.

A model of the P-M system of hybrid dysgenesis is presented which incorporates single-site transposition of P factors in M cytotype, determination of offspring cytotype by both maternal cytotype and maternal or offspring nuclear genotype, and strong fertility selection in dysgenic individuals. The conditions required for the initial invasion of P factors into a pure M population, information concerning stable polymorphisms, and results of numerical iterations depicting the dynamic, nonequilibrium behavior of the system are summarized. While conditions for initial increase are independent of the rate of cytotype switching, the rate of evolution is accelerated by increased production of dysgenic individuals. If the transposition rate is sufficiently high to overcome the fertility barrier opposing P factors introduced into M populations, then convergence to high frequencies of the P factor occurs very rapidly. Under intense fertility depression, the phase of rapid increase may be preceded by an extended period of gradual increase at low frequencies.