The types of equilibria possible with an inversion in a two-locus system are considered, and their stability properties investigated. With complete suppression of crossing-over in inversion heterozygotes, there are three possible types of stable equilibria; which of these is reached by a new inversion depends on the fitness effects of the two loci concerned. With one of these equilibria, basically involving cumulative overdominance of the selected loci, the inverted and standard sequences are genetically homogeneous and differ with respect to both loci. With the other types of equilibrium, the standard sequence remains heterogeneous for one or both loci. It is shown that this situation may lead to variations in karyotypic fitnesses when the inversion is changing in frequency. It is also found that, with certain fitness relationships, two alternative stable equilibria may coexist; the final frequency reached by an inversion may therefore depend on the population's history.
The effects of double crossing-over in inversion heterozygotes were also investigated, and it was shown that the equilibria with double crossing-over are closely related to the corresponding equilibria without it, except that both sequences are more heterogeneous genetically. Within each sequence there is almost complete linkage equilibrium between the selected loci, although both are in linkage disequilibrium with the inversion itself. It was also found that, with double crossing-over, the population tends to remain for many thousands of generations in a state of quasi-equilibrium. In this state, the inversion tends not to return to its original frequency after a perturbation; also, it may remain for a long time relatively homogeneous genetically, especially when rare.
These results were compared with those from experiments and observations on inversion polymorphisms.