The Spread of an Inversion with Migration and Selection

We re-examine the model of Kirkpatrick and Barton for the spread of an inversion into a local population. This model assumes that local selection maintains alleles at two or more loci, despite immigration of alternative alleles at these loci from another population. We show that an inversion is favored because it prevents the breakdown of linkage disequilibrium generated by migration; the selective advantage of an inversion is dependent on the amount of recombination between the loci involved, as in other cases where inversions are selected for as a result of their effects on recombination. We derive expressions for the rate of spread of an inversion; when the loci covered by the inversion are tightly linked, these conditions deviate substantially from those proposed previously, and imply that an inversion can then have only a small advantage.