Dynamics of gametic disequilibria between loci linked to chromosome inversions: The recombination redistributing effect of inversions

The total gametic disequilibrium between two loci linked to polymorphic inversions can be partitioned into two types of components: within and between chromosome arrangements. The within components depend on the gametic disequilibrium within each chromosome arrangement. The between components depend on the locus-inversion disequilibria. This partitioning has practical applications and is indispensable for studying the dynamics of these systems because inversions greatly reduce recombination in the heterokaryotypes while allowing free, and sometimes different, recombination in each of the homokaryotypes. We provide equations for the per generation change of the various disequilibria for systems with two and three chromosome arrangements, and the general recursive equations predicting the disequilibria after any number of generations for the case of two arrangements, Simulation studies were carried out using different values of the recombination parameters and all possible initial conditions. The results show a complex convergence to linkage equilibrium in inversion systems. The various disequilibria can have local maxima and minima while approaching equilibrium and, moreover, their dynamics cannot be described, in general, using a single parameter, i.e. an effective recombination rate. We conclude that the effects of inversions on gametic disequilibria must be carefully considered when dealing with disequilibria in inversion systems. The formulae provided in this paper can be used for such purpose.