The effect of Wolbachia on genetic divergence between populations: models with two-way migration

Wolbachia are intracellular bacteria that cause various reproduction alterations in their hosts, including cytoplasmic incompatibility (CI), an incompatibility between sperm and egg that typically results in embryonic death. We investigate theoretically the effects of Wolbachia-induced bidirectional CI on levels of divergence between two populations, where there is migration in both directions and differential selection at a single locus. The main findings are as follows: Wolbachia differences in the two populations are maintained up to a threshold migration rate, above which the system collapses to a single Wolbachia type; differential selection at a nuclear locus increases the threshold migration rate below which Wolbachia polymorphisms are maintained; Wolbachia differences between the populations enhance their genetic divergence at the selected locus by reducing the "effective migration rate," and even moderate levels of CI can cause large population differences in allele frequencies; and asymmetric CI can induce strong asymmetries in effective migration rate and dramatically alter the pattern of genetic divergence compared with the No Wolbachia situation. We derive an analytical approximation for the effective migration rate, which matches the simulation results for most parameter values. These results generally support the view that CI Wolbachia can contribute to genetic divergence between populations.