Vertically transmitted parasites proliferate in a host population by manipulating their host reproduction. A bacterial symbiont, Wolbachia, is commonly known to induce cytoplasmic incompatibility (CI) resulting in reduction of host reproduction. Strong CI intensity enhances the spread of Wolbachia effectively. However, recent studies propose that Wolbachia evolves from strong into benign parasitism. Furthermore, moderate CI prevails in a wild population with perfect maternal transmission of Wolbachia.

This prevalence of the moderate CI first requires that a small amount of mutant phenotypes in CI intensity invade a host population infected by resident Wolbachia. The mutants then proliferate in the host population to coexist with or overwhelm the resident Wolbachia. Kriesner et al. (2013) proposed that a host fitness advantage enables the Wolbachia invasion from low frequency. Here we propose another possibility of the invasion of Wolbachia with moderate CI with simulations based on the theoretical model of Fine's formula (Fine 1978) and individual-based approaches.