Theory of coevolution of cytoplasmic male-sterility, nuclear restorer and selfing

Gynodioecy is a sexual polymorphism in angiosperms, where hermaphroditic and female individuals coexist. This is often caused by a cytoplasmic genetic element (CGE) that destroys male functions, which is called cytoplasmic male-sterility (CMS). On the other hand, nuclear genes tend to evolve the ability to restore male function. The coevolutionary process of CMS and the restoration has been studied theoretically. Recently, a theoretical study suggested that these coevolutionary dynamics could be influenced by the rate of selfing within populations, although it assumed that the selfing rate of a population was a fixed parameter. Accordingly, we theoretically study the coevolution of three traits in this paper: CMS, nuclear restorer and selfing rate, in which we hypothesize that selfing evolution can suppress CMS evolution under some conditions. The analysis indicates three significant properties of the system; (1) CMS-restorer evolution can result in bistability under a given selfing rate, (2) the coevolution of three traits can realize intermediate levels of selfing, and (3) the evolution of high levels of selfing is conditionally associated with no CMS and/or no restoration, which may support our hypothesis.