Sex-ratio evolution in nuclear-cytoplasmic gynodioecy when restoration is a threshold trait

Gynodioecious plant species, which have populations consisting of female and hermaphrodite individuals, usually have complex sex determination involving cytoplasmic male sterility (CMS) alleles interacting with nuclear restorers of fertility. In response to recent evidence, we present a model of sexratio evolution in which restoration of male fertility is a threshold trait. We find that females are maintained at low frequencies for all biologically relevant parameter values. Furthermore, this model predicts periodically high female frequencies (> 50%) under conditions of lower female seed fecundity advantages (compensation, x = 5%) and pleiotropic fitness effects associated with restorers of fertility (costs of restoration, y = 20%) than in other models. This model explains the maintenance of females in species that have previously experienced invasions of CMS alleles and the evolution of multiple restorers. Sensitivity of the model to small changes in cost and compensation values and to initial conditions may explain why populations of the same species vary widely for sex ratio.