The Effective Size of Populations Infected With Cytoplasmic Sex-Ratio Distorters

Many arthropod species are infected with maternally inherited endosymbionts that induce a shift in the sex ratio of their hosts by feminizing or killing males (cytoplasmic sex-ratio distorters, or SRDs). These endosymbionts can have profound impacts on evolutionary processes of their hosts. Here, I derive analytical expressions for the coalescent effective size N(e) of populations that are infected with SRDs. Irrespective of the type of SRD, N(e) for mitochondrial genes is given by the number of infected females. For nuclear genes, the effective population size generally decreases with increasing prevalence of the SRD and can be considerably lower than the actual size of the population. For example, with male-killing bacteria that have near perfect maternal transmission, N(e) is reduced by a factor that is given to a good approximation by the proportion of uninfected individuals in the population. The formulae derived here also yield the effective size of populations infected with mutualistic endosymbionts or maternally inherited bacteria that induce cytoplasmic incompatibility, although in these cases, the reduction in N(e) is expected to be less severe than for cytoplasmic SRDs.