The effective size of populations infected with cytoplasmic sex-ratio distorters

Abstract

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.

Figure 1.—

Scaling factor for the effective population size of mitochondrial genes in an SRD-infected population, depending on the relative numbers and of infected and uninfected daughters that an infected female produces. In this contour plot, the factor by which is altered through SRD infection is indicated by areas of different color, where the small numbers in the plot give at the borders of these areas. The relative number of sons, , that an infected female produces, is assumed to be equal to the number of uninfected daughters . The dashed red line marks the situation where infected females produce as many offspring as uninfected females.

Figure 2.—

Scaling factor for the effective population size of nuclear genes in an SRD-infected population, depending on the relative numbers of infected daughters and of uninfected daughters and sons that an infected female produces. The dashed red line marks the situation where infected females produce as many offspring as uninfected females.

Figure 3.—

Scaling factor for the effective population size of nuclear genes in an SRD-infected population, with . is expressed as a function of the equilibrium frequency of the SRD and in relation to the following rates of maternal transmission : 0.9 (solid line), 0.95 (dotted line), and 0.99 (dashed line). Note that can never be greater than any given transmission rate. The thick line gives the value for that is obtained with the approximation (see Equation 11).

Figure 4.—

Scaling factor for the effective population size of nuclear genes in endosymbiont harboring populations that do not induce sex-ratio distortion (i.e., ). The dashed green line marks endosymbionts with a transmission rate of 0.95.