Figure 4 .

Properties of the frequency spectrum with sweeps occurring at a fixed genetic distance. Coalescent rates are given by Equation 9, with q fixed to $q_x=x{e}^{-t_{x}r}$ and t_xr = 0.6, across a range of x. (A) The percentage of segregating sites found at frequency 1 ≤ k ≤ 20, relative to the neutral expectation (i.e., $F_{20,k}/F_{20,k}^{\text{N}}$). In these simulations the rate of sweeps Nν has been fixed to result in a 50% reduction in diversity. The dashed gray line gives the neutral expectation. (B) The mean number of singletons divided by mean number of segregating sites, from mssel simulations with a sample size of 10 at a neutral site a distance 2Nr = 200 from a selected site. The selected allele performs a recurrent top-hat trajectory (with N = 10,000 and t_x/2N = 0.003, giving rt_x = 0.6, and pausing T/2N = 0.01) to frequency x = 0.2, x = 0.5, or x = 0.9 across a range of 2Nν. Note the span of π/θ is smaller in the low-x simulations as the effect on diversity of a given 2Nν is smaller. Solid lines show the analytical approximation for $\mathbb{E}$[T₁]/$\mathbb{E}$[T_tot] of Appendix B. The dashed gray line gives the neutral value of the expected proportion of singletons $1/{\displaystyle {\sum }_{j=1}^{n-1}1/j}$.