Figure 2.

Diffusion model visualized in one spatial dimension. Our model is in fact two dimensional, but is qualitatively similar. Left panel: One realization of the movement of ancestry of two homologous loci initially separated by distance r. In our model, there is a chance that they coalesce every time they come close, which is indirectly proportional to the local effective density parameter $D_e$ (see Appendix A). Right panel: In our model, the probability density function of having moved distance $\Delta x$ at time t generations back spreads out as a Gaussian distribution $N\left(0,{\sigma }^{2}t\right)$ with linearly increasing variance of ${\sigma }^{2}t.$