Fig. 6.

A comparison between the probability distributions P(M, t) at different snaphots in time (denoted by different colours) using $r=0.1{\mu }_2$ (top panels) and $r=10{\mu }_2$ (bottom panels) migration rates, having initialised $P(M,t_0)={\delta }_{\mathrm{D}}(M_{*}-M)$ (where δ_D is a Dirac delta function) at the unstable (left column) and stable (right column) equilibrium points M_*, given a choice of $R_0=R_{0†}(z,k)+0.1\simeq 2.18$. The solid lines indicate that the fully non-Markovian process given by Eq. (36) is used, whereas the dashed lines indicate the corresponding choice of approximate Markovian process, given by Eq. (37). The distributions themselves have been numerically obtained by binning 10³ realisations of Eq. (40).