Figure 3.

Establishment probability as a function of migration rate. (A) Weak selection ($s_1=0.02$ and $s_2=-0.01$) and (B) strong selection ($s_1=0.1$ and $s_2=-0.01$) are assumed in a symmetric model $\left(N_1=N_2\right)$. (C and D) Asymmetric population settings are considered ($N_1=3N_2$ in C and $N_1=N_2/3$ in D). Our result in red is compared with those of Yeaman and Otto (2011) and Tomasini and Peischl (2018), together with the result of our forward simulation. The establishment probability for a mutation that arises in subpopulation I $\left(F\left(1/2N_1,0\right)\right)$ is shown by solid lines and closed circles, and that for a mutation that arises in subpopulation II $\left(F\left(0,1/2N_2\right)\right)$ is shown by broken lines and open triangles. The establishment probability at the high migration limit $\left(m=0.5\right)$ is shown by a yellow triangle. In each panel, a gray region is placed such that the proportion of the replications where two alleles (A and a) coexisted $\left(Pc\right)$ $>0.9$ in the left, while $Pc<0.1$ in the right. The vertical line presents the critical migration rate, above which allele A fixes in the entire population, obtained by Equation 6 (see text for detail).