Figure 3.

The difference between the fixation probability of a meta-star and the equivalent well-mixed population of size with $M=4$ patches and identical local size in each patch $N_1=N/M=5$ for different fitness values. Lines show analytical results for low migration probabilities (Eq. 18) and migration probability $\lambda =1$ (Eq. 19) symbols show numerical results based on a transition matrix approach³⁹ for $\lambda ={10}^{-6}$, $\lambda =0.01$, $\lambda =0.1$, and $\lambda =0.5$. For migration probability $\lambda ={10}^{-6}$, we observe an almost perfect agreement, the low migration result serves as a good approximation. The fixation probability in $\lambda =1$ is obtained analytically using the Martingale approach. For extremely high and low migration probability the meta-star acts as an amplifier of selection (such that the lines only pass through the white shaded area of the plot) while in the intermediate migration regime shows a very different behavior where it could be an amplifier or a suppressor of selection depending on the fitness value.