Quantifying the impact of genotype-dependent gene flow on mutation fixation in subdivided populations

In the wild, any population is likely to be spatially structured. Whereas we deeply understand evolutionary dynamics in well-mixed populations, our understanding of evolutionary dynamics in subdivided populations needs to be improved. In this work, I quantify the impact of genotype-dependent gene flow on the evolutionary dynamics of a subdivided population. Specifically, I build a model of a population structured as the island or the stepping stone model in which genotype-dependent gene flow is represented by individuals migrating between its sub-populations at a rate depending on their genotype. I analytically calculate the fixation probability and time of a mutation arising in the subdivided population under the low migration limit, which I validate with numerical simulations. I find that the island and the stepping stone models lead to the same fixation probability. Moreover, comparing the fixation probability in these models to the one in a well-mixed population of the same total census size allows me to identify an effective selection coefficient and population size. In the island and the stepping stone models, the effective selection coefficient differs from the selection coefficient if the wild-type and the mutant migration rates are different, whereas the effective population size equals the total census size. Finally, I show that genotype-dependent gene flow increases the fixation time, which allows for distinguishing the island and the stepping stone models, as opposed to the fixation probability.