The Behaviour of F-statistics over Time

We study the behaviour of the F 2-statistic and F st-statistic, respectively, over time in a Wright-Fisher model with mutation and migration. We give precise conditions for when the F 2-statistic is non-monotonic, that is, increases over time until a certain point and then starts decreasing. We show that even for small population sizes, the two statistics are well approximated by population size scaled expressions. ### Competing Interest Statement The authors have declared no competing interest.