Fig. 2

Steps to fixation in strong amplifiers. Residents are shown in yellow, mutants in purple. a Our construction partitions a graph into a “hub” (orange) and a number of “branches” (blue) in such a way that the first mutant appears in one of the branches. The fixation of advantageous mutants is then reached in three stages. b The mutant lineage reaches the vertex of the branch adjacent to the hub. c, d Next, the mutants place offspring into the hub several times and eventually fixate there. In the worst case, the initial branch can become all residents again. e, f Finally, the mutants fixate in the branches one after the other and thereby occupy the whole population