Fig. 1

Evolutionary dynamics in structured populations. Residents (yellow) and mutants (purple) differ in their reproductive rate. a A single mutant appears. The lineage of the mutant becomes extinct or reaches fixation. The probability that the mutant takes over the population is called “fixation probability”. b The classical, well-mixed population is described by a complete graph with self-loops. (Self-loops are not shown here.) (c) Isothermal structures do not change the fixation probability compared to the well-mixed population. d The Star is an amplifier for uniform initialization. e A self-loop means the offspring can replace the parent. Self-loops are a mathematical tool to assign different reproduction rates to different places. f The Superstar, which has unbounded degree in the limit of large population size, is a strong amplifier for uniform initialization. Its edges (shown as arrows) are directed which means that the connections are one-way