Fig. 1: Probability-timescale landscape of population structures.
On a large well-mixed population (KN, green), a single mutant with a fixed relative fitness advantage r > 1 fixates with a constant probability 1 − 1/r after a number of generations that scales logarithmically with the population size N. On a Star graph (SN, brown), the fixation probability increases to 1 − 1/r2, but the process takes roughly \(N{\mathrm{log}}\,N\) generations, an exponential slowdown in timescale relative to KN. Dense Incubators (DN, purple) push the fixation probability to 1 within a polynomial timescale. Selection reactors (SRN, blue), introduced here (see Theorem 2), guarantee fixation with high probability while almost matching the timescale of well-mixed populations (here β(N) is an arbitrarily slowly growing unbounded function). No population structure can appear in the red region (see Theorem 1).
