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A review of the discovery of the surprising dynamical properties of evolutionary amplifiers (Lieberman, Hauert & Nowak, 2005). In the spatial Moran process the geometrical arrangement of individuals can have surprising effects on the evolutionary dynamics. The key determinants of the evolutionary process in finite populations are the fixation probabilities and times. Both can be significantly affected by the geometrical arrangement of individuals. This contrasts and indeed refutes the conjectures by Maruyama (1970) and Slatkin (1981) stating that fixation probabilities are independent of population structure. Most intriguingly, the geometrical arrangement of individuals alone can amplify selection and suppress random drift. In fact, for strong amplifiers the fixation probability converges to certainty for beneficial mutants with an arbitrarily small advantage over the resident and sufficiently large structures. This claim was later challenged for the super-star graph (Diaz et al. 2013). The resolution turned out to be unexpectedly challenging but revealed further interesting and fairly subtle dynamical features of the super-star graph (Jamieson-Lane & Hauert, 2015).
