  This work studies the generalized Moran process, as introduced by Lieberman
et al. [Nature, 433:312-316, 2005]. We introduce the parameterized notions of
selective amplifiers and selective suppressors of evolution, i.e. of networks
(graphs) with many "strong starts" and many "weak starts" for the mutant,
respectively. We first prove the existence of strong selective amplifiers and
of (quite) strong selective suppressors. Furthermore we provide strong upper
bounds and almost tight lower bounds (by proving the "Thermal Theorem") for the
traditional notion of fixation probability of Lieberman et al., i.e. assuming a
random initial placement of the mutant.
