title: Fixation probabilities on superstars, revisited and revised.
abstract: Population structures can be crucial determinants of evolutionary processes. For the Moran process on graphs certain structures suppress selective pressure, while others amplify it (Lieberman et al., 2005). Evolutionary amplifiers suppress random drift and enhance selection. Recently, some results for the most powerful known evolutionary amplifier, the superstar, have been invalidated by a counter example (Díaz et al., 2013). Here we correct the original proof and derive improved upper and lower bounds, which indicate that the fixation probability remains close to 1-1/(r(4)H) for population size N→∞ and structural parameter H⪢1. This correction resolves the differences between the two aforementioned papers. We also confirm that in the limit N,H→∞ superstars remain capable of eliminating random drift and hence of providing arbitrarily strong selective advantages to any beneficial mutation. In addition, we investigate the robustness of amplification in superstars and find that it appears to be a fragile phenomenon with respect to changes in the selection or mutation processes.
authors.affiliation: Mathematics Department, University of British Columbia, 1984 Mathematics Road, Vancouver BC V6T 1Z2, Canada. Electronic address: aja107@math.ubc.ca.
authors.forename: Alastair
authors.initials: A
authors.lastname: Jamieson-Lane
authors.affiliation: Mathematics Department, University of British Columbia, 1984 Mathematics Road, Vancouver BC V6T 1Z2, Canada. Electronic address: christoph.hauert@math.ubc.ca.
authors.forename: Christoph
authors.initials: C
authors.lastname: Hauert
mesh_terms: D008954:Models, Biological; D009154:Mutation / Q000235:genetics; D011157:Population Dynamics; D011336:Probability
keywords: Evolution; Evolutionary graph theory; Moran process; Structured populations