Downloaded from hit pi' rspa.royalsocietypublishi ng.orgi on September 3, 2015 PROCEEDINGS A Amplifiers of selection rspa.royalsocietypublishing.org Research CrossMark tglhe wain Cite this article: Adlam B,Chatterjee K, Nowak MA. 2015 Amplifiers of selection. hoc. R.Soc A 411: 20150114. http://dx.doi.org/10.1098/rspa2015.0114 Received: 20 February 2015 Accepted: 30 July 2015 Subject Areas: applied mathematics, graph theory, mathematical modelling Keywords: fixation probabilities, evolutionary graph theory, martingales, mutation, star graph, temperature initialization Author for correspondence: M. A. Nowak e-mail: Electronic supplementary material is available at http://dx.doi.org/10.1098/rspa.2015.0114 or via http://rspanyalsocietypublishing.org. B. Adlaml, K. Chatterjee3 and M. A. Nowak1'2 'Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, and ]Department of Mathematics, Harvard University, Cambridge, MA 02138, USA 31ST Austria, Klosterneuburg 3400, Austria When a new mutant arises in a population, there is a probability it outcompetes the residents and fixes. The structure of the population can affect this fixation probability. Suppressing population structures reduce the difference between two competing variants, while amplifying population structures enhance the difference. Suppressors are ubiquitous and easy to construct, but amplifiers for the large population limit are more elusive and only a few examples have been discovered. Whether or not a population structure is an amplifier of selection depends on the probability distribution for the placement of the invading mutant. First, we prove that there exist only bounded amplifiers for adversarial placement—that is, for arbitrary initial conditions. Next, we show that the Star population structure, which is known to amplify for mutants placed uniformly at random, does not amplify for mutants that arise through reproduction and ar