Amplifiers of selection Journal Article


Author(s): Adlam, Ben; Chatterjee, Krishnendu; Nowak, Martin A
Article Title: Amplifiers of selection
Affiliation IST Austria
Abstract: 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 are therefore placed proportional to the temperatures of the vertices. Finally, we construct population structures that amplify for all mutational events that arise through reproduction, uniformly at random, or through some combination of the two.
Keywords: Mutation; Evolutionary graph theory; Fixation probabilities; Martingales; Star graph; Temperature initialization
Journal Title: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume: 471
Issue 2181
ISSN: 1364-5021
Publisher: Royal Society of London  
Date Published: 2015-09-08
Start Page: Article number: 20150114
Sponsor: K.C. gratefully acknowledges support from ERC Start grant no. (279307: Graph Games), Austrian Science Fund (FWF) grant no. P23499-N23, and FWF NFN grant no. S11407-N23 (RiSE).
DOI: 10.1098/rspa.2015.0114
Open access: no