title: Amplification on Undirected Population Structures: Comets Beat Stars.
abstract: The fixation probability is the probability that a new mutant introduced in a homogeneous population eventually takes over the entire population. The fixation probability is a fundamental quantity of natural selection, and known to depend on the population structure. Amplifiers of natural selection are population structures which increase the fixation probability of advantageous mutants, as compared to the baseline case of well-mixed populations. In this work we focus on symmetric population structures represented as undirected graphs. In the regime of undirected graphs, the strongest amplifier known has been the Star graph, and the existence of undirected graphs with stronger amplification properties has remained open for over a decade. In this work we present the Comet and Comet-swarm families of undirected graphs. We show that for a range of fitness values of the mutants, the Comet and Comet-swarm graphs have fixation probability strictly larger than the fixation probability of the Star graph, for fixed population size and at the limit of large populations, respectively.
authors.affiliation: IST Austria, Klosterneuburg, A-3400, Austria. pavlogiannis@ist.ac.at.
authors.forename: Andreas
authors.initials: A
authors.lastname: Pavlogiannis
authors.affiliation: IST Austria, Klosterneuburg, A-3400, Austria.
authors.forename: Josef
authors.initials: J
authors.lastname: Tkadlec
authors.affiliation: IST Austria, Klosterneuburg, A-3400, Austria.
authors.forename: Krishnendu
authors.initials: K
authors.lastname: Chatterjee
authors.affiliation: Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA.
authors.forename: Martin A
authors.initials: MA
authors.lastname: Nowak