Amplification on Undirected Population Structures: Comets Beat Stars

Pavlogiannis, Andreas and Tkadlec, Josef and Chatterjee, Krishnendu and Nowak, Martin A (2016) Amplification on Undirected Population Structures: Comets Beat Stars. Technical Report. IST Austria.

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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.

Item Type: Monograph (Technical Report)
Subjects: 500 Science > 510 Mathematics > 519 Probabilities & applied mathematics
Research Group: Chatterjee Group
Depositing User: Andreas Pavlogiannis
Date Deposited: 09 Nov 2016 08:33
Last Modified: 16 Jul 2019 22:40
URI: https://repository.ist.ac.at/id/eprint/648

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