Most undirected random graphs are amplifiers of selection for birth-death 
dynamics, but suppressors of selection for death-birth dynamics

Hindersin, Laura; Traulsen, Arne

doi:10.1371/journal.pcbi.1004437

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Most undirected random graphs are amplifiers of selection for birth-death dynamics, but suppressors of selection for death-birth dynamics

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Hindersin, Laura
Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Traulsen, Arne
Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Citation

Hindersin, L., & Traulsen, A. (2015). Most undirected random graphs are amplifiers of selection for birth-death dynamics, but suppressors of selection for death-birth dynamics. PLoS Computational Biology, 11(11): e1004437. doi:10.1371/journal.pcbi.1004437.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0026-D121-F

Abstract

We analyze evolutionary dynamics on graphs, where the nodes represent individuals of a
population. The links of a node describe which other individuals can be displaced by the off-
spring of the individual on that node. Amplifiers of selection are graphs for which the fixation
probability is increased for advantageous mutants and decreased for disadvantageous
mutants. A few examples of such amplifiers have been developed, but so far it is unclear
how many such structures exist and how to construct them. Here, we show that almost any
undirected random graph is an amplifier of selection for Birth-death updating, where an indi-
vidual is selected to reproduce with probability proportional to its fitness and one of its neigh-
bors is replaced by that offspring at random. If we instead focus on death-Birth updating, in
which a random individual is removed and its neighbors compete for the empty spot, then
the same ensemble of graphs consists of almost only suppressors of selection for which the
fixation probability is decreased for advantageous mutants and increased for disadvanta-
geous mutants. Thus, the impact of population structure on evolutionary dynamics is a sub-
tle issue that will depend on seemingly minor details of the underlying evolutionary process.