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Free keywords:
evolution on static networks; fixation time; evolutionary graph theory
Abstract:
Evolutionary dynamics on graphs can lead to many interesting and counterintuitive
findings. We study the Moran process, a discrete time birth–death
process, that describes the invasion of a mutant type into a population
of wild-type individuals. Remarkably, the fixation probability of a single
mutant is the same on all regular networks. But non-regular networks can
increase or decrease the fixation probability. While the time until fixation formally
depends on the same transition probabilities as the fixation probabilities,
there is no obvious relation between them. For example, an amplifier of selection,
which increases the fixation probability and thus decreases the number of
mutations needed until one of them is successful, can at the same time slow
down the process of fixation. Based on small networks, we show analytically
that (i) the time to fixation can decrease when links are removed from the network
and (ii) the node providing the best starting conditions in terms of the
shortest fixation time depends on the fitness of the mutant. Our results are
obtained analytically on small networks, but numerical simulations show
that they are qualitatively valid even in much larger populations.
