Counterintuitive properties of the fixation time in network-structured populations

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.

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• Takeover times for a simple model of network infection
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• Mutant fate in spatially structured populations on graphs: connecting models to experiments
• Motion, fixation probability and the choice of an evolutionary process
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• Fixation properties of multiple cooperator configurations on regular graphs
• Effect of the degree of an initial mutant in Moran processes in structured populations
• On a Voter Model with Context-Dependent Opinion Adoption