Counterintuitive properties of the fixation time in network-structured populations

TL;DR

This paper investigates the fixation time in network-structured populations, revealing counterintuitive effects where network modifications can both increase or decrease fixation times, challenging assumptions about amplification and speed of evolution.

Contribution

It provides analytical and numerical insights into how network structure influences fixation time, showing that removal of links can speed up fixation and that optimal starting nodes depend on mutant fitness.

Findings

Fixation time can decrease when links are removed from the network.

The best starting node for fixation depends on mutant fitness.

Amplifiers of selection can slow down fixation despite increasing fixation probability.

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.