View source for EvoLudoLab: Fixation times on the superstar graph

{{EvoLudoLab:Moran|
options="--module Moran --run --delay 10 --view Statistics_-_Fixation_time --timestep 10 --popupdate B --popsize 96 --geometry S5,5 --init mutant 1,0 --fitness 1,2"|
title=Fixation times on the superstar graph|
doc=Note that the fixation times are not the same for all vertices. In particular, if the mutant is placed in the hub (vertex \(0\)) or the linear chain (vertices \(1-15\)), its fixation probability is very small. The worst places for the mutant to arise are the 'hot' vertices with many links feeding into them, i.e. the hub as well as the first vertices of the linear chain (vertices \(1-5\)). In the rare case where the mutant does not get wiped out, the fixation time is essentially the same as for any reservoir vertex. For symmetry reasons, all reservoir vertices have the same fixation times. The fixation times for the original Moran process are shown as a dark red line for reference.

For the simulations, the population size is \(N=96\) with \(5\) branches and \(k=5\). The fitness of residents is set to \(1\) and that of mutants to \(2\). Interestingly, the fixation times on the superstar graph are slightly less than on the star graph of equal size - even though the superstar acts as a slightly stronger evolutionary amplifier despite the stronger finite size effects.}}