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EvoLudoLab: Fixation times on the complete graph: Difference between revisions
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{{EvoLudoLab:Moran| | {{EvoLudoLab:Moran| | ||
options="--game Moran --run --delay 50 --view Statistics_-_Fixation_time --reportfreq 1 --popupdate B --popsize 81 --geometry c -- | options="--game Moran --run --delay 50 --view Statistics_-_Fixation_time --reportfreq 1 --popupdate B --popsize 81 --geometry c --init 1,0 --inittype mutant --mutation 0 --basefit 1 --selection 1 --fitness 1,2"| | ||
title=Fixation times on the complete graph | | title=Fixation times on the complete graph | | ||
doc=Even though fixation probabilities are the same on the complete graph as on any other circulation, the corresponding fixation and absorption times can be vastly different. The diameter of the complete graph (the average minimal number of steps to reach any vertex from any other one) is constant \(1\) and, in particular, independent of \(N\). Hence, fixation times are short and essentially indistinguishable from unstructured populations. Possibly the fixation times on the complete graph are the shortest on any circulation with undirected links. | doc=Even though fixation probabilities are the same on the complete graph as on any other circulation, the corresponding fixation and absorption times can be vastly different. The diameter of the complete graph (the average minimal number of steps to reach any vertex from any other one) is constant \(1\) and, in particular, independent of \(N\). Hence, fixation times are short and essentially indistinguishable from unstructured populations. Possibly the fixation times on the complete graph are the shortest on any circulation with undirected links. | ||
For the simulations, the population size is \(N=81\) with \(k=80\) neighbours and hence a total of \(3'240\) links. The fitness of residents is set to \(1\) and that of mutants to \(2\). Thus, a single mutant has approximately a \(50\%\) chance to take over the population. For reference, the analytical fixation and absorption times of the original Moran process are indicated by a dark red line.}} | For the simulations, the population size is \(N=81\) with \(k=80\) neighbours and hence a total of \(3'240\) links. The fitness of residents is set to \(1\) and that of mutants to \(2\). Thus, a single mutant has approximately a \(50\%\) chance to take over the population. For reference, the analytical fixation and absorption times of the original Moran process are indicated by a dark red line.}} | ||
