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EvoLudoLab: Fixation times on the rectangular lattice: Difference between revisions
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EvoLudoLab: Fixation times on the rectangular lattice (view source)
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{{EvoLudoLab:Moran| | {{EvoLudoLab:Moran| | ||
options="--game Moran --run --delay 50 --view Statistics_-_Fixation_time --reportfreq 1 --popupdate B --popsize 9x9 --geometry n --initfreqs 0 | options="--game Moran --run --delay 50 --view Statistics_-_Fixation_time --reportfreq 1 --popupdate B --popsize 9x9 --geometry n --initfreqs 1:0 --mutation 0 --basefit 1 --selection 1 --fitness 1:2"| | ||
title=Fixation times on the rectangular lattice | | title=Fixation times on the rectangular lattice | | ||
doc=Even though fixation probabilities are the same on the rectangular lattice as on any other circulation, the corresponding fixation and absorption times can be vastly different. The diameter of rectangular lattices (every vertex can be reached with a few steps from every other one) scales with \(\sqrt{N}\) and hence fixation times are longer than on complete graphs or in unstructured populations. | doc=Even though fixation probabilities are the same on the rectangular lattice as on any other circulation, the corresponding fixation and absorption times can be vastly different. The diameter of rectangular lattices (every vertex can be reached with a few steps from every other one) scales with \(\sqrt{N}\) and hence fixation times are longer than on complete graphs or in unstructured populations. | ||
For the simulations, the population size is \(N=9\times9=81\) with \(k=4\) neighbours, which results in a total of \(162\) 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 \(N=9\times9=81\) with \(k=4\) neighbours, which results in a total of \(162\) 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.}} | ||
