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EvoLudoLab: Moran process on the cycle graph: Difference between revisions
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EvoLudoLab: Moran process on the cycle graph (view source)
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options="--game Moran --run --delay 100 --view Strategies_-_Structure --reportfreq 1 --popupdate B --popsize 100 --geometry l --initfreqs 0:1 --mutation 0 --basefit 1 --selection 1 --resident 1 --mutant 2"| | options="--game Moran --run --delay 100 --view Strategies_-_Structure --reportfreq 1 --popupdate B --popsize 100 --geometry l --initfreqs 0:1 --mutation 0 --basefit 1 --selection 1 --resident 1 --mutant 2"| | ||
title=Evolutionary dynamics on the complete graph| | title=Evolutionary dynamics on the complete graph| | ||
doc= | doc=The Moran process on a cycle is best illustrated as a linear graph (1D lattice) with periodic boundaries such that every vertex is connected to its two neighbours on the left and right. The invasion process of a mutant can then be easily illustrated over time by stacking subsequent snapshots of the population state. Each row indicates the population state at a particular time such that the most recent state is at the top and and towards the bottom of the figure are population states in the increasingly distant past. | ||
In this graphical representation it is easy to see that mutants invade by forming a single, growing cluster. Due to the structure of the graph, there will always be at most two clusters, one of residents and another of mutants. Because of the limited opportunities for mutants to spread, the invasion process is significantly slower than on the complete graph or in unstructured populations. | In this graphical representation it is easy to see that mutants invade by forming a single, growing cluster. Due to the structure of the graph, there will always be at most two clusters, one of residents and another of mutants. Because of the limited opportunities for mutants to spread, the invasion process is significantly slower than on the complete graph or in unstructured populations. | ||
For the simulations, the population size is \(N=100\). 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. Typically it takes around \(120\) generations for the mutant to reach fixation (as compared to around \(12\) on the complete graph).}} | For the simulations, the population size is \(N=100\). 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. Typically it takes around \(120\) generations for the mutant to reach fixation (as compared to around \(12\) on the complete graph).}} | ||
