EvoLudoLab: Moran process on random regular graphs: Difference between revisions

Revision as of 19:31, 11 October 2023

Color code:	Residents	Mutants
	New resident	New mutant

Payoff code:	Residents	Mutants

Evolutionary dynamics on the complete graph

On random regular graphs any vertex can be reached from any other one in relatively few steps. Consequentially, the invasion process of mutants is similar to the complete graph (or even unstructured populations) and no characteristic invasion patterns emerge, with the only difference that it takes a little longer.

For the simulations, the population size is \(N=1000\) and every vertex has \(k=3\) neighbours. 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 \(40\) generations for the mutant to reach fixation, which is around twice as long as in an unstructured population.

Data views

Strategies - Structure	Snapshot of the spatial arrangement of strategies.
Strategies - Structure 3D	3D view of snapshot of the spatial arrangement of strategies.
Strategies - Mean	Time evolution of the strategy frequencies.
Fitness - Structure	Snapshot of the spatial distribution of payoffs.
Fitness - Structure 3D	3D view of snapshot of the spatial distribution of payoffs.
Fitness - Mean	Time evolution of average population payoff bounded by the minimum and maximum individual payoff.
Fitness - Histogram	Snapshot of payoff distribution in population.
Structure - Degree	Degree distribution in structured populations.
Statistics - Fixation probability	Statistics of fixation probability for each vertex where the initial mutant arose.
Statistics - Fixation times	Statistics of conditional fixation times of residents and mutants as well as absorption time for each vertex where the initial mutant arose.
Console log	Message log from engine.

Game parameters

The list below describes only the few parameters related to the evolutionary dynamics of residents and mutants with fixed fitness (constant selection). Numerous other parameters are available to set population structures or update rules on the player as well as population level.

--fitness <r,m>: fitness of residents r and of mutants m.

@@ Line 1: / Line 1: @@
 {{EvoLudoLab:Moran|
-options="--game Moran --run --delay 100 --view Strategies_-_Structure --reportfreq 1 --popupdate B --popsize 1000 --geometry r3 --initfreqs 1:0 --mutation 0 --basefit 1 --selection 1 --fitness 1:2"|
+options="--game Moran --run --delay 100 --view Strategies_-_Structure --reportfreq 1 --popupdate B --popsize 1000 --geometry r3 --init 1,0 --inittype mutant --mutation 0 --basefit 1 --selection 1 --fitness 1,2"|
 title=Evolutionary dynamics on the complete graph|
 doc=On random regular graphs any vertex can be reached from any other one in relatively few steps. Consequentially, the invasion process of mutants is similar to the complete graph (or even unstructured populations) and no characteristic invasion patterns emerge, with the only difference that it takes a little longer.
 For the simulations, the population size is \(N=1000\) and every vertex has \(k=3\) neighbours. 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 \(40\) generations for the mutant to reach fixation, which is around twice as long as in an unstructured population.}}