EvoLudoLab: Moran process on the Superstar graph: Difference between revisions

Revision as of 15:39, 9 August 2024

Color code:	Residents	Mutants
	New resident	New mutant

Payoff code:	Residents	Mutants

Evolutionary dynamics on the superstar graph

Just as for the star graph, invasion dynamics of a beneficial mutation typically occurs in three phases: (i) first, rare mutants increase at a slower rate; (ii) once established, mutants quickly take over the majority of the population; (iii) during the last phase it takes a long time until the last remaining resident has been replaced. Extinction of mutants almost always happens in the first phase and the mutant fails to establish itself in the population.

For the simulations, the population size is \(N=498\) and the superstar has \(7\) branches with \(k=7\). The fitness of residents is set to \(1\) and that of mutants to \(2\). Now, a single mutant has a very high probability of \(\approx 98.5\%\) to reach fixation - a tremendous increase when compared to a \(50\%\) chance in the original Moran process. Interestingly, the typical time to reach fixation is less than on the star graph of the same size with typically \(2'500-4'500\) generations instead of \(4'500-6'500\).

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 10 --view Strategies_-_Structure --reportfreq 10 --popupdate B --popsize 498 --geometry S7,7 --init 1,0 --inittype mutant --mutation 0 --basefit 1 --selection 1 --fitness 1,2"|
+options="--module Moran --run --delay 10 --view Strategies_-_Structure --timestep 10 --popupdate B --popsize 498 --geometry S7,7 --inittype mutant 1,0 --fitness 1,2"|
 title=Evolutionary dynamics on the superstar graph|
 doc=Just as for the star graph, invasion dynamics of a beneficial mutation typically occurs in three phases: (i) first, rare mutants increase at a slower rate; (ii) once established, mutants quickly take over the majority of the population; (iii) during the last phase it takes a long time until the last remaining resident has been replaced. Extinction of mutants almost always happens in the first phase and the mutant fails to establish itself in the population.
 For the simulations, the population size is \(N=498\) and the superstar has \(7\) branches with \(k=7\). The fitness of residents is set to \(1\) and that of mutants to \(2\). Now, a single mutant has a very high probability of \(\approx 98.5\%\) to reach fixation - a tremendous increase when compared to a \(50\%\) chance in the original Moran process. Interestingly, the typical time to reach fixation is less than on the star graph of the same size with typically \(2'500-4'500\) generations instead of \(4'500-6'500\).}}