EvoLudoLab: Fixation probabilities on the superstar graph

Color code:	Residents	Mutants
	New resident	New mutant

Payoff code:	Residents	Mutants

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samples: 0

Strategies - 2D StructureStrategies - 3D StructureStrategies - MeanFitness - 2D StructureFitness - 3D StructureFitness - MeanFitness - HistogramStructure - DegreeStatistics - Fixation probabilityStatistics - Fixation timeStatistics - Stationary distributionConsole log

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--module Moran --run --delay 10 --view Statistics_-_Fixation_probability --timestep 10 --popupdate B --popsize 96 --geometry S5,5 --init mutant 1,0 --fitness 1,2

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Avg. fix. prob: Resident: 0.000, Mutant: 0.000

 

 

 

Fixation probabilities on the superstar graph

Note that the fixation probabilities are not the same for all vertices. In particular, if the mutant is placed in the hub (vertex $0$) or the linear chain (vertices $1-15$), its fixation probability is very small. The worst places for the mutant to arise are the 'hot' vertices with many links feeding into them, i.e. the hub as well as the first vertices of the linear chain (vertices $1-5$). For symmetry reasons, all reservoir vertices have the same fixation probabilities. The fixation probability for the original Moran process is shown as a dark red line for reference.

For the simulations, the population size is $N=96$ with $5$ branches and $k=5$. The fitness of residents is set to $1$ and that of mutants to $2$. Note that the overall fixation probability of mutants is systematically (and significantly) less than the analytical prediction of $97\mathrm{\%}$. The deviations are due to different kinds of finite size effects but again the primary cause is an unfortunate initial location of the mutant. Assuming that mutants in the hub and linear chain never succeed would account for $16.7\mathrm{\%}$ of the deviation.

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.