EvoLudoLab: Fixation probabilities on the star graph

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Color code: Residents Mutants
New resident New mutant
Payoff code: Residents Mutants

Fixation probabilities on the star graph

Note that the fixation probabilities are not the same for all vertices. In particular, if the mutant is placed in the hub (vertex \(0\)), it almost certainly gets wiped out in the very first update. For symmetry reasons, all other 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 \(N=96\). The fitness of residents is set to \(1\) and that of mutants to \(2\). Note that the overall fixation probability of mutants is systematically less than the analytical prediction of \(75\%\). The deviations are due to different kinds of finite size effects but primarily because the mutant may arise in the hub and almost certainly go extinct. This alone accounts for \(1\%\) 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.

--resident <r>
fitness of resident r.
--mutant <m>
fitness of mutant m.
--initfreqs <m:r>
initial frequencies of residents r and mutants m. Frequencies that do not add up to 100% are scaled accordingly. If either frequency is zero, the population is initialized to a homogenous state with just a single, randomly placed individual of the opposite type.