EvoLudoLab: Fixation times on the superstar graph

Color code:	Residents	Mutants
	New resident	New mutant

Payoff code:	Residents	Mutants

Fixation times on the superstar graph

Note that the fixation times 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 \(1-5\)). In the rare case where the mutant does not get wiped out, the fixation time is essentially the same as for any reservoir vertex. For symmetry reasons, all reservoir vertices have the same fixation times. The fixation times for the original Moran process are 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 \(2\). Interestingly, the fixation times on the superstar graph are slightly less than on the star graph of equal size - even though the superstar acts as a slightly stronger evolutionary amplifier despite the stronger finite size effects.

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.

--init <r,m>

initial frequencies of residents r and mutants m. Frequencies that do not add up to 100% are scaled accordingly.

--inittype <type>

type of initial configuration:

frequency

random distribution with given frequency

uniform

uniform random distribution

monomorphic

monomorphic initialization

mutant

single mutant in homogeneous population of another type. Mutant and resident types are determined by the types with the lowest and highest frequency, respectively (see option --init).

stripes

stripes of traits

kaleidoscopes

(optional) configurations that produce evolutionary kaleidoscopes for deterministic updates (players and population). Not available for all types of games.