# EvoLudoLab: Fixation probabilities on the superstar graph

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

## 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 \(97\%\). 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 \(16.7\%\) of the deviation.

### Data views

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