# EvoLudoLab: Moran process on the Superstar graph

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. 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.