# EvoLudoLab: Fixation times on the star graph

Color code: | Residents | Mutants |
---|---|---|

New resident | New mutant |

Payoff code: | Residents | Mutants |
---|

## Fixation times on the star graph

Note that the fixation times are not the same for all vertices. In particular, if the mutant is placed in the hub (vertex \(0\)), it almost certainly gets wiped out in the very first update. For symmetry reasons, all other vertices have the same fixation times. The fixation times on the star graph are orders of magnitude longer than for the original Moran process, which 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 fixation time for residents is essentially zero for the hub but for mutants it is the same as for all other vertices. The difference is only that the chances for the latter to happen are very small and is also reflected in the very small absorption time for the hub.

### 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.

`--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.