# EvoLudoLab: Fixation probabilities on the linear chain graph

From EvoLudo

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

New resident | New mutant |

Payoff code: | Residents | Mutants |
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## Fixation probabilities on the linear chain graph

The fixation probability is zero for all vertices except for the root (vertex \(0\)) for which it is one.

For the simulations, the population size is \(N=100\), the fitness of residents is set to \(1\) and that of mutants to \(2\). As a reference, the fixation probabilities for the original Moran process are indicated by a dark red line at approximately \(50\%\) for these settings.

### 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.