# EvoLudoLab: Moran process on the linear chain graph

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

New resident | New mutant |

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

## Evolutionary dynamics on the linear chain graph

The invasion dynamics of a beneficial mutation typically unfolds by mutants taking over all downstream vertices. Nevertheless, this is a fleeting success because subsequently, the offspring of the slower reproducing resident vertices upstream of the initial mutant gradually, and inevitably, recapture the mutants' territory. With slightly smaller chances, the initial mutant gets wiped out before managing to establish a lineage of its own.

For the simulations, the population size is \(N=150\), the fitness of residents is set to \(1\) and that of mutants to \(2\). Initially, a single mutant is placed in a random position along the linear chain. The state of the population is shown as a function of time such that each row displays the state of the population at a particular time such that the present is at the top and the past at the bottom.

### 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.