# EvoLudoLab: Fixation times on the rectangular lattice

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

New resident | New mutant |

Payoff code: | Residents | Mutants |
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## Fixation times on the rectangular lattice

Even though fixation probabilities are the same on the rectangular lattice as on any other circulation, the corresponding fixation and absorption times can be vastly different. The diameter of rectangular lattices (every vertex can be reached with a few steps from every other one) scales with \(\sqrt{N}\) and hence fixation times are longer than on complete graphs or in unstructured populations.

For the simulations, the population size is \(N=9\times9=81\) with \(k=4\) neighbours, which results in a total of \(162\) links. The fitness of residents is set to \(1\) and that of mutants to \(2\). Thus, a single mutant has approximately a \(50\%\) chance to take over the population. For reference, the analytical fixation and absorption times of the original Moran process are indicated by a dark red line.

### 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.