# EvoLudoLab: Moran process on the rectangular lattice

Color code: Residents Mutants New resident New mutant
 Payoff code: Residents Mutants

## Evolutionary dynamics on the complete graph

For the rectangular (or 2D) lattice with four neighbours (von Neumann neighbourhood) and periodic boundary conditions, mutants typically invade by forming a compact, expanding cluster with a frazzled boundary. The width of the frazzled zone increases for decreasing fitness differences between residents and mutants. This also increases the chance that the initial cluster of mutants gets split into several smaller ones.

For the simulations, the population size is $$N=100\times100=10'000$$. 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. Typically it takes around $$140$$ generations for the mutant to reach fixation.

### 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.