# EvoLudoLab: Fixation times on the linear chain graph

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

## Fixation times on the linear chain graph

The fixation time of mutants is zero for all vertices except for the root (vertex $$0$$) because the fixation probabilities are zero. For the root vertex the fixation time is proportional to $$r N$$, the mutant's fitness $$r$$ times the length of the chain $$N$$. The fixation time of residents (and because of the corresponding fixation probabilities also the absorption times) is zero for the root and linearly decreases with distance from the root. More specifically, the fixation time for a mutant in vertex $$i$$ is proportional to $$N-i$$.

For the simulations, the population size is $$N=100$$, the fitness of residents is set to $$1$$ and that of mutants to $$2$$. Hence the fixation time of the mutant in the root must be almost half the time until the residents reach fixation after a mutant occurred in the adjacent vertex $$1$$. Similarly, the absorption time of vertex $$1$$ is almost twice that of the root vertex $$0$$. As a reference, the fixation times for the corresponding 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.

--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.