EvoLudoLab: Fixation probabilities on the rectangular lattice: Difference between revisions

Latest revision as of 13:30, 12 August 2024

Color code:	Residents	Mutants
	New resident	New mutant

Payoff code:	Residents	Mutants

Fixation probabilities on the rectangular lattice

Since the rectangular lattice is a circulation, the fixation probability of a mutant has to be the same irrespective of its initial location and must be identical to the one of the original Moran process in unstructured populations.

For the simulations, the population size is \(N=9\times9=81\) and arranged on a rectangular lattice with periodic boundary conditions such that each vertex has four neighbours to the north, east, south and west (von Neumann neighbourhood). The resulting graph has 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 probabilities of the original Moran process are indicated by a dark red line.

Data views

Strategies - Structure	Snapshot of the spatial arrangement of strategies.
Strategies - Structure 3D	3D view of snapshot of the spatial arrangement of strategies.
Strategies - Mean	Time evolution of the strategy frequencies.
Fitness - Structure	Snapshot of the spatial distribution of payoffs.
Fitness - Structure 3D	3D view of snapshot of the spatial distribution of payoffs.
Fitness - Mean	Time evolution of average population payoff bounded by the minimum and maximum individual payoff.
Fitness - Histogram	Snapshot of payoff distribution in population.
Structure - Degree	Degree distribution in structured populations.
Statistics - Fixation probability	Statistics of fixation probability for each vertex where the initial mutant arose.
Statistics - Fixation times	Statistics of conditional fixation times of residents and mutants as well as absorption time for each vertex where the initial mutant arose.
Console log	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.

@@ Line 1: / Line 1: @@
 {{EvoLudoLab:Moran|
-options="--game Moran --run --delay 50 --view Statistics_-_Fixation_probability --reportfreq 1 --popupdate B --popsize 9x9 --geometry n --initfreqs 0:1 --mutation 0 --basefit 1 --selection 1 --resident 1 --mutant 2"|
+options="--module Moran --run --delay 50 --view Statistics_-_Fixation_probability --timestep 1 --popupdate B --popsize 9x9 --geometry n --init mutant 1,0 --fitness 1,2"|
 title=Fixation probabilities on the rectangular lattice |
 doc=Since the rectangular lattice is a circulation, the fixation probability of a mutant has to be the same irrespective of its initial location and must be identical to the one of the original Moran process in unstructured populations.
 For the simulations, the population size is \(N=9\times9=81\) and arranged on a rectangular lattice with periodic boundary conditions such that each vertex has four neighbours to the north, east, south and west (von Neumann neighbourhood). The resulting graph has 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 probabilities of the original Moran process are indicated by a dark red line.}}