EvoLudoLab: Moran process on the rectangular lattice: Difference between revisions

Latest revision as of 13:28, 12 August 2024

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

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="--module Moran --run --delay 100 --view Strategies_-_Structure --timestep 1 --popupdate B --popsize 100x100 --geometry n --inittype mutant 1,0 --fitness 1,2"|
+options="--module Moran --run --delay 100 --view Strategies_-_Structure --timestep 1 --popupdate B --popsize 100x100 --geometry n --init mutant 1,0 --fitness 1,2"|
 title=Evolutionary dynamics on the complete graph|
 doc=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.}}