EvoLudoLab: Moran process on the linear chain graph: Difference between revisions

Latest revision as of 13:33, 12 August 2024

Color code:	Residents	Mutants
	New resident	New mutant

Payoff code:	Residents	Mutants

Evolutionary dynamics on the linear chain graph

The invasion dynamics of a beneficial mutation typically unfolds by mutants taking over all downstream vertices. Nevertheless, this is a fleeting success because subsequently, the offspring of the slower reproducing resident vertices upstream of the initial mutant gradually, and inevitably, recapture the mutants' territory. With slightly smaller chances, the initial mutant gets wiped out before managing to establish a lineage of its own.

For the simulations, the population size is \(N=150\), the fitness of residents is set to \(1\) and that of mutants to \(2\). Initially, a single mutant is placed in a random position along the linear chain. The state of the population is shown as a function of time such that each row displays the state of the population at a particular time such that the present is at the top and the past at the bottom.

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 Strategies_-_Structure --reportfreq 0.5 --popupdate B --popsize 150 --geometry af --init 0,1 --inittype mutant --mutation 0 --basefit 1 --selection 1 --fitness 1,2"|
+options="--module Moran --run --delay 50 --view Strategies_-_Structure --timestep 0.5 --popupdate B --popsize 150 --geometry l0,1f --init mutant 1,0 --fitness 1,2"|
 title=Evolutionary dynamics on the linear chain graph|
 doc=The invasion dynamics of a beneficial mutation typically unfolds by mutants taking over all downstream vertices. Nevertheless, this is a fleeting success because subsequently, the offspring of the slower reproducing resident vertices upstream of the initial mutant gradually, and inevitably, recapture the mutants' territory. With slightly smaller chances, the initial mutant gets wiped out before managing to establish a lineage of its own.
 For the simulations, the population size is \(N=150\), the fitness of residents is set to \(1\) and that of mutants to \(2\). Initially, a single mutant is placed in a random position along the linear chain. The state of the population is shown as a function of time such that each row displays the state of the population at a particular time such that the present is at the top and the past at the bottom.}}