EvoLudoLab: Moran process on the Heawood graph - Revision history

Hauert at 07:27, 19 February 2026

2026-02-19T07:27:59Z

← Older revision		Revision as of 00:27, 19 February 2026
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	{{EvoLudoLab:Moran\|		{{EvoLudoLab:Moran\|
	options="--~~game~~ Moran --run --delay 200 --view Statistics_-_Fixation_time ~~--reportfreq 1~~ --popupdate B --geometry 3 --init 1,0 ~~--inittype mutant~~ --mutation 0 ~~--basefit 1 --selection 1~~ --fitness 1,2"\|		options="--module Moran --run --delay 200 --view Statistics_-_Fixation_time --popupdate B --geometry 3 --init mutant 1,0 --mutation 0 --fitness 1,2"\|
	title=Fixation and absorption times on the Heawood graph\|		title=Fixation and absorption times on the Heawood graph\|
	doc=The Heawood graph is a symmetric (arc-transitive) graph and hence the expected times until a single mutant fixes in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), is independent of the vertex where the initial mutant arose.		doc=The Heawood graph is a symmetric (arc-transitive) graph and hence the expected times until a single mutant fixes in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), is independent of the vertex where the initial mutant arose.

Hauert at 07:13, 12 October 2023

2023-10-12T07:13:13Z

← Older revision		Revision as of 00:13, 12 October 2023
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	{{EvoLudoLab:Moran\|		{{EvoLudoLab:Moran\|
	options="--game Moran --run --delay 200 --view Statistics_-_Fixation_time --reportfreq 1 --popupdate B --geometry 3 --~~initfreqs~~ 0:1 --mutation 0 --basefit 1 --selection 1 --~~resident~~ 1 ~~--mutant~~ 2"\|		options="--game Moran --run --delay 200 --view Statistics_-_Fixation_time --reportfreq 1 --popupdate B --geometry 3 --init 1,0 --inittype mutant --mutation 0 --basefit 1 --selection 1 --fitness 1,2"\|
	title=Fixation and absorption times on the Heawood graph\|		title=Fixation and absorption times on the Heawood graph\|
	doc=The Heawood graph is a symmetric (arc-transitive) graph and hence the expected times until a single mutant fixes in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), is independent of the vertex where the initial mutant arose.		doc=The Heawood graph is a symmetric (arc-transitive) graph and hence the expected times until a single mutant fixes in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), is independent of the vertex where the initial mutant arose.

Hauert at 00:54, 25 August 2016

2016-08-25T00:54:05Z

← Older revision		Revision as of 17:54, 24 August 2016
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	{{EvoLudoLab:Moran\|		{{EvoLudoLab:Moran\|
	options="--game Moran --run --delay 200 --view Statistics_-_Fixation_time --reportfreq 0 --popupdate B --geometry 3 --initfreqs 0:1 --mutation 0 --basefit 1 --selection 1 --resident 1 --mutant 2"\|		options="--game Moran --run --delay 200 --view Statistics_-_Fixation_time --reportfreq 1 --popupdate B --geometry 3 --initfreqs 0:1 --mutation 0 --basefit 1 --selection 1 --resident 1 --mutant 2"\|
	title=Fixation and absorption times on the Heawood graph\|		title=Fixation and absorption times on the Heawood graph\|
	doc=The Heawood graph is a symmetric (arc-transitive) graph and hence the expected times until a single mutant fixes in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), is independent of the vertex where the initial mutant arose.		doc=The Heawood graph is a symmetric (arc-transitive) graph and hence the expected times until a single mutant fixes in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), is independent of the vertex where the initial mutant arose.

Hauert: Created page with "{{EvoLudoLab:Moran| options="--game Moran --run --delay 200 --view Statistics_-_Fixation_time --reportfreq 0 --popupdate B --geometry 3 --initfreqs 0:1 --mutation 0 --basefit..."

2016-08-24T16:30:14Z

Created page with "{{EvoLudoLab:Moran| options="--game Moran --run --delay 200 --view Statistics_-_Fixation_time --reportfreq 0 --popupdate B --geometry 3 --initfreqs 0:1 --mutation 0 --basefit..."

New page

{{EvoLudoLab:Moran|
options="--game Moran --run --delay 200 --view Statistics_-_Fixation_time --reportfreq 0 --popupdate B --geometry 3 --initfreqs 0:1 --mutation 0 --basefit 1 --selection 1 --resident 1 --mutant 2"|
title=Fixation and absorption times on the Heawood graph|
doc=The Heawood graph is a symmetric (arc-transitive) graph and hence the expected times until a single mutant fixes in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), is independent of the vertex where the initial mutant arose.

The histogram shows the statistics for the conditional fixation times of a single mutant, i.e. the expected time it takes for a mutant to take over the population, the expected time for the mutant to go extinct (fixation of resident), as well as the expected time to reach an absorbing states for each vertex where the initial mutant was placed. The initial mutant is sequentially placed on every vertex. For reference, the corresponding fixation times for the original [[Moran process]], or, equivalently, for the [[spatial Moran process]] on [[Spatial Moran process#Circulation graphs|circulations]] is indicated by a dark red line (may not be visible if its outside the range of displayed values).

Also check out the statistics for the fixation probabilities of mutants and residents. The Heawood graph is another a circulation and hence the probabilities are the same for all vertices and are also identical to the original Moran process (indicated by the dark red line). However, also note that a considerable number of sample runs are required to obtain a good estimate of the the fixation probabilities. Unfortunately, an even significantly larger number of samples is required for accurate estimates of fixation times because of large variation - fixation times appear to be following an exponential distribution.

For the simulations, 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.}}