EvoLudoLab: Moran process on the Frucht graph - Revision history

Hauert at 07:27, 19 February 2026

2026-02-19T07:27:14Z

← 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 0 --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 0 --init mutant 1,0 --mutation 0 --fitness 1,2"\|
	title=Fixation and absorption times on the Frucht graph\|		title=Fixation and absorption times on the Frucht graph\|
	doc=On the Frucht graph the expected times until a single mutant has fixed in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), depends on which vertex the initial mutant arose. In fact, due to the lack of further structural symmetries (in addition to regularity) the fixation times are different for each vertex. 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).		doc=On the Frucht graph the expected times until a single mutant has fixed in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), depends on which vertex the initial mutant arose. In fact, due to the lack of further structural symmetries (in addition to regularity) the fixation times are different for each vertex. 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).

Hauert at 07:10, 12 October 2023

2023-10-12T07:10:59Z

← Older revision		Revision as of 00:10, 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 0 --init 0,1 --inittype mutant --mutation 0 --basefit 1 --selection 1 --fitness 1,2"\|		options="--game Moran --run --delay 200 --view Statistics_-_Fixation_time --reportfreq 1 --popupdate B --geometry 0 --init 1,0 --inittype mutant --mutation 0 --basefit 1 --selection 1 --fitness 1,2"\|
	title=Fixation and absorption times on the Frucht graph\|		title=Fixation and absorption times on the Frucht graph\|
	doc=On the Frucht graph the expected times until a single mutant has fixed in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), depends on which vertex the initial mutant arose. In fact, due to the lack of further structural symmetries (in addition to regularity) the fixation times are different for each vertex. 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).		doc=On the Frucht graph the expected times until a single mutant has fixed in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), depends on which vertex the initial mutant arose. In fact, due to the lack of further structural symmetries (in addition to regularity) the fixation times are different for each vertex. 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).

Hauert at 07:06, 12 October 2023

2023-10-12T07:06:47Z

← Older revision		Revision as of 00:06, 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 0 --~~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 0 --init 0,1 --inittype mutant --mutation 0 --basefit 1 --selection 1 --fitness 1,2"\|
	title=Fixation and absorption times on the Frucht graph\|		title=Fixation and absorption times on the Frucht graph\|
	doc=On the Frucht graph the expected times until a single mutant has fixed in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), depends on which vertex the initial mutant arose. In fact, due to the lack of further structural symmetries (in addition to regularity) the fixation times are different for each vertex. 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).		doc=On the Frucht graph the expected times until a single mutant has fixed in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), depends on which vertex the initial mutant arose. In fact, due to the lack of further structural symmetries (in addition to regularity) the fixation times are different for each vertex. 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).

Hauert at 00:53, 25 August 2016

2016-08-25T00:53:01Z

← Older revision		Revision as of 17:53, 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 0 --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 0 --initfreqs 0:1 --mutation 0 --basefit 1 --selection 1 --resident 1 --mutant 2"\|
	title=Fixation and absorption times on the Frucht graph\|		title=Fixation and absorption times on the Frucht graph\|
	doc=On the Frucht graph the expected times until a single mutant has fixed in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), depends on which vertex the initial mutant arose. In fact, due to the lack of further structural symmetries (in addition to regularity) the fixation times are different for each vertex. 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).		doc=On the Frucht graph the expected times until a single mutant has fixed in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), depends on which vertex the initial mutant arose. In fact, due to the lack of further structural symmetries (in addition to regularity) the fixation times are different for each vertex. 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).

Hauert at 02:09, 24 August 2016

2016-08-24T02:09:54Z

← Older revision		Revision as of 19:09, 23 August 2016
Line 2:		Line 2:
	options="--game Moran --run --delay 200 --view Statistics_-_Fixation_time --reportfreq 0 --popupdate B --geometry 0 --initfreqs 0:1 --mutation 0 --basefit 1 --selection 1 --resident 1 --mutant 2"\|		options="--game Moran --run --delay 200 --view Statistics_-_Fixation_time --reportfreq 0 --popupdate B --geometry 0 --initfreqs 0:1 --mutation 0 --basefit 1 --selection 1 --resident 1 --mutant 2"\|
	title=Fixation and absorption times on the Frucht graph\|		title=Fixation and absorption times on the Frucht graph\|
	doc=On the Frucht graph the expected times until a single mutant has fixed in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), depends on which vertex the initial mutant arose. In fact, due to the lack of further structural symmetries (in addition to regularity) the fixation times are different for each vertex. 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 dark red line indicates~~ the corresponding fixation times for the original [[Moran process]], or, equivalently, for the [[spatial Moran process]] on [[Spatial Moran process#Circulation graphs\|circulations]].		doc=On the Frucht graph the expected times until a single mutant has fixed in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), depends on which vertex the initial mutant arose. In fact, due to the lack of further structural symmetries (in addition to regularity) the fixation times are different for each vertex. 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. Because the Frucht graph is a circulation 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. To make matters worse, differences in fixation times between different nodes are rather small and hence it becomes very challenging to prove the differences through simulations. Fortunately, however, for sufficiently small graphs the fixation times can be calculated numerically and simulations easily confirm the trends observed in the exact numerical analysis.		Also check out the statistics for the fixation probabilities of mutants and residents. Because the Frucht graph is a circulation 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. To make matters worse, differences in fixation times between different nodes are rather small and hence it becomes very challenging to prove the differences through simulations. Fortunately, however, for sufficiently small graphs the fixation times can be calculated numerically and simulations easily confirm the trends observed in the exact numerical analysis.

	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.}}		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.}}

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

2016-08-24T02:01:17Z

Created page with "{{EvoLudoLab:Moran| options="--game Moran --run --delay 200 --view Statistics_-_Fixation_time --reportfreq 0 --popupdate B --geometry 0 --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 0 --initfreqs 0:1 --mutation 0 --basefit 1 --selection 1 --resident 1 --mutant 2"|
title=Fixation and absorption times on the Frucht graph|
doc=On the Frucht graph the expected times until a single mutant has fixed in the population, or until either one of the absorbing states is reached (homogenous population of residents or mutants), depends on which vertex the initial mutant arose. In fact, due to the lack of further structural symmetries (in addition to regularity) the fixation times are different for each vertex. 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 dark red line indicates the corresponding fixation times for the original [[Moran process]], or, equivalently, for the [[spatial Moran process]] on [[Spatial Moran process#Circulation graphs|circulations]].

Also check out the statistics for the fixation probabilities of mutants and residents. Because the Frucht graph is a circulation 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. To make matters worse, differences in fixation times between different nodes are rather small and hence it becomes very challenging to prove the differences through simulations. Fortunately, however, for sufficiently small graphs the fixation times can be calculated numerically and simulations easily confirm the trends observed in the exact numerical analysis.

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.}}