Felsenstein's tree-pruning algorithm - Revision history

1234qwer1234qwer4: fix spacing around math (via WP:JWB)

2024-10-04T15:27:47Z

fix spacing around math (via WP:JWB)

← Previous revision		Revision as of 15:27, 4 October 2024
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	<math> w_k (X) = ( \sum_Y p_{X \rightarrow Y} \centerdot w_i (Y)) \centerdot ( \sum_Z p_{X \rightarrow Z} \centerdot w_j (Z)) </math>		<math> w_k (X) = ( \sum_Y p_{X \rightarrow Y} \centerdot w_i (Y)) \centerdot ( \sum_Z p_{X \rightarrow Z} \centerdot w_j (Z)) </math>

	where <math> Y </math> and <math> Z </math> are also DNA bases. <math> p_{ X\rightarrow Y} </math>is the transition probability from nucleotide <math>X</math> to nucleotide <math> Y </math> (idem for <math> p_{X \rightarrow Z} </math>). <math> w_i(Y) </math> is the partial likelihood of the daughter node <math>		where <math> Y </math> and <math> Z </math> are also DNA bases. <math> p_{ X\rightarrow Y} </math> is the transition probability from nucleotide <math>X</math> to nucleotide <math> Y </math> (idem for <math> p_{X \rightarrow Z} </math>). <math> w_i(Y) </math> is the partial likelihood of the daughter node <math>
	i		i
	</math>, evaluated on nucleotide <math> Y </math> (idem for <math>		</math>, evaluated on nucleotide <math> Y </math> (idem for <math>

98.47.60.50: Replace misspelling "exemple" with "example"

2024-05-22T03:09:57Z

Replace misspelling "exemple" with "example"

← Previous revision		Revision as of 03:09, 22 May 2024
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	== Details ==		== Details ==
	[[File:Tree_exemple.png\|thumb\|A simple phylogenetic tree ~~exemple~~ made from arbitrary data D]]		[[File:Tree_exemple.png\|thumb\|A simple phylogenetic tree example made from arbitrary data D]]
	The '''likelihood''' of a tree <math>T</math> is, by definition, the probability of observing certain data <math>D</math> (<math>D</math> being a nucleotide sequence alignment for example ''i.e.'' a succession of <math> n </math> DNA site <math> s </math>) given the tree. It is often written : <math>P(D\|T)</math>.		The '''likelihood''' of a tree <math>T</math> is, by definition, the probability of observing certain data <math>D</math> (<math>D</math> being a nucleotide sequence alignment for example ''i.e.'' a succession of <math> n </math> DNA site <math> s </math>) given the tree. It is often written : <math>P(D\|T)</math>.

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	</math>		</math>

	If I reuse the ~~exemple~~ above, <math>D_1</math> tree would be:		If I reuse the example above, <math>D_1</math> tree would be:


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	== Algorithm ==		== Algorithm ==

	== Simple ~~Exemple~~ ==		== Simple Example ==

	==References==		==References==

137.132.26.135: spelling

2024-04-11T07:14:13Z

spelling

← Previous revision		Revision as of 07:14, 11 April 2024
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	This is a key value and is often quite complicated to compute. To ease the computations, Felsenstein and his colleagues used several assumptions that are still widely used today. The '''main assumption''' is that '''mutations between DNA sites are ~~independant~~''' of each other. This permits to compute the likelihood as a simple product of probabilities. Now you can divide the data <math>D</math> between several <math>D_s</math> for each nucleotide site <math>s</math> inside of <math>D</math>. The global likelihood of the tree will be the product of the likelihoods of each site:		This is a key value and is often quite complicated to compute. To ease the computations, Felsenstein and his colleagues used several assumptions that are still widely used today. The '''main assumption''' is that '''mutations between DNA sites are independent''' of each other. This permits to compute the likelihood as a simple product of probabilities. Now you can divide the data <math>D</math> between several <math>D_s</math> for each nucleotide site <math>s</math> inside of <math>D</math>. The global likelihood of the tree will be the product of the likelihoods of each site:
	[[File:Tree_partial_exemple.png\|thumb\|Same tree but made from D1, which consists in the first DNA sites from D]]		[[File:Tree_partial_exemple.png\|thumb\|Same tree but made from D1, which consists in the first DNA sites from D]]
	<math>		<math>

Eugene-elgato: sp

2024-01-23T18:22:17Z

← Previous revision		Revision as of 18:22, 23 January 2024
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	== Details ==		== Details ==
	[[File:Tree_exemple.png\|thumb\|A simple phylogenetic tree exemple made from arbitrary data D]]		[[File:Tree_exemple.png\|thumb\|A simple phylogenetic tree exemple made from arbitrary data D]]
	The '''likelihood''' of a tree <math>T</math> is, by definition, the probability of observing certain data <math>D</math> (<math>D</math> being a nucleotide sequence ~~alignement~~ for example ''i.e.'' a ~~succesion~~ of <math> n </math> DNA site <math> s </math>) given the tree. It is often written : <math>P(D\|T)</math>.		The '''likelihood''' of a tree <math>T</math> is, by definition, the probability of observing certain data <math>D</math> (<math>D</math> being a nucleotide sequence alignment for example ''i.e.'' a succession of <math> n </math> DNA site <math> s </math>) given the tree. It is often written : <math>P(D\|T)</math>.

	Here is an example of an evolutionary tree on arbitrary sequence data <math>D</math>:		Here is an example of an evolutionary tree on arbitrary sequence data <math>D</math>:

Fallog: Adding pictures of phylogenetic trees to illustrate my points.

2024-01-12T07:49:06Z

Adding pictures of phylogenetic trees to illustrate my points.

← Previous revision		Revision as of 07:49, 12 January 2024
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	== Details ==		== Details ==
			[[File:Tree_exemple.png\|thumb\|A simple phylogenetic tree exemple made from arbitrary data D]]
	The '''likelihood''' of a tree <math>T</math> is, by definition, the probability of observing certain data <math>D</math> (<math>D</math> being a nucleotide sequence alignement for example ''i.e.'' a succesion of <math> n </math> DNA site <math> s </math>) given the tree. It is often written : <math>P(D\|T)</math>.		The '''likelihood''' of a tree <math>T</math> is, by definition, the probability of observing certain data <math>D</math> (<math>D</math> being a nucleotide sequence alignement for example ''i.e.'' a succesion of <math> n </math> DNA site <math> s </math>) given the tree. It is often written : <math>P(D\|T)</math>.

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	This is a key value and is often quite complicated to compute. To ease the computations, Felsenstein and his colleagues used several assumptions that are still widely used today. The '''main assumption''' is that '''mutations between DNA sites are independant''' of each other. This permits to compute the likelihood as a simple product of probabilities. Now you can divide the data <math>D</math> between several <math>D_s</math> for each nucleotide site <math>s</math> inside of <math>D</math>. The global likelihood of the tree will be the product of the likelihoods of each site:		This is a key value and is often quite complicated to compute. To ease the computations, Felsenstein and his colleagues used several assumptions that are still widely used today. The '''main assumption''' is that '''mutations between DNA sites are independant''' of each other. This permits to compute the likelihood as a simple product of probabilities. Now you can divide the data <math>D</math> between several <math>D_s</math> for each nucleotide site <math>s</math> inside of <math>D</math>. The global likelihood of the tree will be the product of the likelihoods of each site:
			[[File:Tree_partial_exemple.png\|thumb\|Same tree but made from D1, which consists in the first DNA sites from D]]

	<math>		<math>
	P(D\|T) = \prod_{s=1}^{n} {P(D_s\|T)}		P(D\|T) = \prod_{s=1}^{n} {P(D_s\|T)}
	</math>		</math>

	If I reuse the exemple above, <math>D_1</math> would be:		If I reuse the exemple above, <math>D_1</math> tree would be:


	The '''second assumption''' concerns the [[Substitution model\|models of ~~DNA~~ DNA sequence evolution]]. The computation of the likelihood needs the nucleotide frequencies as well as the transition probabilities (when a mutation occurs, probability of going from a nucleotide to another). The simplest model is the Jukes-Cantor model, assuming equal nucleotide frequencies <math>\left(\pi_A = \pi_G = \pi_C = \pi_T = {1\over4}\right)</math> and equal transition probabilities from <math>X</math> to <math>Y</math> (<math>p_{A \rightarrow T} = p_{A \rightarrow C} = p_{A \rightarrow G} = \frac{1}{4} (1 - e^{-\mu l}) </math> and <math>p_{A \rightarrow A} = e^{-\mu l} + \frac{1}{4} (1 - e^{-\mu l}) </math>) and idem for the other bases). Here <math> \mu </math> is the global [[mutation rate]] of the model.		The '''second assumption''' concerns the [[Substitution model\|models of DNA sequence evolution]]. The computation of the likelihood needs the nucleotide frequencies as well as the transition probabilities (when a mutation occurs, probability of going from a nucleotide to another). The simplest model is the [[Jukes-Cantor model]], assuming equal nucleotide frequencies <math>\left(\pi_A = \pi_G = \pi_C = \pi_T = {1\over4}\right)</math> and equal transition probabilities from <math>X</math> to <math>Y</math> (<math>p_{A \rightarrow T} = p_{A \rightarrow C} = p_{A \rightarrow G} = \frac{1}{4} (1 - e^{-\mu l}) </math> and <math>p_{A \rightarrow A} = e^{-\mu l} + \frac{1}{4} (1 - e^{-\mu l}) </math>) and idem for the other bases. Here <math> \mu </math> is the global [[mutation rate]] of the model.

	Felsenstein proposed to decomposed computations even more by using "partial likelihoods" in the computation of <math>		Felsenstein proposed to decomposed computations even more by using "partial likelihoods" in the computation of <math>
	P( D_s \| T)		P( D_s \| T)
	</math>. Here is how it works. Assume we are on a node <math>		</math>. Here is how it works.

			Assume we are on a node <math>
	k		k
	</math> on the tree <math>		</math> on the tree <math>
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	<math> P(D_s\|T) = \sum_X p_X \centerdot w_r (X) </math>		<math> P(D_s\|T) = \sum_X p_X \centerdot w_r (X) </math>

	After doing so for every site <math>s</math>, one can finally obtain the likelihood of the global evolutionary tree.		After doing so for every site <math>s</math>, one can finally obtain the likelihood of the global evolutionary tree by multiplying each "sublikelihood".

	== Algorithm ==		== Algorithm ==

			== Simple Exemple ==

	==References==		==References==

IntentionallyDense: v2.05b - WPcleaner - Fix errors for CW project (Heading start with three "=" and later with level two)

2024-01-08T14:54:05Z

v2.05b - WPcleaner - Fix errors for CW project (Heading start with three "=" and later with level two)

← Previous revision		Revision as of 14:54, 8 January 2024
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	The algorithm is often used as a subroutine in a search for a [[maximum likelihood]] estimate for an evolutionary tree. Further, it can be used in a hypothesis test for whether evolutionary rates are constant (by using [[likelihood ratio test]]s). It can also be used to provide error estimates for the parameters describing an evolutionary tree.		The algorithm is often used as a subroutine in a search for a [[maximum likelihood]] estimate for an evolutionary tree. Further, it can be used in a hypothesis test for whether evolutionary rates are constant (by using [[likelihood ratio test]]s). It can also be used to provide error estimates for the parameters describing an evolutionary tree.

	=== Details ===		== Details ==
	The '''likelihood''' of a tree <math>T</math> is, by definition, the probability of observing certain data <math>D</math> (<math>D</math> being a nucleotide sequence alignement for example ''i.e.'' a succesion of <math> n </math> DNA site <math> s </math>) given the tree. It is often written : <math>P(D\|T)</math>.		The '''likelihood''' of a tree <math>T</math> is, by definition, the probability of observing certain data <math>D</math> (<math>D</math> being a nucleotide sequence alignement for example ''i.e.'' a succesion of <math> n </math> DNA site <math> s </math>) given the tree. It is often written : <math>P(D\|T)</math>.

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	After doing so for every site <math>s</math>, one can finally obtain the likelihood of the global evolutionary tree.		After doing so for every site <math>s</math>, one can finally obtain the likelihood of the global evolutionary tree.

	=== Algorithm ===		== Algorithm ==

	==References==		==References==

Fallog: Extend the previous stub. I started to detail the functionning of Felsenstein's pruning algorith. It still needs exemples, illustrations and, of course, the algorithme itselfs.

2024-01-07T18:54:10Z

Extend the previous stub. I started to detail the functionning of Felsenstein's pruning algorith. It still needs exemples, illustrations and, of course, the algorithme itselfs.

@@ Line 1: / Line 1: @@
 {{Short description|Technique in statistical genetics}}
-In [[statistical genetics]], '''Felsenstein's tree-pruning algorithm''' (or '''Felsenstein's tree-peeling algorithm'''), attributed to [[Joe_Felsenstein|Joseph Felsenstein]], is an [[algorithm]] for computing the [[likelihood]] of an [[evolutionary tree]] from [[nucleic acid]] sequence data. <ref>{{Cite journal | last1 = Felsenstein | first1 = J.| author-link1 =Joseph Felsenstein| title = Maximum Likelihood and Minimum-Steps Methods for Estimating Evolutionary Trees from Data on Discrete Characters | doi = 10.1093/sysbio/22.3.240 | journal = Systematic Biology | volume = 22 | issue = 3 | pages = 240–249 | year = 1973 }}</ref><ref>{{Cite journal | last1 = Felsenstein | first1 = J.| author-link1 = Joseph Felsenstein| title = Evolutionary trees from DNA sequences: A maximum likelihood approach | doi = 10.1007/BF01734359 | journal = Journal of Molecular Evolution | volume = 17 | issue = 6 | pages = 368–376 | year = 1981 | pmid =  7288891| bibcode = 1981JMolE..17..368F| s2cid = 8024924}}</ref>
+In [[statistical genetics]], '''Felsenstein's tree-pruning algorithm''' (or '''Felsenstein's tree-peeling algorithm'''), attributed to [[Joe_Felsenstein|Joseph Felsenstein]], is an [[algorithm]] for efficiently computing the [[likelihood]] of an [[evolutionary tree]] from [[nucleic acid]] sequence data. <ref>{{Cite journal | last1 = Felsenstein | first1 = J.| author-link1 =Joseph Felsenstein| title = Maximum Likelihood and Minimum-Steps Methods for Estimating Evolutionary Trees from Data on Discrete Characters | doi = 10.1093/sysbio/22.3.240 | journal = Systematic Biology | volume = 22 | issue = 3 | pages = 240–249 | year = 1973 }}</ref><ref>{{Cite journal | last1 = Felsenstein | first1 = J.| author-link1 = Joseph Felsenstein| title = Evolutionary trees from DNA sequences: A maximum likelihood approach | doi = 10.1007/BF01734359 | journal = Journal of Molecular Evolution | volume = 17 | issue = 6 | pages = 368–376 | year = 1981 | pmid =  7288891| bibcode = 1981JMolE..17..368F| s2cid = 8024924}}</ref>
-The algorithm is often used as a subroutine in a search for a [[maximum likelihood]] estimate for an evolutionary tree.  Further, it can be used in a hypothesis test for whether evolutionary rates are constant (by using [[likelihood ratio test]]s).  It can also be used to provide error estimates for the parameters describing an evolutionary tree.
+The algorithm is often used as a subroutine in a search for a [[maximum likelihood]] estimate for an evolutionary tree. Further, it can be used in a hypothesis test for whether evolutionary rates are constant (by using [[likelihood ratio test]]s).  It can also be used to provide error estimates for the parameters describing an evolutionary tree.
 ==References==

Mtb-za: #suggestededit-add 1.0

2022-01-11T18:23:25Z

#suggestededit-add 1.0

← Previous revision		Revision as of 18:23, 11 January 2022
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			{{Short description\|Technique in statistical genetics}}
	In [[statistical genetics]], '''Felsenstein's tree-pruning algorithm''' (or '''Felsenstein's tree-peeling algorithm'''), attributed to [[Joe_Felsenstein\|Joseph Felsenstein]], is an [[algorithm]] for computing the [[likelihood]] of an [[evolutionary tree]] from [[nucleic acid]] sequence data. <ref>{{Cite journal \| last1 = Felsenstein \| first1 = J.\| author-link1 =Joseph Felsenstein\| title = Maximum Likelihood and Minimum-Steps Methods for Estimating Evolutionary Trees from Data on Discrete Characters \| doi = 10.1093/sysbio/22.3.240 \| journal = Systematic Biology \| volume = 22 \| issue = 3 \| pages = 240–249 \| year = 1973 }}</ref><ref>{{Cite journal \| last1 = Felsenstein \| first1 = J.\| author-link1 = Joseph Felsenstein\| title = Evolutionary trees from DNA sequences: A maximum likelihood approach \| doi = 10.1007/BF01734359 \| journal = Journal of Molecular Evolution \| volume = 17 \| issue = 6 \| pages = 368–376 \| year = 1981 \| pmid = 7288891\| bibcode = 1981JMolE..17..368F\| s2cid = 8024924}}</ref>		In [[statistical genetics]], '''Felsenstein's tree-pruning algorithm''' (or '''Felsenstein's tree-peeling algorithm'''), attributed to [[Joe_Felsenstein\|Joseph Felsenstein]], is an [[algorithm]] for computing the [[likelihood]] of an [[evolutionary tree]] from [[nucleic acid]] sequence data. <ref>{{Cite journal \| last1 = Felsenstein \| first1 = J.\| author-link1 =Joseph Felsenstein\| title = Maximum Likelihood and Minimum-Steps Methods for Estimating Evolutionary Trees from Data on Discrete Characters \| doi = 10.1093/sysbio/22.3.240 \| journal = Systematic Biology \| volume = 22 \| issue = 3 \| pages = 240–249 \| year = 1973 }}</ref><ref>{{Cite journal \| last1 = Felsenstein \| first1 = J.\| author-link1 = Joseph Felsenstein\| title = Evolutionary trees from DNA sequences: A maximum likelihood approach \| doi = 10.1007/BF01734359 \| journal = Journal of Molecular Evolution \| volume = 17 \| issue = 6 \| pages = 368–376 \| year = 1981 \| pmid = 7288891\| bibcode = 1981JMolE..17..368F\| s2cid = 8024924}}</ref>

Citation bot: Add: s2cid, bibcode. | Use this bot. Report bugs. | Suggested by Abductive | Category:Genetics stubs | via #UCB_Category 551/578

2021-03-30T22:38:51Z

Add: s2cid, bibcode. | Use this bot. Report bugs. | Suggested by Abductive | Category:Genetics stubs | via #UCB_Category 551/578

← Previous revision		Revision as of 22:38, 30 March 2021
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	In [[statistical genetics]], '''Felsenstein's tree-pruning algorithm''' (or '''Felsenstein's tree-peeling algorithm'''), attributed to [[Joe_Felsenstein\|Joseph Felsenstein]], is an [[algorithm]] for computing the [[likelihood]] of an [[evolutionary tree]] from [[nucleic acid]] sequence data. <ref>{{Cite journal \| last1 = Felsenstein \| first1 = J.\| author-link1 =Joseph Felsenstein\| title = Maximum Likelihood and Minimum-Steps Methods for Estimating Evolutionary Trees from Data on Discrete Characters \| doi = 10.1093/sysbio/22.3.240 \| journal = Systematic Biology \| volume = 22 \| issue = 3 \| pages = 240–249 \| year = 1973 }}</ref><ref>{{Cite journal \| last1 = Felsenstein \| first1 = J.\| author-link1 = Joseph Felsenstein\| title = Evolutionary trees from DNA sequences: A maximum likelihood approach \| doi = 10.1007/BF01734359 \| journal = Journal of Molecular Evolution \| volume = 17 \| issue = 6 \| pages = 368–376 \| year = 1981 \| pmid = 7288891}}</ref>		In [[statistical genetics]], '''Felsenstein's tree-pruning algorithm''' (or '''Felsenstein's tree-peeling algorithm'''), attributed to [[Joe_Felsenstein\|Joseph Felsenstein]], is an [[algorithm]] for computing the [[likelihood]] of an [[evolutionary tree]] from [[nucleic acid]] sequence data. <ref>{{Cite journal \| last1 = Felsenstein \| first1 = J.\| author-link1 =Joseph Felsenstein\| title = Maximum Likelihood and Minimum-Steps Methods for Estimating Evolutionary Trees from Data on Discrete Characters \| doi = 10.1093/sysbio/22.3.240 \| journal = Systematic Biology \| volume = 22 \| issue = 3 \| pages = 240–249 \| year = 1973 }}</ref><ref>{{Cite journal \| last1 = Felsenstein \| first1 = J.\| author-link1 = Joseph Felsenstein\| title = Evolutionary trees from DNA sequences: A maximum likelihood approach \| doi = 10.1007/BF01734359 \| journal = Journal of Molecular Evolution \| volume = 17 \| issue = 6 \| pages = 368–376 \| year = 1981 \| pmid = 7288891\| bibcode = 1981JMolE..17..368F\| s2cid = 8024924}}</ref>

	The algorithm is often used as a subroutine in a search for a [[maximum likelihood]] estimate for an evolutionary tree. Further, it can be used in a hypothesis test for whether evolutionary rates are constant (by using [[likelihood ratio test]]s). It can also be used to provide error estimates for the parameters describing an evolutionary tree.		The algorithm is often used as a subroutine in a search for a [[maximum likelihood]] estimate for an evolutionary tree. Further, it can be used in a hypothesis test for whether evolutionary rates are constant (by using [[likelihood ratio test]]s). It can also be used to provide error estimates for the parameters describing an evolutionary tree.

Monkbot: Task 18 (cosmetic): eval 2 templates: del empty params (3×); hyphenate params (2×);

2020-12-18T09:48:30Z

Task 18 (cosmetic): eval 2 templates: del empty params (3×); hyphenate params (2×);

← Previous revision		Revision as of 09:48, 18 December 2020
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	In [[statistical genetics]], '''Felsenstein's tree-pruning algorithm''' (or '''Felsenstein's tree-peeling algorithm'''), attributed to [[Joe_Felsenstein\|Joseph Felsenstein]], is an [[algorithm]] for computing the [[likelihood]] of an [[evolutionary tree]] from [[nucleic acid]] sequence data. <ref>{{Cite journal \| last1 = Felsenstein \| first1 = J.\| ~~authorlink1~~ =Joseph Felsenstein\| title = Maximum Likelihood and Minimum-Steps Methods for Estimating Evolutionary Trees from Data on Discrete Characters \| doi = 10.1093/sysbio/22.3.240 \| journal = Systematic Biology \| volume = 22 \| issue = 3 \| pages = 240–249 \| year = 1973 ~~\| pmid = \| pmc =~~ }}</ref><ref>{{Cite journal \| last1 = Felsenstein \| first1 = J.\| ~~authorlink1~~ = Joseph Felsenstein\| title = Evolutionary trees from DNA sequences: A maximum likelihood approach \| doi = 10.1007/BF01734359 \| journal = Journal of Molecular Evolution \| volume = 17 \| issue = 6 \| pages = 368–376 \| year = 1981 \| pmid = 7288891~~\| pmc =~~ }}</ref>		In [[statistical genetics]], '''Felsenstein's tree-pruning algorithm''' (or '''Felsenstein's tree-peeling algorithm'''), attributed to [[Joe_Felsenstein\|Joseph Felsenstein]], is an [[algorithm]] for computing the [[likelihood]] of an [[evolutionary tree]] from [[nucleic acid]] sequence data. <ref>{{Cite journal \| last1 = Felsenstein \| first1 = J.\| author-link1 =Joseph Felsenstein\| title = Maximum Likelihood and Minimum-Steps Methods for Estimating Evolutionary Trees from Data on Discrete Characters \| doi = 10.1093/sysbio/22.3.240 \| journal = Systematic Biology \| volume = 22 \| issue = 3 \| pages = 240–249 \| year = 1973 }}</ref><ref>{{Cite journal \| last1 = Felsenstein \| first1 = J.\| author-link1 = Joseph Felsenstein\| title = Evolutionary trees from DNA sequences: A maximum likelihood approach \| doi = 10.1007/BF01734359 \| journal = Journal of Molecular Evolution \| volume = 17 \| issue = 6 \| pages = 368–376 \| year = 1981 \| pmid = 7288891}}</ref>

	The algorithm is often used as a subroutine in a search for a [[maximum likelihood]] estimate for an evolutionary tree. Further, it can be used in a hypothesis test for whether evolutionary rates are constant (by using [[likelihood ratio test]]s). It can also be used to provide error estimates for the parameters describing an evolutionary tree.		The algorithm is often used as a subroutine in a search for a [[maximum likelihood]] estimate for an evolutionary tree. Further, it can be used in a hypothesis test for whether evolutionary rates are constant (by using [[likelihood ratio test]]s). It can also be used to provide error estimates for the parameters describing an evolutionary tree.