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Maximum Likelihood Jukes-Cantor Triplets: Analytic Solutions

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Benny Chor, Michael D. Hendy, Sagi Snir

Populations and Evolution · Submitted 27 May 2005

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this work we give, for the first time, analytic solutions for a family of trees with four state characters, like normal DNA or RNA.

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arXiv IDq-bio/0505054 (version 1)
Pith IDORTX6PXV, Pith's permanent record of this paper and its review
CitationBenny Chor, Michael D. Hendy, Sagi Snir. "Maximum Likelihood Jukes-Cantor Triplets: Analytic Solutions." arXiv:q-bio/0505054 (2005). https://pith.science/paper/ORTX6PXV
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,964 input tokens.

What the abstract itself states, as probabilities: claims first 0.94 · states limitation 0.28 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.87 · mentions code or data availability 0.03.

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arXiv listing abstract v1. Results and the main claim are underlined; .

Complex systems of polynomial equations have to be set up and solved algebraically in order to obtain analytic solutions for maximum likelihood on phylogenetic trees. This has restricted the types of systems previously resolved to the simplest models - three and four taxa under a molecular clock, with just two state characters. In this work we give, for the first time, analytic solutions for a family of trees with four state characters, like normal DNA or RNA. The model of substitution we use is the Jukes-Cantor model, and the trees are on three taxa under molecular clock, namely rooted triplets. We employ a number of approaches and tools to solve this system: Spectral methods (Hadamard conjugation), a new representation of variables (the path-set spectrum), and algebraic geometry tools (the resultant of two polynomials). All these, combined with heavy application of computer algebra packages (Maple), let us derive the desired solution.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Complex systems of polynomial equations have to be set up and solved algebraically in order to obtain analytic solutions for maximum likelihood on phylogenetic trees. background 1.00 0.08 0.04 asserted 1.00
s1 This has restricted the types of systems previously resolved to the simplest models - three and four taxa under a molecular clock, with just two state characters. gap 0.68 0.04 0.03 asserted 1.00
s2 In this work we give, for the first time, analytic solutions for a family of trees with four state characters, like normal DNA or RNA. contribution 0.97 0.95 0.78 asserted 1.00
s3 The model of substitution we use is the Jukes-Cantor model, and the trees are on three taxa under molecular clock, namely rooted triplets. method 0.78 0.51 0.11 asserted 1.00
s4 We employ a number of approaches and tools to solve this system: Spectral methods (Hadamard conjugation), a new representation of variables (the path-set spectrum), and algebraic geometry tools (the resultant of two polynomials). method 1.00 0.92 0.04 asserted 1.00
s5 All these, combined with heavy application of computer algebra packages (Maple), let us derive the desired solution. method 0.98 0.95 0.07 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Complex systems of polynomial equations have to be set up and solved algebraically in order to obtain analytic solutions for maximum likelihood on phylogenetic trees. This has restricted the types of systems previously resolved to the simplest models - three and four taxa under a molecular clock, with just two state characters. In this work we give, for the first time, analytic solutions for a family of trees with four state characters, like normal DNA or RNA. The model of substitution we use is the Jukes-Cantor model, and the trees are on three taxa under molecular clock, namely rooted triplets. We employ a number of approaches and tools to solve this system: Spectral methods (Hadamard conjugation), a new representation of variables (the path-set spectrum), and algebraic geometry tools (the resultant of two polynomials). All these, combined with heavy application of computer algebra packages (Maple), let us derive the desired solution.

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